From rr-Spin Intersection Numbers to Hodge Integrals

Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of $r$-spin intersection numbers. We represent this GKMM in terms of fermions and expand it in terms of the Schur polynomials by boson-fermion correspondence, and link it with a Hurwitz partition function and a Hodge partition by operators in a $\widehat{GL}(\infty)$ group. Then, from a $W_{1+\infty}$ constraint of the partition function of $r$-spin intersection numbers, we get a $W_{1+\infty}$ constraint for the Hodge partition function. The $W_{1+\infty}$ constraint completely determines the Schur polynomials expansion of the Hodge partition function.Comment: 51 pages, 1 figur

The role of a previously unrecognized pericytes progenitor-like cell in glioma expansion and progression

Pericytes are vascular mural cell, which can regulate vessel-tone and -remodeling. In the brain pericytes are maintained in a 1:1 ratio with endothelial cells, they are essential for the function of the blood-brain barrier and control vessel-architecture. Previous studies suggested that pericytes are generated in embryonic development and that mature pericytes would proliferate and expand during neo-angiogenesis. Furthermore, it was proposed that pathological angiogenesis in glioblastomas (GBM) is supported by bone marrow-derived pericytes. In the present study, applying newly established transgenic lineage-tracing glioma mouse models (Nes-CreERT2; Td-Tomato), I newly observed that pericytes origin from a previously unknown pericyte progenitor cells (PPCs). These nesting-RFP positive PPCs are negative for mature pericyte markers, including Desmin, PDGFR-β, NG2, CD146 at 7 days after tumor inoculation. However, most PPCs (88.10%) developed into mature pericytes and expressed pericyte markers like Desmin, PGGFR-ß, NG2, or CD146 at 21 days after tumor injection. I suggested that pericytes marker negative RFP+ cells are a previously unrecognized PPCs. Interestingly, in the tumor area, more than 30% of all pericytes express RFP. Since we used cell lineage tracing mouse models, we indicated that these intratumoral newly generated mature pericytes are derived from PPCs. The RFP positive cells do not differentiate into mature pericyte in the peritumoral and the contralateral tumor-free brain hemisphere. The bone marrow chimeric glioma mouse model was applied to investigate if RFP expressing cells derived from the brain or from bone marrow. In the BM/PU1-GFP mice, we confirm that bone marrow derived PU1-GFP+ myeloid cells could migrate to the tumor area through the BBB. However, in the BM/Nes-Td-Tomato group, no RFP expressing cells are detected in glioma. These findings indicated that PPCs are not generated from bone marrow derived cells. In the final experiments of my thesis, a cell lineage ablation glioma mouse model was used to investigate the role of PPCs during glioma growth. The ablation of Cre recombined RFP + cells was applied at 4 days after tumor inoculation, due to most RFP positive cells are PPCs during this stage. The results showed that we ablate approximately half of the RFP+ cells in the Nes-iDTA group compared to the Nes-RFP group. After ablation of RFP+ cells in the Nes-iDTA group, we observed significant reductions in the tumor volume, tumor angiogenesis, and the number of pericytes as compared with the Nes-RFP group. This study suggests that the RFP+ PPCs contribute important roles in glioma progression and angiogenesis. Altogether our data hypothesize that pericyte progenitor cells are a new target for anti-angiogenesis in GBM, which will allow a specific and efficient therapeutic treatment