A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion
A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion
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DOI：
10.1016/j.jtbi.2014.06.011
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发表时间：
2014-10-21
影响因子：
2
通讯作者：
Grima, Ramon
中科院分区：
文献类型：
--
作者：
Middleton, Alistair M.;Fleck, Christian;Grima, Ramon
细胞-细胞粘附在细胞的集体迁移和确定相对细胞位置和速度的相关性中起着关键作用。最近，它被证明，基于非格子个体细胞的模型（IBM）可以准确地捕捉实验中观察到的迁移细胞群体的相关性。然而，IBM通常在计算上是昂贵的，并且难以进行数学分析。相比之下，传统的基于连续统的模型适合于数学分析，并且计算要求较低，但通常对应于细胞迁移的平均场近似，因此忽略了细胞间的相关性。在这项工作中，我们解决这个问题，通过使用一个非格IBM推导出一个连续近似，考虑到相关性。我们还表明，一个平均场近似的非晶格IBM导致一个单一的偏积分微分方程的相同形式提出的Sherratt和同事模型细胞粘附。后者被发现是唯一有效的近似系综平均细胞数密度时，细胞之间的机械相互作用是弱的。相比之下，我们的新的连续模型的预测的时间演化的系综细胞数密度分布和密度-密度相关函数是在密切的协议从IBM获得的广泛的机械相互作用强度。特别是，我们观察到的“前”的细胞在模拟中使用我们的IBM和我们的连续模型的传播，但不是在连续模型模拟使用平均场近似。(C)2014爱思唯尔有限公司版权所有。
Cell-cell adhesion plays a key role in the collective migration of cells and in determining correlations in the relative cell positions and velocities. Recently, it was demonstrated that off-lattice individual cell based models (IBMs) can accurately capture the correlations observed experimentally in a migrating cell population. However, IBMs are often computationally expensive and difficult to analyse mathematically. Traditional continuum-based models, in contrast, are amenable to mathematical analysis and are computationally less demanding, but typically correspond to a mean-field approximation of cell migration and so ignore cell-cell correlations. In this work, we address this problem by using an off-lattice IBM to derive a continuum approximation which does take into account correlations. We furthermore show that a mean-field approximation of the off-lattice IBM leads to a single partial integro-differential equation of the same form as proposed by Sherratt and co-workers to model cell adhesion. The latter is found to be only effective at approximating the ensemble averaged cell number density when mechanical interactions between cells are weak. In contrast, the predictions of our novel continuum model for the time-evolution of the ensemble cell number density distribution and of the density-density correlation function are in close agreement with those obtained from the IBM for a wide range of mechanical interaction strengths. In particular, we observe 'front-like' propagation of cells in simulations using both our IBM and our continuum model, but not in the continuum model simulations obtained using the mean-field approximation. (C) 2014 Elsevier Ltd. All rights reserved.