School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia.
Bull Math Biol. 2019 Jul;81(7):2220-2238. doi: 10.1007/s11538-019-00601-4. Epub 2019 Apr 3.
Growth in biological systems occurs as a consequence of cell proliferation fueled by a nutrient supply. In general, the nutrient gradient of the system will be nonconstant, resulting in biased cell proliferation. We develop a uniaxial discrete cellular automaton with biased cell proliferation using a probability distribution which reflects the nutrient gradient of the system. An explicit probability mass function for the displacement of any tracked cell under the cellular automaton model is derived and verified against averaged simulation results; this displacement distribution has applications in predicting cell trajectories and evolution of expected site occupancies.
生物系统的生长是细胞增殖的结果，而细胞增殖则由营养物质供应所驱动。通常，系统的营养物质梯度是不均匀的，从而导致细胞增殖出现偏差。我们使用反映系统营养物质梯度的概率分布，开发了一个具有细胞增殖偏差的单轴离散细胞自动机。推导出了任何跟踪细胞在细胞自动机模型下位移的显式概率质量函数，并将其与平均模拟结果进行了验证；该位移分布可用于预测细胞轨迹和预期位置占有率的演化。
