On a Minimal Model for the Initiation of Cell Movement
On a Minimal Model for the Initiation of Cell Movement
复制标题
细胞运动启动的最小模型
DOI：
10.11588/heidok.00013659
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
J. Fuhrmann
中科院分区：
文献类型：
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作者：
J. Fuhrmann
肌动蛋白驱动的真核细胞运动在许多生物过程中起着至关重要的作用，因此几十年来一直受到激烈的实验和理论研究。在[10]中，我们引入了一个最小模型，用于在平坦衬底上的对称静止细胞中制备运动。该系统由至少四个描述肌动蛋白丝尖密度演变的双曲守恒定律和至少一个肌动蛋白单体浓度的抛物方程组成。对于这个耦合的双曲-抛物系统，我们现在将制定一个自由边界问题，以考虑单元的实际运动。对于这个具有特定边界条件的模型，我们将展示短时间的适定性，并提出解决方案可能在长时间内分解的几种机制。特别是，可能的爆炸现象被描述和研究，分析和数值。此外，我们讨论了溶液的停止存在如何在物理上解释为肌动蛋白聚合前沿的出现。最后，给出了各种可能的边界条件，并解释了它们的生物学意义。我们进一步在一定的假设下对模型进行了重新表述，并导出了一个由两个抛物方程组成的系统，该系统描述了两种相互作用的相反方向的细丝的运动。第二部分研究了这种简化模型，我们要求特定稳态的稳定性并构造行波解。后者的存在也可以在模拟中发现，我们将讨论演变波剖面的类型和速度。将特别注意描述相互作用的不同类型非线性之间的显著差异。特别令人感兴趣的是与稳定性预测的偏差和从模型在其平衡点周围的线性化得到的行波解。这些预测在某些版本的非线性项中得到了很好的满足，而在另一些版本中则严重遗漏了这些预测。因此，我们处理的是一个极简的反应平流扩散方程系统，它的行为不能用线性化来预测，而是强烈地依赖于特定的非线性。
Actin-driven motility of eucaryotic cells plays a crucial role in many biological processes and has therefore been under intense experimental and theoretical investigation throughout several decades. In [10], we introduced a minimal model for the preparation of movement in a symmetric resting cell on a flat substrate. This system consists of at least four hyperbolic conservation laws describing the evolution of densities of actin filament tips and at least one parabolic equation for the actin monomer concentration. For this coupled hyperbolic-parabolic system, we shall now formulate a free boundary problem to allow for actual motion of the cell. For this model with some specific boundary conditions, we will show short time well posedness and present several mechanisms by which the solutions might break down for large times. In particular, possible blow-up phenomena are described and investigated, both analytically and numerically. Moreover, we discuss how the cease of existence of solutions can be interpreted physically as the emergence of actin polymerization fronts. Finally, different possible boundary conditions are presented, and their biological meanings are explained. We furthermore reformulate the model under certain assumptions and derive a system of two parabolic equations describing the motion of two interacting species of filaments moving in opposite directions. This simplified model is investigated in part II where we ask for stability of particular steady states and construct traveling wave solutions. The existence of the latter can also be found in simulations, and we will discuss the type and velocity of the evolving wave profiles. Particular attention will be paid to the remarkable differences between different types of nonlinearities describing the mutual interaction. Of special interest are the deviations from the predictions about stability and the traveling wave solutions obtained from the linearization of the model around its equilibria. These predictions are met quite well by some versions of the nonlinear terms whereas for others they are missed significantly. We are thus dealing with a quite minimalistic system of reaction advection diffusion equations whose behavior cannot be predicted by linearization but strongly depends on the particular nonlinearity.