School of Mathematical Sciences, The University of Adelaide, Adelaide 5005, Australia.
College of Science and Engineering, Flinders University, GPO Box 2100, Adelaide5001, Australia.
J Theor Biol. 2021 Aug 21;523:110715. doi: 10.1016/j.jtbi.2021.110715. Epub 2021 Apr 20.
Biological experiments have shown that yeast can be restricted to grow in a uniaxial direction, vertically upwards from an agar plate to form a colony. The growth occurs as a consequence of cell proliferation driven by a nutrient supply at the base of the colony, and the height of the colony has been observed to increase linearly with time. Within the colony the nutrient concentration is non-constant and yeast cells throughout the colony will therefore not have equal access to nutrient, resulting in non-uniform growth. In this work, an agent based model is developed to predict the microscopic spatial distribution of labelled cells within the colony when the probability of cell proliferation can vary in space and time. We also describe a method for determining the average trajectories or pathlines of labelled cells within a colony growing in a uniaxial direction, enabling us to connect the microscopic and macroscopic behaviours of the system. We present results for six cases, which involve different assumptions for the presence or absence of a quiescent region (where no cell proliferation occurs), the size of the proliferative region, and the spatial variation of proliferation rates within the proliferative region. These six cases are designed to provide qualitative insight into likely growth scenarios whilst remaining amenable to analysis. We compare our macroscopic results to experimental observations of uniaxial colony growth for two cases where only a fixed number of cells at the base of the colony can proliferate. The model predicts that the height of the colony will increase linearly with time in both these cases, which is consistent with experimental observations. However, our model shows how different functional forms for the spatial dependence of the proliferation rate can be distinguished by tracking the pathlines of cells at different positions in the colony. More generally, our methodology can be applied to other biological systems exhibiting uniaxial growth, providing a framework for classifying or determining regions of uniform and non-uniform growth.
生物实验表明，酵母可以被限制在琼脂平板上沿单轴方向向上生长，形成菌落。这种生长是由于菌落底部的营养供应驱动的细胞增殖引起的，并且观察到菌落的高度随时间呈线性增加。在菌落内，营养浓度不是恒定的，因此菌落中的酵母细胞不会平等地获得营养，导致生长不均匀。在这项工作中，我们开发了一个基于代理的模型，用于预测当细胞增殖概率可以随空间和时间变化时，标记细胞在菌落内的微观空间分布。我们还描述了一种方法，用于确定在单轴方向上生长的菌落中标记细胞的平均轨迹或路径线，从而使我们能够将系统的微观和宏观行为联系起来。我们提出了六种情况的结果，这些情况涉及到有无静止区（无细胞增殖发生）、增殖区大小以及增殖区内增殖率的空间变化的不同假设。这六种情况旨在提供定性的增长情景洞察，同时仍易于分析。我们将我们的宏观结果与两种情况下单轴菌落生长的实验观察结果进行了比较，在这两种情况下，只有菌落底部的固定数量的细胞可以增殖。模型预测在这两种情况下，菌落的高度将随时间呈线性增加，这与实验观察结果一致。然而，我们的模型表明，通过跟踪菌落中不同位置的细胞路径线，可以区分增殖率的空间依赖性的不同函数形式。更一般地说，我们的方法可以应用于表现出单轴生长的其他生物系统，为分类或确定均匀和不均匀生长区域提供框架。
