When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, ...When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.展开更多
Triple-negative breast cancer(TNBC)is characterized by fast growth,high metastasis,high invasion,and a lack of therapeutic targets.Mitosis and metastasis of TNBC cells are two important biological behaviors in TNBC ma...Triple-negative breast cancer(TNBC)is characterized by fast growth,high metastasis,high invasion,and a lack of therapeutic targets.Mitosis and metastasis of TNBC cells are two important biological behaviors in TNBC malignant progression.It is well known that the long noncoding RNA AFAP1-AS1 plays a crucial role in various tumors,but whether AFAP1-AS1 is involved in the mitosis of TNBC cells remains unknown.In this study,we investigated the functional mechanism of AFAP1-AS1 in targeting Polo-like Kinase 1(PLK1)activation and participating in mitosis of TNBC cells.We detected the expression of AFAP1-AS1 in the TNBC patient cohort and primary cells by in situ hybridization(ISH),northern blot,fluorescent in situ hybridization(FISH)and cell nucleus/cytoplasm RNA fraction isolation.High AFAP1-AS1 expression was negatively correlated with overall survival(OS),disease-free survival(DFS),metastasis-free survival(MFS)and recurrence-free survival(RFS)in TNBC patients.We explored the function of AFAP1-AS1 by transwell,apoptosis,immunofluorescence(IF)and patient-derived xenograft(PDX)models in vitro and in vivo.We found that AFAP1-AS1 promoted TNBC primary cell survival by inhibiting mitotic catastrophe and increased TNBC primary cell growth,migration and invasion.Mechanistically,AFAP1-AS1 activated phosphorylation of the mitosis-associated kinase PLK1 protein.Elevated levels of AFAP1-AS1 in TNBC primary cells increased PLK1 pathway downstream gene expression,such as CDC25C,CDK1,BUB1 and TTK.More importantly,AFAP1-AS1 increased lung metastases in a mouse metastasis model.Taken together,AFAP1-AS1 functions as an oncogene that activates the PLK1 signaling pathway.AFAP1-AS1 could be used as a potential prognostic marker and therapeutic target for TNBC.展开更多
文摘When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.
基金supported by the Natural Science Foundation of China(Nos.82002782,82202657)the Guangdong Basic and Applied Basic Research Foundation(2022A1515012021,2020A1515110930).
文摘Triple-negative breast cancer(TNBC)is characterized by fast growth,high metastasis,high invasion,and a lack of therapeutic targets.Mitosis and metastasis of TNBC cells are two important biological behaviors in TNBC malignant progression.It is well known that the long noncoding RNA AFAP1-AS1 plays a crucial role in various tumors,but whether AFAP1-AS1 is involved in the mitosis of TNBC cells remains unknown.In this study,we investigated the functional mechanism of AFAP1-AS1 in targeting Polo-like Kinase 1(PLK1)activation and participating in mitosis of TNBC cells.We detected the expression of AFAP1-AS1 in the TNBC patient cohort and primary cells by in situ hybridization(ISH),northern blot,fluorescent in situ hybridization(FISH)and cell nucleus/cytoplasm RNA fraction isolation.High AFAP1-AS1 expression was negatively correlated with overall survival(OS),disease-free survival(DFS),metastasis-free survival(MFS)and recurrence-free survival(RFS)in TNBC patients.We explored the function of AFAP1-AS1 by transwell,apoptosis,immunofluorescence(IF)and patient-derived xenograft(PDX)models in vitro and in vivo.We found that AFAP1-AS1 promoted TNBC primary cell survival by inhibiting mitotic catastrophe and increased TNBC primary cell growth,migration and invasion.Mechanistically,AFAP1-AS1 activated phosphorylation of the mitosis-associated kinase PLK1 protein.Elevated levels of AFAP1-AS1 in TNBC primary cells increased PLK1 pathway downstream gene expression,such as CDC25C,CDK1,BUB1 and TTK.More importantly,AFAP1-AS1 increased lung metastases in a mouse metastasis model.Taken together,AFAP1-AS1 functions as an oncogene that activates the PLK1 signaling pathway.AFAP1-AS1 could be used as a potential prognostic marker and therapeutic target for TNBC.
