From a discrete to a continuous model of biological cell movement.
From a discrete to a continuous model of biological cell movement.
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从生物细胞运动的离散模型到连续模型。
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
N. Savill
中科院分区：
文献类型：
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作者：
Stephen Turner;J. Sherratt;K. Painter;N. Savill
人们可以采用生物物理过程的离散模型并基于它构建连续模型的过程是数学兴趣和实际使用的过程。在这项工作中，我们将应用于生物细胞运动的扩展模型达到其连续极限。从单个维度上的单个单元开始在晶格上移动并遵守POTTS模型运动规则，我们为非相互作用细胞集合的扩散系数开发了一种表达式，这明确取决于Potts模型参数。我们展示了当细胞膜弹性和细胞中粘附的POTTS参数变化时，该系数如何变化，并执行支持我们理论结果的计算机模拟。我们解释了晶格点占用率与连续极限中的密度谱之间的关系，并通过包括细胞之间的相互作用来扩展我们的分析。在这样做时，我们能够开发一组耦合的普通微分方程，以显示存在明显的细胞细胞粘附的情况下密度谱的演变，并显示这种粘附强度的增加如何调节扩散。在这样做时，我们就可以基于描述相同系统的离散模型来开发一些有关物理系统的连续模型的见解。
The process by which one may take a discrete model of a biophysical process and construct a continuous model based upon it is of mathematical interest as well as being of practical use. In this work, we take the extended Potts model applied to biological cell movement to its continuous limit. Beginning with a single cell moving in one dimension on a lattice and obeying Potts model rules of movement we develop an expression for the diffusion coefficient of a collection of noninteracting cells which depends explicitly on the Potts model parameters. We show how this coefficient varies when the Potts parameters for cell membrane elasticity and cell-medium adhesion are varied, and perform computer simulations which support our theoretical result. We explain the relationship between the probability of occupancy of lattice points and the density profile in the continuous limit, and extend our analysis by including interactions between the cells. In so doing we are able to develop a set of coupled ordinary differential equations showing the evolution of a density profile in the presence of significant cell-cell adhesion, and show how increases in the strength of this adhesion modulates diffusion. In so doing we develop some insights into how continuous models of physical systems can be based upon discrete models which describe the same system.