Simpson Matthew J, Landman Kerry A, Bhaganagarapu Kaushik
Department of Mathematics and Statistics, University of Melbourne, Vic. 3010, Australia.
J Theor Biol. 2007 Aug 7;247(3):525-43. doi: 10.1016/j.jtbi.2007.02.020. Epub 2007 Mar 14.
We analyse the coalescence of invasive cell populations by studying both the temporal and steady behaviour of a system of coupled reaction-diffusion equations. This problem is relevant to recent experimental observations of the dynamics of opposingly directed invasion waves of cells. Two cell types, u and v, are considered with the cell motility governed by linear or nonlinear diffusion. The cells proliferate logistically so that the long-term total cell density, u+v approaches a carrying capacity. The steady-state solutions for u and v are denoted u(s) and v(s). The steady solutions are spatially invariant and satisfy u(s)+v(s)=1. However, this expression is underdetermined so the relative proportion of each cell type u(s) and v(s) cannot be determined a priori. Various properties of this model are studied, such as how the relative proportion of u(s) and v(s) depends on the relative motility and relative proliferation rates. The model is analysed using a combination of numerical simulations and a comparison principle. This investigation unearths some novel outcomes regarding the role of overcrowding and cell death in this type of cell migration assay. These observations have relevance to experimental design and interpretation regarding the identification and parameterisation of mechanisms involved in cell invasion.
我们通过研究耦合反应扩散方程组的时间行为和稳态行为，来分析侵袭性细胞群体的聚结。这个问题与最近关于细胞反向定向侵袭波动力学的实验观察相关。考虑两种细胞类型u和v，其细胞运动性由线性或非线性扩散控制。细胞以逻辑斯蒂方式增殖，使得长期总细胞密度u + v接近一个承载能力。u和v的稳态解记为u(s)和v(s)。稳态解在空间上是不变的，且满足u(s) + v(s) = 1。然而，这个表达式是欠定的，所以每种细胞类型u(s)和v(s)的相对比例不能先验确定。研究了该模型的各种性质，例如u(s)和v(s)的相对比例如何依赖于相对运动性和相对增殖率。使用数值模拟和比较原理相结合的方法对该模型进行分析。这项研究揭示了关于过度拥挤和细胞死亡在这类细胞迁移实验中的作用的一些新结果。这些观察结果与关于细胞侵袭所涉及机制的识别和参数化的实验设计及解释相关。
