Data-driven reverse engineering of signaling pathways using ensembles of dynamic models

Despite significant efforts and remarkable progress, the inference of signaling networks from experimental data remains very challenging. The problem is particularly difficult when the objective is to obtain a dynamic model capable of predicting the effect of novel perturbations not considered during model training. The problem is ill-posed due to the nonlinear nature of these systems, the fact that only a fraction of the involved proteins and their post-translational modifications can be measured, and limitations on the technologies used for growing cells in vitro, perturbing them, and measuring their variations. As a consequence, there is a pervasive lack of identifiability. To overcome these issues, we present a methodology called SELDOM (enSEmbLe of Dynamic lOgic-based Models), which builds an ensemble of logic-based dynamic models, trains them to experimental data, and combines their individual simulations into an ensemble prediction. It also includes a model reduction step to prune spurious interactions and mitigate overfitting. SELDOM is a data-driven method, in the sense that it does not require any prior knowledge of the system: the interaction networks that act as scaffolds for the dynamic models are inferred from data using mutual information. We have tested SELDOM on a number of experimental and in silico signal transduction case-studies, including the recent HPN-DREAM breast cancer challenge. We found that its performance is highly competitive compared to state-of-the-art methods for the purpose of recovering network topology. More importantly, the utility of SELDOM goes beyond basic network inference (i.e. uncovering static interaction networks): it builds dynamic (based on ordinary differential equation) models, which can be used for mechanistic interpretations and reliable dynamic predictions in new experimental conditions (i.e. not used in the training). For this task, SELDOM’s ensemble prediction is not only consistently better than predictions from individual models, but also often outperforms the state of the art represented by the methods used in the HPN-DREAM challenge.

尽管已投入大量研究并取得显著进展，但从实验数据中推断信号网络仍是极具挑战性的任务。当目标是构建可预测模型训练阶段未涉及的新型扰动效应的动态模型时，该问题的难度尤甚。该问题属于不适定问题，原因在于这类系统具有非线性特性、仅能检测到所涉及蛋白质及其翻译后修饰的一小部分，以及体外细胞培养、施加扰动及检测其变化的技术存在局限。因此，普遍存在可辨识性不足的问题。为解决上述问题，本文提出一种名为SELDOM（全称为enSEmbLe of Dynamic lOgic-based Models，即动态基于逻辑的模型集成）的方法：该方法构建基于逻辑的动态模型集成，基于实验数据对各模型进行训练，并将各模型的模拟结果整合为集成预测结果。该方法还包含模型约简步骤，用以剪除虚假交互并缓解过拟合问题。SELDOM属于数据驱动方法，无需预先掌握系统的任何先验知识：作为动态模型基础框架的交互网络，可通过互信息从实验数据中推断得到。我们已在多项实验及计算机模拟（in silico）信号转导案例研究中对SELDOM进行了测试，其中包括近期的HPN-DREAM乳腺癌挑战赛。实验结果表明，在恢复网络拓扑结构的任务中，SELDOM的性能与当前顶尖方法相比极具竞争力。更重要的是，SELDOM的应用价值不限于基础网络推断（即挖掘静态交互网络）：其构建的基于常微分方程（ordinary differential equation）的动态模型，可用于机制阐释以及在未参与训练的全新实验条件下实现可靠的动态预测。针对该任务，SELDOM的集成预测结果不仅始终优于单一模型的预测结果，且往往优于HPN-DREAM挑战赛中所采用方法代表的当前顶尖水平。