Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada.
J Theor Biol. 2013 Oct 7;334:149-61. doi: 10.1016/j.jtbi.2013.06.020. Epub 2013 Jul 2.
Waves and dynamic patterns in chemical and physical systems have long interested experimentalists and theoreticians alike. Here we investigate a recent example within the context of cell biology, where waves of actin (a major component of the cytoskeleton) and its regulators (nucleation promoting factors, NPFs) are observed experimentally. We describe and analyze a minimal reaction diffusion model depicting the feedback between signalling proteins and filamentous actin (F-actin). Using numerical simulation, we show that this model displays a rich variety of patterning regimes. A relatively recent nonlinear stability method, the Local Perturbation Analysis (LPA), is used to map the parameter space of this model and explain the genesis of patterns in various linear and nonlinear patterning regimes. We compare our model for actin waves to others in the literature, and focus on transitions between static polarization, transient waves, periodic wave trains, and reflecting waves. We show, using LPA, that the spatially distributed model gives rise to dynamics that are absent in the kinetics alone. Finally, we show that the width and speed of the waves depend counter-intuitively on parameters such as rates of NPF activation, negative feedback, and the F-actin time scale.
波和动力模式在化学和物理系统中长期以来一直引起实验家和理论家的兴趣。在这里，我们在细胞生物学的背景下研究了一个最近的例子，在这个例子中，实验观察到肌动蛋白（细胞骨架的主要成分）及其调节剂（成核促进因子，NPFs）的波。我们描述和分析了一个描述信号蛋白和丝状肌动蛋白（F-actin）之间反馈的最小反应扩散模型。使用数值模拟，我们表明该模型显示出丰富的图案形成机制。相对较新的非线性稳定性方法，局部微扰分析（LPA），用于映射该模型的参数空间，并解释各种线性和非线性图案形成机制中图案的起源。我们将我们的肌动蛋白波模型与文献中的其他模型进行比较，并重点关注静态极化、瞬态波、周期性波列和反射波之间的转变。我们使用 LPA 表明，空间分布模型产生的动力学在单独的动力学中不存在。最后，我们表明，波的宽度和速度反直觉地取决于 NPF 激活、负反馈和 F-actin 时间尺度等参数。
