Department of Psychology, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA.
Bull Math Biol. 2011 Sep;73(9):2132-51. doi: 10.1007/s11538-010-9615-3. Epub 2011 Jan 6.
The PU.1 and GATA1 genes play an important role in the differentiation of blood stem cells. The protein levels expressed by these genes are thought to be regulated by a self-excitatory feedback loop for each gene and a cross-inhibitory feedback loop between the two genes. A mathematical model that captures the dynamical interaction between these two genes reveals that constant levels of self-excitation and cross-inhibition allow the most self-exciting or cross-inhibiting gene to dominate the system. However, since biological systems rarely exist in an unchanging equilibrium, we modeled this gene circuit using discrete time-dependent changes in the parameters in lieu of steady state parameters. These time-dependent parameters lead to new phenomena, including the development of new limit cycles and basins of attraction. These phenomena are not present in models using constant parameter values. Our findings suggest that even small perturbations in the PU.1 and GATA1 feedback loops may substantially alter the gene expression and therefore the cell phenotype. These time-dependent parameter models may also have implications for other gene systems and provide new ways to understand the mechanisms of cellular differentiation.
PU.1 和 GATA1 基因在血液干细胞的分化中发挥着重要作用。这些基因表达的蛋白质水平被认为受到每个基因的自我激励反馈环和两个基因之间的交叉抑制反馈环的调节。一个捕捉这两个基因之间动态相互作用的数学模型表明，恒定的自我激励和交叉抑制水平允许最自我激励或交叉抑制的基因主导系统。然而，由于生物系统很少处于不变的平衡状态，我们使用离散的时变参数来代替稳态参数来对这个基因回路进行建模。这些时变参数导致了新的现象，包括新的极限环和吸引域的发展。这些现象在使用恒定参数值的模型中不存在。我们的研究结果表明，即使在 PU.1 和 GATA1 反馈回路中发生微小的扰动，也可能会极大地改变基因表达，从而改变细胞表型。这些时变参数模型也可能对其他基因系统有影响，并为理解细胞分化的机制提供新的途径。
