We discuss a competition-diffusion system to study coexistence problems of two competing species in a homogeneous environment. In particular, by using invariant manifold theory, effects of domain-shape are considered on this problem.
We consider the Lotka-Volterra competition model with diffusion in R, and establish a theorem on the asymptotic stability of monotone travelling waves relative to the space of bounded uniformly continuous functions with the supremum norm. In consideration of the result of Alexander et al. [1] and Derndinger [4], we shall arrive ata study of the non-negative eigenvalues of the linearized operator around the travelling wave.
The drug-resistant AML cell line HL-60R was significantly less sensitive to cytarabine and daunorubicin than HL-60 cells. HO-1 mRNA and proteins were highly expressed in HL-60R cells. However, down-regulating HO-1 significantly enhanced the sensitivity of HL-60R to chemotherapy, and the expressions of HIF-1ɑ and GLUT1 mRNA and proteins decreased. Meanwhile, the expressions of caspase-3 and caspase-8 proteins increased, while that of bcl-2 decreased. Overexpressions of HO-1, HIF-1ɑ, and GLUT1 were associated with poor response of AML to chemotherapy. Conclusions Overexpressions of HO-1, HIF-1ɑ, and GLUT1 might be involved in the chemoresistance of AML. HO-1 is a potential target to overcome the drug resistance of AML.
Nature uses self-organized
spatiotemporal
patterns to construct systems with robustness and flexibility. Furthermore,
understanding the principles underlying self-organization in nature
enables programmable design of artificial patterns driven by chemical
energy. The related mechanisms are however not clearly understood
because most of these patterns are formed in reaction–diffusion
(RD) systems consisting of intricate interaction between diffusion
and reaction. Therefore, comprehensive understanding of the pattern
formation may provide critical knowledge for developing novel strategies
in both natural science and chemical engineering. Liesegang patterns
(LPs) are one of the typical programmable patterns. This study demonstrates
that appropriate tuning of gel concentration distribution is a key programming factor for controlling LP periodicities. The
gel distribution was realized in bi- or multilayered gels constructed
by stacking agarose gels of different concentrations. Thus, exceptional
LP periodicities were achieved locally in bilayered gels. Furthermore,
RD simulations revealed that the nucleation process modulated by the
gel distribution determines the LP periodicity in bilayered gels.
Finally, based on this concept, desired LP periodicities were successfully
realized by programming gel distributions in multilayered
gels. Thus, deep insights into the fundamental role of nucleation
in designing LPs can lead to the practical applications of LPs and
the understanding of self-organization in nature.
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