Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks
Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks
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DOI：
10.1088/0951-7715/27/8/1805
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发表时间：
2014-08-01
期刊：
影响因子：
1.7
通讯作者：
Roeger, Matthias
中科院分区：
文献类型：
--
作者：
Raetz, Andreas;Roeger, Matthias
信号分子在许多细胞功能中发挥着重要作用。我们在这里研究两个膜反应扩散方程的一般系统，通过罗宾型边界条件和膜方程中的通量项与细胞内的扩散方程耦合。作者最近针对细胞中的 GTP 酶循环提出了这种形式的特定模型。我们在这里研究扩散不稳定性在细胞极化中的假定作用。通过线性稳定性分析，我们确定了两种不同的机制。第一个类似于膜子系统的经典图灵不稳定性，并且需要（不切实际的）活化剂和底物的横向扩散存在巨大差异。另一方面，第二种可能性是由细胞质和横向扩散的差异引起的，并且看起来更现实。我们通过数值模拟补充了我们的理论分析，证实了新的稳定性机制，并使我们能够研究线性化应用范围之外的演化。
Signalling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and a flux term in the membrane equations. A specific model of this form was recently proposed by the authors for the GTPase cycle in cells. We investigate here a putative role of diffusive instabilities in cell polarization. By a linearized stability analysis, we identify two different mechanisms. The first resembles a classical Turing instability for the membrane subsystem and requires (unrealistically) large differences in the lateral diffusion of activator and substrate. On the other hand, the second possibility is induced by the difference in cytosolic and lateral diffusion and appears much more realistic. We complement our theoretical analysis by numerical simulations that confirm the new stability mechanism and allow us to investigate the evolution beyond the regime where the linearization applies.