Department of Molecular Biology, Institute of Biochemistry and Molecular Biology, Semmelweis University, Budapest, Hungary.
Channing Division of Network Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, United States of America.
PLoS Comput Biol. 2022 Oct 10;18(10):e1010536. doi: 10.1371/journal.pcbi.1010536. eCollection 2022 Oct.
Biological systems are noisy by nature. This aspect is reflected in our experimental measurements and should be reflected in the models we build to better understand these systems. Noise can be especially consequential when trying to interpret specific regulatory interactions, i.e. regulatory network edges. In this paper, we propose a method to explicitly encode edge-noise in Boolean dynamical systems by probabilistic edge-weight (PEW) operators. PEW operators have two important features: first, they introduce a form of edge-weight into Boolean models through the noise, second, the noise is dependent on the dynamical state of the system, which enables more biologically meaningful modeling choices. Moreover, we offer a simple-to-use implementation in the already well-established BooleanNet framework. In two application cases, we show how the introduction of just a few PEW operators in Boolean models can fine-tune the emergent dynamics and increase the accuracy of qualitative predictions. This includes fine-tuning interactions which cause non-biological behaviors when switching between asynchronous and synchronous update schemes in dynamical simulations. Moreover, PEW operators also open the way to encode more exotic cellular dynamics, such as cellular learning, and to implementing edge-weights for regulatory networks inferred from omics data.
生物系统本质上是嘈杂的。这一方面反映在我们的实验测量中，我们应该在构建更好地理解这些系统的模型时反映这一点。当试图解释特定的调节相互作用（即调节网络边缘）时，噪声尤其重要。在本文中，我们提出了一种通过概率边权重（PEW）算子将边噪声显式编码到布尔动态系统中的方法。PEW 算子具有两个重要特征：首先，它们通过噪声将边权重引入布尔模型中；其次，噪声取决于系统的动态状态，从而可以进行更具生物学意义的建模选择。此外，我们在已经成熟的 BooleanNet 框架中提供了一个易于使用的实现。在两个应用案例中，我们展示了如何在布尔模型中引入少量的 PEW 算子可以微调涌现动态并提高定性预测的准确性。这包括微调在动态模拟中从异步更新方案切换到同步更新方案时会导致非生物学行为的相互作用。此外，PEW 算子还为从组学数据推断出的调节网络的边缘权重编码以及实现更奇特的细胞动力学（例如细胞学习）开辟了道路。
