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arXiv 2103.15988physics.bio-phmath.AP
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细胞收缩运动的稳定性

Stability of Contraction-Driven Cell Motion

C. Alex Safsten, Volodymyr Rybalko, Leonid Berlyand

摘要:

我们认为运动的角质形成细胞肌球蛋白收缩驱动,并介绍了一个二维自由边界模型,这样的运动。该模型通过将2D Keller-Segel模型和Hele-Shaw型边界条件与Young-Laplace定律相结合来推广[12]中的1D模型,从而产生提供正则化效果的边界曲率项。我们发现,该模型有一个家庭的旅行的解决方案,具有恒定的形状和速度,从一个家庭的径向对称的定态分叉。我们的目标是建立可观察到的稳定运动的细胞与恒定的速度。从数学上讲,这相当于建立旅行解决方案的稳定性。我们的主要结果是一个明确的渐近公式的稳定性确定的线性化问题的特征值。这个公式大大简化了数值计算这个特征值的符号的任务,并揭示了稳定性的物理机制。这个公式的推导是基于一个特殊的对应的本征向量,表现出一个有趣的奇异行为,使它渐近(在小速度限制)成为平行于另一个本征向量的ananximity。这反映了线性化问题的非自伴性质,这是生命系统的一个特征。最后,我们的结果描述了运动的发病通过从不稳定的径向固定解决方案,稳定的非对称旅行解决方案的过渡。

英文摘要:

We consider motility of keratocyte cells driven by myosin contraction and introduce a 2D free boundary model for such motion. This model generalizes a 1D model from [12] by combining a 2D Keller-Segel model and a Hele-Shaw type boundary condition with the Young-Laplace law resulting in a boundary curvature term which provides a regularizing effect. We show that this model has a family of traveling solutions with constant shape and velocity which bifurcates from a family of radially symmetric stationary states. Our goal is to establish observable steady motion of the cell with constant velocity. Mathematically, this amounts to establishing stability of the traveling solutions. Our key result is an explicit asymptotic formula for the stability-determining eigenvalue of the linearized problem. This formula greatly simplifies the task of numerically computing the sign of this eigenvalue and reveals the physical mechanisms of stability. The derivation of this formula is based on a special ansatz for the corresponding eigenvector which exhibits an interesting singular behavior such that it asymptotically (in the small-velocity limit) becomes parallel to another eigenvector. This reflects the non-self-adjoint nature of the linearized problem, a signature of living systems. Finally, our results describe the onset of motion via a transition from unstable radial stationary solutions to stable asymmetric traveling solutions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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