Possible effects of interaction (cross-talk) between signaling pathways is studied in a system of Reaction–Diffusion (RD) equations. Furthermore, the relevance of spontaneous neurite symmetry breaking and Turing instability has been examined through numerical simulations. The interaction between Retinoic Acid (RA) and Notch signaling pathways is considered as a perturbation to RD system of axon-forming potential for N2a neuroblastoma cells. The present work suggests that large increases to the level of RA–Notch interaction can possibly have substantial impacts on neurite outgrowth and on the process of axon formation. This can be observed by the numerical study of the homogeneous system showing that in the absence of RA–Notch interaction the unperturbed homogeneous system may exhibit different saddle-node bifurcations that are robust under small perturbations by low levels of RA–Notch interactions, while large increases in the level of RA–Notch interaction result in a number of transitions of saddle-node bifurcations into Hopf bifurcations. It is speculated that near a Hopf bifurcation, the regulations between the positive and negative feedbacks change in such a way that spontaneous symmetry breaking takes place only when transport of activated Notch protein takes place at a faster rate.

中文翻译：

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受相互作用信号通路影响的反应-扩散系统的研究和模拟

在反应-扩散 (RD) 方程系统中研究了信号通路之间相互作用（串扰）的可能影响。此外，已经通过数值模拟检查了自发神经突对称性破坏和图灵不稳定性的相关性。视黄酸 (RA) 和 Notch 信号通路之间的相互作用被认为是对 N2a 神经母细胞瘤细胞轴突形成潜力的 RD 系统的扰动。目前的工作表明，RA-Notch 相互作用水平的大幅增加可能对神经突生长和轴突形成过程产生重大影响。这可以通过均质系统的数值研究观察到，表明在没有 RA-Notch 相互作用的情况下，未受扰动的均质系统可能表现出不同的鞍节点分岔，这些分岔在低水平的 RA-Notch 相互作用的小扰动下是稳健的，而大RA-Notch 相互作用水平的增加导致鞍节点分叉向 Hopf 分叉的许多转变。据推测，在 Hopf 分叉附近，正负反馈之间的规则发生变化，只有当激活的 Notch 蛋白以更快的速度运输时才会发生自发的对称性破坏。而 RA-Notch 相互作用水平的大幅增加导致鞍节点分叉向 Hopf 分叉的许多转变。据推测，在 Hopf 分叉附近，正负反馈之间的规则发生变化，只有当激活的 Notch 蛋白以更快的速度运输时才会发生自发的对称性破坏。而 RA-Notch 相互作用水平的大幅增加导致鞍节点分叉向 Hopf 分叉的许多转变。据推测，在 Hopf 分叉附近，正负反馈之间的规则发生变化，只有当激活的 Notch 蛋白以更快的速度运输时才会发生自发的对称性破坏。