Landman K A, Pettet G J, Newgreen D F
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.
Bull Math Biol. 2003 Mar;65(2):235-62. doi: 10.1016/S0092-8240(02)00098-8.
During the development of vertebrate embryos, cell migrations occur on an underlying tissue domain in response to some factor, such as nutrient. Over the time scale of days in which this cell migration occurs, the underlying tissue is itself growing. Consequently cell migration and colonization is strongly affected by the tissue domain growth. Numerical solutions for a mathematical model of chemotactic migration with no domain growth can lead to travelling waves of cells with constant velocity; the addition of domain growth can lead to travelling waves with nonconstant velocity. These observations suggest a mathematical approximation to the full system equations, allowing the method of characteristics to be applied to a simplified chemotactic migration model. The evolution of the leading front of the migrating cell wave is analysed. Linear, exponential and logistic uniform domain growths are considered. Successful colonization of a growing domain depends on the competition between cell migration velocity and the velocity and form of the domain growth, as well as the initial penetration distance of the cells. In some instances the cells will never successfully colonize the growing domain. These models provide an insight into cell migration during embryonic growth, and its dependence upon the form and timing of the domain growth.
在脊椎动物胚胎发育过程中，细胞迁移会在潜在的组织区域内发生，以响应某些因素，如营养物质。在细胞迁移发生的数天时间尺度内，潜在组织自身也在生长。因此，细胞迁移和定植受到组织区域生长的强烈影响。无区域生长的趋化性迁移数学模型的数值解可导致细胞以恒定速度的行波；加入区域生长会导致速度非恒定的行波。这些观察结果提示了对完整系统方程的一种数学近似，使得特征线法能够应用于简化的趋化性迁移模型。分析了迁移细胞波前沿的演化。考虑了线性、指数和逻辑斯蒂均匀区域生长。生长区域的成功定植取决于细胞迁移速度与区域生长速度和形式之间的竞争，以及细胞的初始穿透距离。在某些情况下，细胞将永远无法成功定植生长区域。这些模型为胚胎生长过程中的细胞迁移及其对区域生长形式和时间的依赖性提供了见解。
