In this paper, we consider a generalized predator–prey system with prey-taxis under Neumann boundary condition, that is, the predators can survive even in the absence of the prey species. It is proved that for an arbitrary spatial dimension, the corresponding initial boundary value problem possesses a unique global bounded classical solution when the prey-taxis is restricted to a small range. Moreover, the local stabilities of constant steady states (including trivial, semi-trivial and positive constant steady states) are investigated. A further study on the coexistence steady state implies that the prey-taxis term suppresses the global asymptotical stability and influences the steady-state/Hopf bifurcations (if they exist). Analyses of steady-state bifurcation, Hopf bifurcation, and even Hopf/steady-state mode interaction are carried out in detail by means of the Lyapunov–Schmidt procedure. In particular, we obtain stable or unstable steady states, time-periodic solutions, quasi-periodic solutions, and sphere-like surfaces of solutions. These results provide theoretical evidences to the complex spatiotemporal dynamics found in numerical simulations.

This paper deals with the following two-species chemotaxis system        ut = ∆u − χ 1 ∇ • (u∇v) + µ 1 u(1 − u − a 1 w), x ∈ Ω, t > 0, vt = ∆v − v + h(w), x ∈ Ω, t > 0, wt = ∆w − χ 2 ∇ • (w∇z) + µ 2 w(1 − w − a 2 u), x ∈ Ω, t > 0, zt = ∆z − z + h(u), x ∈ Ω, t > 0, under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ R n with smooth boundary. The parameters in the system are positive and the signal production function h is a prescribed C 1-regular function. The main objectives of this paper are twofold: One is the existence and boundedness of global solutions, the other is the large time behavior of the global bounded solutions in three competition cases (i.e., a weak competition case, a partially strong competition case and a fully strong competition case). It is shown that the unique positive spatially homogeneous equilibrium (u * , v * , w * , z *) may be globally attractive in the weak competition case (i.e., 0 < a 1 , a 2 < 1), while the constant stationary solution (0, h(1), 1, 0) may be globally attractive and globally stable in the partially strong competition case (i.e., a 1 > 1 > a 2 > 0). In the fully strong competition case (i.e. a 1 , a 2 > 1), however, we can only obtain the local stability of the two semi-trivial stationary solutions (0, h(1), 1, 0) and (1, 0, 0, h(1)) and the instability of the positive spatially homogeneous (u * , v * , w * , z *). The matter which species ultimately wins out depends crucially on the starting advantage each species has.

Objective: This study aimed to investigate the effect of Wnt/β-catenin signal pathway mediated by miR-342-5p targeting CBX2 gene on the proliferation, metastasis, invasion and apoptosis of ovarian cancer cells, and to explore its related regulatory mechanism. Methods: Human normal ovarian epithelial cell line IOSE80, human ovarian cancer cell line SKOV3 and OVCAR3 were the subjects. Software were used to predict the binding site of miR-342-5p targeting CBX2 gene. The proliferation rate of ovarian cancer cells was detected by MTT method; the cell viability of each group was observed by colony formation test; the apoptosis of cells in each group was detected by flow cytometry; the invasive ability of cells was determined by transwell test, and the migration ability of cells was detected by scratch test. The mRNA expression levels of miR-342-5p, CBX2, Wnt1, β-catenin, C-myc and Cyclin D1 were measured by qRT-PCR. Also, Western blot was used to determine the protein expression levels of CBX2, Wnt1, β-catenin, C-myc and Cyclin D1. Results: CBX2 was identified as the target gene of miR-342-5p. MTT test results showed that miR-342-5p could significantly inhibit the proliferation of SKOV3 and OVCAR3 cells, colony formation assay results indicated that the viability of SKOV3 and OVCAR3 cells transfected with miR-342-5p decreased significantly, and flow cytometry results suggested that miR-342-5p could promote the apoptosis of SKOV3 and OVCAR3 cells. Also, the results of transwell showed that miR-342-5p could significantly inhibit the invasive ability of SKOV3 and OVCAR3 cells, and the results of scratch assay suggested that miR-342-5p could significantly inhibit the migration of SKOV3 and OVCAR3 cells. Moreover, qRT-PCR and Western blot results indicated that the mRNA and protein expression levels of CBX2, Wnt1, β-catenin, C-myc and Cyclin D1 decreased in SKOV3 and OVCAR3 cells transfected with miR-342-5p, while the mRNA expression levels of miR-342-5p increased significantly (P<0.05). Conclusion: MiR-342-5p targeted gene is CBX2, which can significantly reduce the proliferation, invasion, migration and viability of ovarian cancer cell lines SKOV3 and OVCAR3, and promote their apoptosis. The mechanism may be related to the mediation of Wnt/β-catenin signal pathway and down-regulation of the related genes expression.

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