Liu Yanwei, Li Shanshan, Liu Zengrong, Wang Ruiqi
Department of Mathematics, Shanghai University, Shanghai, China.
J Biol Phys. 2016 Jun;42(3):399-414. doi: 10.1007/s10867-016-9414-7. Epub 2016 Apr 14.
Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.
细胞通过一系列二元选择完成命运决定过程并形成终末谱系，在此过程中，随着调节因子相互作用强度不断变化，细胞从一个分支切换到另一个稳定状态。由于几乎所有调节过程都是以组合方式进行管理的，因此可能会出现各种组合效应。组合调节对于细胞命运决定至关重要，因为它可以有效地整合许多不同的信号通路，以满足细胞发育过程中更高的调节需求。然而，从生物学和数学角度来看，组合调节对状态转变的贡献是否优于单一调节，以及如果是这样，最佳组合策略是什么，似乎都是重要问题。我们使用组合扰动和分岔分析方法，提供了一个用于分子网络协同作用定量分析的通用框架。与已知方法不同，基于分岔的方法仅依赖于对刺激的稳定状态响应，因为组合扰动引起的状态转变发生在稳定状态之间。更重要的是，通过研究协同扰动对的分岔曲线与特定目标函数的水平集之间的关系，可以确定最佳组合扰动策略。该方法应用于两个模型，即理论多稳态决策模型和生物学上现实的CREB模型，以展示其有效性，尽管该方法适用于一般类别的生物系统。
