Asymptotic stability of contraction-driven cell motion
Asymptotic stability of contraction-driven cell motion
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收缩驱动的细胞运动的渐近稳定性
DOI：
10.1103/physreve.105.024403
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发表时间：
2022
影响因子：
2.4
通讯作者：
Berlyand, Leonid
中科院分区：
文献类型：
--
作者：
Safsten, C. Alex;Rybalko, Volodmyr;Berlyand, Leonid
我们研究活细胞运动的开始（例如，角膜细胞），其由肌球蛋白收缩驱动，重点在于从不稳定的径向静止状态到稳定的不对称运动状态的转变。我们引入了一个二维自由边界模型，该模型推广了先前的一维模型[P. Recho，T. Putelat和L. Truskinovsky，Phys. Rev. Lett. 111，108102（2013）10.1103/PhysRevLett.111.108102]，通过将Keller-Segel模型、Hele-Shaw边界条件和Young-Laplace定律与正则化项相结合，该正则化项通过确保膜-皮质相互作用足够强来排除爆破或塌陷。我们发现一族不对称的行波解从定态解分支出来。我们的主要结果是非线性渐近稳定的模型可观察到的稳定细胞运动的旅行解决方案。通过在小速度下的渐近展开，我们得到了一个显式的渐近公式的稳定性决定的特征值。这个公式大大简化了这个本征值的计算，并表明稳定性是由总肌球蛋白质量的变化时，固定的解决方案分叉的旅行解决方案。我们的光谱分析揭示了稳定性的物理机制。
We study the onset of motion of a living cell (e.g., a keratocyte) driven by myosin contraction with focus on a transition from unstable radial stationary states to stable asymmetric moving states. We introduce a two- dimensional free-boundary model that generalizes a previous one-dimensional model [P. Recho, T. Putelat, and L. Truskinovsky, Phys. Rev. Lett. 111, 108102 (2013)10.1103/PhysRevLett.111.108102] by combining a Keller-Segel model, a Hele-Shaw boundary condition, and the Young-Laplace law with a regularizing term which precludes blowup or collapse by ensuring that membrane-cortex interaction is sufficiently strong. We find a family of asymmetric traveling solutions bifurcating from stationary solutions. Our main result is nonlinear asymptotic stability of traveling solutions that model observable steady cell motion. We derive an explicit asymptotic formula for the stability-determining eigenvalue via asymptotic expansions in small speed. This formula greatly simplifies computation of this eigenvalue and shows that stability is determined by the change in total myosin mass when stationary solutions bifurcate to traveling solutions. Our spectral analysis reveals the physical mechanisms of stability.