Bokes Pavol, King John R
Department of Applied Mathematics and Statistics, Comenius University, Bratislava, Slovakia.
School of Mathematical Sciences and SBRC Nottingham, University of Nottingham, Nottingham, United Kingdom.
Math Med Biol. 2019 Mar 14;36(1):113-137. doi: 10.1093/imammb/dqy003.
Lineage switches are genetic regulatory motifs that govern and maintain the commitment of a developing cell to a particular cell fate. A canonical example of a lineage switch is the pair of transcription factors PU.1 and GATA-1, of which the former is affiliated with the myeloid and the latter with the erythroid lineage within the haematopoietic system. On a molecular level, PU.1 and GATA-1 positively regulate themselves and antagonize each other via direct protein-protein interactions. Here we use mathematical modelling to identify a novel type of dynamic behaviour that can be supported by such a regulatory architecture. Guided by the specifics of the PU.1-GATA-1 interaction, we formulate, using the law of mass action, a system of differential equations for the key molecular concentrations. After a series of systematic approximations, the system is reduced to a simpler one, which is tractable to phase-plane and linearization methods. The reduced system formally resembles, and generalizes, a well-known model for competitive species from mathematical ecology. However, in addition to the qualitative regimes exhibited by a pair of competitive species (exclusivity, bistable exclusivity, stable-node coexpression) it also allows for oscillatory limit-cycle coexpression. A key outcome of the model is that, in the context of cell-fate choice, such oscillations could be harnessed by a differentiating cell to prime alternately for opposite outcomes; a bifurcation-theory approach is adopted to characterize this possibility.
谱系转换是一种遗传调控模式，它控制并维持发育中的细胞对特定细胞命运的定向分化。谱系转换的一个典型例子是转录因子PU.1和GATA-1这一对因子，在造血系统中，前者与髓系相关，后者与红系相关。在分子水平上，PU.1和GATA-1通过直接的蛋白质-蛋白质相互作用实现自我正向调节并相互拮抗。在此，我们使用数学建模来识别由这种调控架构所支持的一种新型动态行为。以PU.1 - GATA-1相互作用的具体细节为指导，我们依据质量作用定律，为关键分子浓度制定了一个微分方程组。经过一系列系统近似后，该系统简化为一个更简单的系统，该系统适用于相平面和线性化方法。简化后的系统在形式上类似于并推广了数学生态学中一个著名的竞争物种模型。然而，除了一对竞争物种所呈现的定性状态（排他性、双稳态排他性、稳定节点共表达）之外，它还允许振荡极限环共表达。该模型的一个关键结果是，在细胞命运选择的背景下，分化中的细胞可以利用这种振荡来交替为相反的结果做好准备；采用分岔理论方法来描述这种可能性。
