Phosphatidylinositol (3,4,5)-trisphosphate (PIP3) is a signaling lipid on the plasma membrane that plays a fundamental role in cell signaling with a strong impact on cell physiology and diseases. It is responsible for the protruding edge formation, cell polarization, macropinocytosis, and other membrane remodeling dynamics in cells. It has been shown that the membrane confinement and curvature affects the wave formation of PIP3 and F-actin. But, even in the absence of F-actin, a complex self-organization of the spatiotemporal PIP3 waves is observed. In recent findings, we have shown that these waves can be guided and pinned on strongly bended membranes caused by molecular crowding and curvature-limited diffusion. Based on these experimental findings, we investigate the spatiotemporal PIP3 wave dynamics on realistic three-dimensional cell-like membranes to explore the effect of curvature-limited diffusion, as observed experimentally. We use an established stochastic reaction-diffusion model with enzymatic Michaelis-Menten-type reactions that mimics the dynamics of cells. As these cells mimic the three-dimensional shape and size observed experimentally, we found that the PIP3 wave directionality can be explained by a Hopf-like and a reverse periodic-doubling bifurcation for uniform diffusion and curvature-limited diffusion properties. Finally, we compare the results with recent experimental findings and discuss the discrepancy between the biological and numerical results.

中文翻译：

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PIP3波的自组织由细胞膜的拓扑结构和曲率控制


磷脂酰肌醇 (3,4,5)-三磷酸 (PIP3) 是质膜上的一种信号脂质，在细胞信号传导中发挥着重要作用，对细胞生理学和疾病具有重大影响。它负责突出边缘的形成、细胞极化、巨胞饮作用和细胞中的其他膜重塑动力学。研究表明，膜的限制和曲率会影响 PIP3 和 F-肌动蛋白的波形成。但是，即使在没有 F-肌动蛋白的情况下，也可以观察到 PIP3 时空波的复杂自组织。在最近的研究中，我们表明这些波可以被引导并固定在由分子拥挤和曲率限制扩散引起的强烈弯曲的膜上。基于这些实验结果，我们研究了真实三维细胞样膜上的时空 PIP3 波动力学，以探索实验观察到的曲率有限扩散的影响。我们使用已建立的随机反应扩散模型和模拟细胞动力学的酶促 Michaelis-Menten 型反应。由于这些细胞模仿实验观察到的三维形状和尺寸，我们发现 PIP3 波的方向性可以通过均匀扩散和曲率限制扩散特性的 Hopf 状和反向周期倍分叉来解释。最后，我们将结果与最近的实验结果进行比较，并讨论生物学结果和数值结果之间的差异。