School of Computer and Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia.
School of Computer and Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia.
J Theor Biol. 2023 Nov 7;575:111631. doi: 10.1016/j.jtbi.2023.111631. Epub 2023 Oct 5.
We consider the uniaxial growth of a tissue or colony of cells, where a nutrient (or some other chemical) required for cell proliferation is supplied at one end, and is consumed by the cells. An example would be the growth of a cylindrical yeast colony in the experiments described by Vulin et al. (2014). We develop a reaction-diffusion model of this scenario which couples nutrient concentration and cell density on a growing domain. A novel element of our model is that the tissue is assumed to be compressible. We define replicative regions, where cells have sufficient nutrient to proliferate, and quiescent regions, where the nutrient level is insufficient for this to occur. We also define pathlines, which allow us to track individual cell paths within the tissue. We begin our investigation of the model by considering an incompressible tissue where cell density is constant before exploring the solution space of the full compressible model. In a large part of the parameter space, the incompressible and compressible models give qualitatively similar results for both the nutrient concentration and cell pathlines, with the key distinction being the variation in density in the compressible case. In particular, the replicative region is located at the base of the tissue, where nutrient is supplied, and nutrient concentration decreases monotonically with distance from the nutrient source. However, for a highly-compressible tissue with small nutrient consumption rate, we observe a counter-intuitive scenario where the nutrient concentration is not necessarily monotonically decreasing, and there can be two replicative regions. For parameter values given in the paper by Vulin et al. (2014), the incompressible model slightly overestimates the colony length compared to experimental observations; this suggests the colony may be somewhat compressible. Both incompressible and compressible models predict that, for these parameter values, cell proliferation is ultimately confined to a small region close to the colony base.
我们考虑组织或细胞群体的单轴生长，其中一种细胞增殖所需的营养物质（或其他一些化学物质）在一端供应，并被细胞消耗。一个例子是 Vulin 等人（2014 年）描述的圆柱状酵母菌落的生长。我们为这种情况开发了一个反应扩散模型，该模型将生长域上的营养浓度和细胞密度耦合在一起。我们模型的一个新元素是假设组织是可压缩的。我们定义了复制区域，其中细胞有足够的营养物质进行增殖，以及静止区域，其中营养水平不足以发生这种情况。我们还定义了路径线，允许我们在组织内跟踪单个细胞的路径。我们通过考虑不可压缩组织开始研究模型，在探索完整可压缩模型的解空间之前，细胞密度在组织中是恒定的。在参数空间的很大一部分中，不可压缩和可压缩模型对于营养浓度和细胞路径线都给出了定性相似的结果，关键区别在于可压缩模型中密度的变化。特别是，复制区域位于组织的底部，即营养物质供应的地方，并且营养浓度随着远离营养源的距离而单调下降。然而，对于具有小营养消耗率的高度可压缩组织，我们观察到一个违反直觉的情况，即营养浓度不一定单调下降，并且可能存在两个复制区域。对于 Vulin 等人（2014 年）论文中给出的参数值，不可压缩模型与实验观察相比略微高估了菌落长度；这表明菌落可能具有一定的可压缩性。不可压缩和可压缩模型都预测，对于这些参数值，细胞增殖最终将局限于菌落基部附近的一个小区域。
