Simpson Matthew J, Landman Kerry A, Hughes Barry D, F Newgreen Donald
Department of Mathematics and Statistics, University of Melbourne, Vic. 3010, Australia.
J Theor Biol. 2006 Dec 7;243(3):343-60. doi: 10.1016/j.jtbi.2006.06.021. Epub 2006 Jun 30.
Recently, a suite of cell migration assays were conducted to investigate the migration of neural crest (NC) cells along the gut during the development of the enteric nervous system (ENS). The NC cells colonise the gastro-intestinal tract as a rostro-caudal wave. Local behaviour was shown to be controlled by position relative to the leading edge of the wavefront. The assays involved chick-quail grafting techniques allowing the total invading population to be considered as a two-species system. A two-species continuum model with logistic proliferation and a migration mechanism is developed here to simulate the chick-quail graft experiments and provide a means of looking at the processes occurring within the invasion wave. Five migration mechanisms are considered--linear diffusion, two cases of nonlinear diffusion, chemokinesis and chemotaxis. The model results agree with the experimental observations, regardless of the specific type of migration mechanism. The results show that NC cell invasion is driven by proliferation and cell motility at the leading edge of the wave. Furthermore, logistic proliferation exerts the dominant control on the system. This observation is confirmed by analysing some simplified invasion models. Once the basic experiments were mathematically replicated, the mathematical models were used in turn to make some predictions that were yet to be experimentally tested. This involved conducting a sensitivity analysis of the system by interrupting the proliferation and/or migration ability of the leading edge. Numerical results show that the system is stable against these changes. Of the three experiments suggested, one was carried out and the experimental results were concordant with the theoretical predictions. The outcome of two other suggested experiments are predicted and left for future experimental validation.
最近，进行了一系列细胞迁移实验，以研究在肠神经系统（ENS）发育过程中神经嵴（NC）细胞沿肠道的迁移情况。NC细胞以头尾波的形式在胃肠道中定植。研究表明，局部行为受相对于波前前沿位置控制。这些实验涉及鸡-鹌鹑移植技术，从而可将整个入侵群体视为一个双物种系统。在此建立了一个具有逻辑斯蒂增殖和迁移机制的双物种连续模型，以模拟鸡-鹌鹑移植实验，并提供一种观察入侵波内发生过程的方法。考虑了五种迁移机制——线性扩散、两种非线性扩散情况、化学增活作用和趋化性。无论迁移机制的具体类型如何，模型结果均与实验观察结果相符。结果表明，NC细胞的入侵是由波前沿的增殖和细胞运动驱动的。此外，逻辑斯蒂增殖对系统起主导控制作用。通过分析一些简化的入侵模型证实了这一观察结果。一旦在数学上复制了基础实验，数学模型便反过来用于做出一些尚未经过实验验证的预测。这涉及通过中断前沿的增殖和/或迁移能力对系统进行敏感性分析。数值结果表明，该系统对这些变化具有稳定性。在提出的三个实验中，有一个已实施，实验结果与理论预测一致。另外两个建议实验的结果已做出预测，留待未来进行实验验证。
