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After this initial period, receptors reach a second phase in which they are transported by MTs towards the gradient source.
Similarly, in the presence of a BDNF (Brain-Derived Neurotrophic Factor) gradient, membrane receptors preferentially associated to lipid rafts localized on the side of the GC facing the gradient source [22], possibly causing a modulation of the cell response [23].
In turn, this oriented elongation causes a redistribution of the GABAARs toward the gradient source, resulting in an enhanced asymmetry in intracellular calcium and in amplification in gradient sensing.
In our model, transient interactions between the receptors and the microtubules, coupled to GABA-induced signaling, provide a positive-feedback loop that leads to redistribution of the receptors towards the gradient source.
Three important properties of effective oriented polarization are tight localization (amplification), directional accuracy (tracking the gradient source), and noise-free output (smoothness).
If this threshold position is closer to the gradient source than the neutral point (which is defined only by the Gli gradient) then an increase in GBS affinity will cause an expansion in the range of gene expression.
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First, the influence of the velocity-pressure gradient source of turbulent kinetic energy is confirmed at a low Karlovitz number, and the unimportance of these effects is confirmed at a high Karlovitz number.
with 1 < p < 2, q > 0 and obtained the result that the solution of (1.6) either remains positive as t → ∞ for q > p − N N + 1 or vanishes in finite time for 0 < q < p 2. For <span class="lh">the porous medium equation with gradient source term and without absorption term, the research of the extinction and nonextinction of solutions has also been performed (see [15]).
We measured invasion by count of total cells that show chemotaxis and invade in the primary tumor toward a gradient source (EGF or FBS as a general chemoattractant source) with the in vivo invasion assay.
We have the following parabolic equation without gradient source term: u t = div ( | ∇ u | p − 2 ∇ u ) + λ u r − β u q, x ∈ Ω, t > 0, (1.4).
Remark 1.1 Compared to the results in [25], we extend the results of p-Laplacian equation to the porous medium equation (1.1) with a nonlinear gradient source.
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