Discovery of Dynamical Network Models for Genetic Circuits from Time-Series Data with Incomplete Measurements

Synthetic biological gene networks are typically conceptualized and visualized as static graphs with nodal and edge dynamics that are time invariant. This conceptualization of biological programming stands in stark contrast to the transient nature of biological dynamics, which are driven by labile biomolecules. Here we demonstrate the use of dynamical structure function theory to evaluate and visualize network dynamics within synthetic biological circuits. We introduce the theory of dynamical structure functions as a tool for understanding network dynamics in synthetic gene networks. We show in particular, that canonical biological crosstalk and resource loading effects in synthetic biology can be quantified directly using dynamical structure functions from simulation and experimental data. We illustrate the importance of knowing these loading effects through several example systems, showing that crosstalk imbalance in feed-forward loops can explain circuit failure or performance limitations. Finally, we show how dynamical structure functions can be used to diagnose crosstalk and network imbalance to explain failure modes in two types of synthetic biocircuits: an in vitro genelet repressilator and an E. coli based transcriptional event detector. We show that dynamical structure functions can be used as a form of inverse modeling, to pinpoint biological parts within a complex biological circuit that need revision or improvement.