Aviziotis I G, Kavousanakis M E, Bitsanis I A, Boudouvis A G
National Technical University of Athens, School of Chemical Engineering, 15780 , Athens, Greece,
J Math Biol. 2015 Jun;70(7):1457-84. doi: 10.1007/s00285-014-0799-2. Epub 2014 Jun 15.
Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and efficient study of their long-time behaviour over a wide range of parameter values, the performance of solely direct temporal simulations requires significantly high computational time. In addition, when the dynamics of the cell populations exhibit non-trivial bistable behaviour, such an analysis becomes a prohibitive task, since a large ensemble of initial states need to be tested for the quest of possibly co-existing steady state solutions. In this work, we study cell populations which carry the lac operon network exhibiting solution multiplicity over a wide range of extracellular conditions (inducer concentration). By adopting ideas from the so-called "equation-free" methodology, we perform systems-level analysis, which includes numerical tasks such as the computation of coarse steady state solutions, coarse bifurcation analysis, as well as coarse stability analysis. Dynamically stable and unstable macroscopic (population level) steady state solutions are computed by means of bifurcation analysis utilising short bursts of fine-scale simulations, and the range of bistability is determined for different sizes of cell populations. The results are compared with the deterministic cell population balance model, which is valid for large populations, and we demonstrate the increased effect of stochasticity in small size populations with asymmetric partitioning mechanisms.
在模拟同基因细胞群体动态的不同计算方法中，离散随机模型能够足够准确地描述小尺寸群体的演化。然而，对于在广泛参数值范围内对其长期行为进行系统且高效的研究，仅直接进行时间模拟的性能需要显著的高计算时间。此外，当细胞群体的动态表现出非平凡的双稳态行为时，这样的分析就成为一项艰巨的任务，因为为了寻找可能共存的稳态解，需要测试大量的初始状态集合。在这项工作中，我们研究携带乳糖操纵子网络的细胞群体，该网络在广泛的细胞外条件（诱导剂浓度）下表现出解的多重性。通过采用所谓“无方程”方法的思想，我们进行系统级分析，其中包括诸如计算粗稳态解、粗分岔分析以及粗稳定性分析等数值任务。利用短时间的精细尺度模拟通过分岔分析计算动态稳定和不稳定的宏观（群体水平）稳态解，并针对不同大小的细胞群体确定双稳态的范围。将结果与适用于大群体的确定性细胞群体平衡模型进行比较，并且我们证明了具有不对称分配机制的小尺寸群体中随机性的增强效应。
