Deligne categories and the limit of categories Rep(GL(m∣n))Rep(GL(m|n))

For each integer $t$ a tensor category $V_t$ is constructed, such that exact tensor functors $V_t \longrightarrow C$ classify dualizable $t$-dimensional objects in $C$ not annihilated by any Schur functor. This means that $V_t$ is the "abelian envelope" of the Deligne category $Rep(GL_t)$. Any tensor functor $Rep(GL_t)\longrightarrow C$ is proved to factor either through $V_t$ or through one of the classical categories $Rep(GL(m|n))$ with $m-n=t$. The universal property of $V_t$ implies that it is equivalent to the categories $Rep_{Rep(GL_{t_1})\otimes Rep(GL_{t_2})}(GL(X),\epsilon)$, ($t=t_1+t_2$, $t_1$ not integer) suggested by Deligne as candidates for the role of abelian envelope.Comment: v3: lemma added to section 9, v4: some typos fixed, v5: fixed support acknowledgement, v:6 minor fix in definition of abelian envelop

Duflo-Serganova functor and superdimension formula for the periplectic Lie superalgebra

In this paper, we study the representations of the periplectic Lie superalgebra using the Duflo-Serganova functor. Given a simple $\mathfrak{p}(n)$-module $L$ and a certain element $x\in \mathfrak{p}(n)$ of rank $1$, we give an explicit description of the composition factors of the $\mathfrak{p}(n-1)$-module $DS_x(L)$, which is defined as the homology of the complex $$\Pi M \xrightarrow{x} M \xrightarrow{x} \Pi M.$$ In particular, we show that this $\mathfrak{p}(n-1)$-module is multiplicity-free. We then use this result to give a simple explicit combinatorial formula for the superdimension of a simple integrable finite-dimensional $\mathfrak{p}(n)$-module, based on its highest weight. In particular, this reproves the Kac-Wakimoto conjecture for $\mathfrak{p}(n)$, which was proved earlier by the authors.Comment: ver 2: proof of prop. 3.2.2 significantly shortene

Real-Time Imaging of HIF-1α Stabilization and Degradation

HIF-1α is overexpressed in many human cancers compared to normal tissues due to the interaction of a multiplicity of factors and pathways that reflect specific genetic alterations and extracellular stimuli. We developed two HIF-1α chimeric reporter systems, HIF-1α/FLuc and HIF-1α(ΔODDD)/FLuc, to investigate the tightly controlled level of HIF-1α protein in normal (NIH3T3 and HEK293) and glioma (U87) cells. These reporter systems provided an opportunity to investigate the degradation of HIF-1α in different cell lines, both in culture and in xenografts. Using immunofluorescence microscopy, we observed different patterns of subcellular localization of HIF-1α/FLuc fusion protein between normal cells and cancer cells; similar differences were observed for HIF-1α in non-transduced, wild-type cells. A dynamic cytoplasmic-nuclear exchange of the fusion protein and HIF-1α was observed in NIH3T3 and HEK293 cells under different conditions (normoxia, CoCl2 treatment and hypoxia). In contrast, U87 cells showed a more persistent nuclear localization pattern that was less affected by different growing conditions. Employing a kinetic model for protein degradation, we were able to distinguish two components of HIF-1α/FLuc protein degradation and quantify the half-life of HIF-1α fusion proteins. The rapid clearance component (t1/2 ∼4–6 min) was abolished by the hypoxia-mimetic CoCl2, MG132 treatment and deletion of ODD domain, and reflects the oxygen/VHL-dependent degradation pathway. The slow clearance component (t1/2 ∼200 min) is consistent with other unidentified non-oxygen/VHL-dependent degradation pathways. Overall, the continuous bioluminescence readout of HIF-1α/FLuc stabilization in vitro and in vivo will facilitate the development and validation of therapeutics that affect the stability and accumulation of HIF-1α

ATP-Binding Cassette Transporters Modulate Both Coelenterazine- and D-Luciferin-Based Bioluminescence Imaging

Bioluminescence imaging (BLI) of luciferase reporters provides a cost-effective and sensitive means to image biological processes. However, transport of luciferase substrates across the cell membrane does affect BLI readout intensity from intact living cells. To investigate the effect of ATP-binding cassette (ABC) transporters on BLI readout, we generated click beetle (cLuc), firefly (fLuc), Renilla (rLuc), and Gaussia (gLuc) luciferase HEK-293 reporter cells that overexpressed different ABC transporters (ABCB1, ABCC1, and ABCG2). In vitro studies showed a significant BLI intensity decrease in intact cells compared to cell lysates, when ABCG2 was overexpressed in HEK-293/cLuc, fLuc, and rLuc cells. Selective ABC transporter inhibitors were also applied. Inhibition of ABCG2 activity increased the BLI intensity more than two-fold in HEK-293/cLuc, fLuc, and rLuc cells; inhibition of ABCB1 elevated the BLI intensity two-fold only in HEK-293/rLuc cells. BLI of xenografts derived from HEK-293/ABC transporter/luciferase reporter cells confirmed the results of inhibitor treatment in vivo. These findings demonstrate that coelenterazine-based rLuc-BLI intensity can be modulated by ABCB1 and ABCG2. ABCG2 modulates d -luciferin-based BLI in a luciferase type–independent manner. Little ABC transporter effect on gLuc-BLI intensity is observed because a large fraction of gLuc is secreted. The expression level of ABC transporters is one key factor affecting BLI intensity, and this may be particularly important in luciferase-based applications in stem cell research

Dual Reporter Gene Imaging

The human and rodent sodium iodide symporters ( NIS ) have recently been cloned and are being investigated as potential therapeutic and reporter genes. We have extended this effort by constructing an internal ribosomal entry site (IRES)-linked human NIS (hNIS) -enhanced green fluorescent protein ( eGFP ) hybrid reporter gene for both nuclear and optical imaging. A self-inactivating retroviral vector, termed pQCNIG, containing hNIS-IRES-eGFP dual reporter gene, driven by a constitutive CMV promoter, was constructed and used to generate RG2-pQCNIG cells and RG2-pQCNIG tumors. 131 I-iodide and 99m TcO 4 -pertechnetate accumulation studies plus fluorescence microscopy and intensity assays were performed in vitro, and gamma camera imaging studies in RG2-pQCNIG and RG2 tumor-bearing athymic rats were performed. RG2-pQCNIG cells expressed high levels of hNIS protein and showed high intensity of eGFP fluorescence compared with RG2 wild-type cells. RG2-pQCNIG cells accumulated Na 131 I and 99m TcO 4 – to a 50:1 and a 170:1 tissue/medium ratio at 10 min, compared with 0.8:1.2 tissue/medium ratio in wild-type RG2 cells. A significant correlation between radiotracer accumulation and eGFP fluorescence intensity was demonstrated. RG2-pQCNIG and RG2 tumors were readily differentiated by in vivo gamma camera imaging; radiotracer uptake increased in RG2-pQCNIG but declined in RG2 tumors over the 50-min imaging period. Stomach and thyroid were the major organs of radionuclide accumulation. The IRES-linked hNIS-eGFP dual reporter gene is functional and stable in transduced RG2-pQCNIG cells. Optical and nuclear imaging of tumors produced from these cell lines provides the opportunity to monitor tumor growth and response to therapy. These studies indicate the potential for a wider application of hNIS reporter imaging and translation into patient studies using radioisotopes that are currently available for human use for both SPECT and PET imaging