凸起活动的随机模型
A stochastic model for protrusion activity
摘要：
在这项工作中，我们接近细胞迁移下的大规模假设，使系统减少到一个粒子的运动。与经典的粒子模型不同，细胞位移是由其内部活动引起的：细胞速度是丝状伪足在基底上施加的（离散）膨胀力的函数。细胞极化能力的反馈，细胞运动施加的突起率建模：更快的细胞形成优先突起的运动方向。通过使用结构化种群过程的数学框架，以前开发的研究种群动力学[Fournier和M{é}l{é}ard，2004]，我们严格介绍了数学模型，我们推导出它的一些基本性质。我们对这个模型进行了数值模拟，表明可以获得不同类型的轨迹：布朗式的，持久的，或间歇性的细胞在两个以前的制度之间切换时。我们发现了文献中通常描述的细胞迁移的轨迹。
英文摘要：
In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a function of the (discrete) protrusive forces exerted by filopodia on the substrate. Cell polarisation ability is modeled in the feedback that the cell motion exerts on the protrusion rates: faster cells form preferentially protrusions in the direction of motion. By using the mathematical framework of structured population processes previously developed to study population dynamics [Fournier and M{é}l{é}ard, 2004], we introduce rigorously the mathematical model and we derive some of its fundamental properties. We perform numerical simulations on this model showing that different types of trajectories may be obtained: Brownian-like, persistent, or intermittent when the cell switches between both previous regimes. We find back the trajectories usually described in the literature for cell migration.
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