Chignola R, Pra P Dai, Morato L M, Siri P
Dipartimento Scientifico e Tecnologico, Universitá di Verona, Verona, Italy.
Bull Math Biol. 2006 Oct;68(7):1661-80. doi: 10.1007/s11538-006-9078-8. Epub 2006 May 20.
The activation, growth and death of animal cells are accompanied by changes in the chemical composition of the surrounding environment. Cells and their microscopic environment constitute therefore a cellular ecosystem whose time-evolution determines processes of interest for either biology (e.g. animal development) and medicine (e.g. tumor spreading, immune response). In this paper, we consider a general stochastic model of the interplay between cells and environmental cellular niches. Niches may be either favourable or unfavourable in sustaining cell activation, growth and death, the state of the niches depending on the state of the cells. Under the hypothesis of random coupling between the state of the environmental niche and the state of the cell, the rescaled model reduces to a set of four non-linear differential equations. The biological meaning of the model is studied and illustrated by fitting experimental data on the growth of multicellular tumor spheroids. A detailed analysis of the stochastic model, of its deterministic limit, and of normal fluctuations is provided.
动物细胞的激活、生长和死亡伴随着周围环境化学成分的变化。因此，细胞及其微观环境构成了一个细胞生态系统，其随时间的演化决定了生物学（如动物发育）和医学（如肿瘤扩散、免疫反应）中感兴趣的过程。在本文中，我们考虑了细胞与环境细胞龛之间相互作用的一般随机模型。龛在维持细胞激活、生长和死亡方面可能是有利的或不利的，龛的状态取决于细胞的状态。在环境龛状态与细胞状态随机耦合的假设下，重新缩放后的模型简化为一组四个非线性微分方程。通过拟合多细胞肿瘤球体生长的实验数据，研究并说明了该模型的生物学意义。提供了对随机模型、其确定性极限和正态波动的详细分析。
