Synthetic gene networks are frequently conceptualized and visualized as static graphs. This view of biological programming stands in stark contrast to the transient nature of biomolecular interaction, which is frequently enacted by labile molecules that are often unmeasured. Thus, the network topology and dynamics of synthetic gene networks can be difficult to verify in vivo or in vitro, due to the presence of unmeasured biological states. Here we introduce the dynamical structure function as a new mesoscopic, data-driven class of models to describe gene networks with incomplete measurements of state dynamics. We develop a network reconstruction algorithm and a code base for reconstructing the dynamical structure function from data, to enable discovery and visualization of graphical relationships in a genetic circuit diagram as time-dependent functions rather than static, unknown weights. We prove a theorem, showing that dynamical structure functions can provide a data-driven estimate of the size of crosstalk fluctuations from an idealized model. We illustrate this idea with numerical examples. Finally, we show how data-driven estimation of dynamical structure functions can explain failure modes in two experimentally implemented genetic circuits, a previously reported in vitro genetic circuit and a new E. coli-based transcriptional event detector.

合成基因网络经常被概念化并可视化为静态图。这种生物编程的观点与生物分子相互作用的瞬态性质形成鲜明对比，生物分子相互作用通常是由往往无法测量的不稳定分子产生的。因此，由于存在未测量的生物状态，合成基因网络的网络拓扑和动力学可能难以在体内或体外验证。在这里，我们引入动态结构函数作为一种新的介观、数据驱动的模型类，用于描述具有不完整状态动态测量的基因网络。我们开发了一种网络重建算法和一个代码库，用于根据数据重建动态结构函数，从而能够将遗传电路图中的图形关系发现和可视化为时间相关的函数，而不是静态的、未知的权重。我们证明了一个定理，表明动态结构函数可以根据理想化模型提供数据驱动的串扰波动大小估计。我们用数值例子来说明这个想法。最后，我们展示了动态结构函数的数据驱动估计如何解释两个实验实现的遗传电路（先前报道的体外遗传电路和新的基于大肠杆菌的转录事件检测器）中的故障模式。