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It is known that in sphere conditions, cells can form a niche prevent differentiation and ensure self-renewal.
Endometrioid cells showed strong ALDH activity under both monolayer and sphere conditions.
In contrast, when cells were cultured under stem cell (sphere) conditions, no disaggregation became apparent upon integrin inhibition, and cell death was not observed.
When integrins were inhibited in nonsphere glioma cells, the TGF- β pathway was strongly impaired, whereas no such effect was observed in glioma cells cultured under sphere conditions.
We also knocked down OTX2 in D341 (Group 3) MB cells that are exclusively grown in suspension culture or sphere conditions (supplementary material Fig. S5E,F and Fig. S7A).
In the mouse glioma model systems used here, we noticed extensive cell death following integrin inhibition in all four mouse glioma cell lines tested when cultured as adherent cells, that is, under standard conditions, whereas no such effect became apparent when the same cells were cultured under sphere conditions that we had explored as a possible in vitro model of stemness.
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It introduces a Lagrange multiplier that allows to enforce the sphere condition.
Let Ω ⊂ G be a bounded open domain which satisfies the outer sphere condition at every point of the boundary ∂Ω.
Based on the work in [3], we construct a barrier function in a domain of the Carnot group (see Lemma 3.10) under the hypothesis of the outer sphere condition to discuss the boundary behaviour of the Perron solutions.
Thus, we get the following existence theorem in the whole space G by making use of Theorem 4.2 and the result in [4] that the gauge balls in H-type group satisfy the outer sphere condition.
A bounded open set Ω ⊂ G is said to satisfy the outer sphere condition at ξ0 ∈ ∂ Ω, if there exists a ball B G (η, r) lying in G Ω such that ∂ B G ( η, r ) ∩ ∂ Ω = { ξ 0 }.
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