趋化细胞聚集多相模型的模式形成。

IF 0.8 4区 数学 Q4 BIOLOGY
J E F Green, J P Whiteley, J M Oliver, H M Byrne, S L Waters
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引用次数: 5

摘要

我们开发了一个连续模型的细胞聚集培养在营养丰富的培养基在培养井。我们考虑二维几何形状,代表通过培养孔的垂直切片,并假设细胞层深度与培养孔的典型长度相比很小。我们采用连续介质力学方法,将细胞和培养基视为两相混合物。具体地说,细胞和培养基被当作液体处理。此外,细胞期可以根据环境因素产生力,其中包括培养基中细胞产生的化学引诱剂的浓度。该模型导出了一个关于细胞相体积分数和速度、培养基压力和化学引诱剂浓度的耦合非线性偏微分方程组,必须在适当的边界和初始条件下求解。为了深入了解该系统,我们考虑了两种模型缩减,适用于细胞层深度与培养井的典型长度尺度相比较薄的情况:一种(简单的)1D和一种(更复杂的)薄膜拉伸流动缩减。通过分析和数值研究得到的方程组,我们确定了均匀稳态(对应于空间均匀的细胞分布)的小振幅扰动可以导致空间变化的稳态(模式形成)的条件。我们的分析表明,在线性和弱非线性体系中,较简单的一维还原与薄膜拉伸流还原具有相同的定性特征,这促使人们在需要对系统进行定性理解时使用较简单的一维建模方法。然而,当需要模型预测和实验数据之间的详细定量一致时,薄膜拉伸流动减少可能更合适。此外,当系统不接近边际稳定性时,两种模型在参数空间区域的完全数值模拟表明,细胞相的体积分数和速度以及化学引诱剂浓度的演变存在显著差异。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Pattern formation in multiphase models of chemotactic cell aggregation.

We develop a continuum model for the aggregation of cells cultured in a nutrient-rich medium in a culture well. We consider a 2D geometry, representing a vertical slice through the culture well, and assume that the cell layer depth is small compared with the typical lengthscale of the culture well. We adopt a continuum mechanics approach, treating the cells and culture medium as a two-phase mixture. Specifically, the cells and culture medium are treated as fluids. Additionally, the cell phase can generate forces in response to environmental cues, which include the concentration of a chemoattractant that is produced by the cells within the culture medium. The model leads to a system of coupled nonlinear partial differential equations for the volume fraction and velocity of the cell phase, the culture medium pressure and the chemoattractant concentration, which must be solved subject to appropriate boundary and initial conditions. To gain insight into the system, we consider two model reductions, appropriate when the cell layer depth is thin compared to the typical length scale of the culture well: a (simple) 1D and a (more involved) thin-film extensional flow reduction. By investigating the resulting systems of equations analytically and numerically, we identify conditions under which small amplitude perturbations to a homogeneous steady state (corresponding to a spatially uniform cell distribution) can lead to a spatially varying steady state (pattern formation). Our analysis reveals that the simpler 1D reduction has the same qualitative features as the thin-film extensional flow reduction in the linear and weakly nonlinear regimes, motivating the use of the simpler 1D modelling approach when a qualitative understanding of the system is required. However, the thin-film extensional flow reduction may be more appropriate when detailed quantitative agreement between modelling predictions and experimental data is desired. Furthermore, full numerical simulations of the two model reductions in regions of parameter space when the system is not close to marginal stability reveal significant differences in the evolution of the volume fraction and velocity of the cell phase, and chemoattractant concentration.

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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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