Dynamic mode decomposition of transcriptome dynamics and optimal sensor placement for discovery of genetic reporters

Accelerating the design of synthetic biological circuits for biosensing requires expanding the currently available genetic toolkit. Although whole-cell biosensors have been successfully engineered and deployed, particularly in applications such as environmental and medical diagnostics, novel sensing applications necessitate the discovery and optimization of novel biosensors. Here we develop a data-driven approach that combines dynamic mode decomposition and observability analysis to extract salient, endogenous genetic sensors for analytes of interest from dynamic gene expression profiles. We show that relatively few dynamic modes are required to capture the transcriptome dynamics. The concept of system observability is then used to rank genes based on their ability to reconstruct the cell state. Genes which contribute to the system's observability are dubbed encoder genes. As a demonstration of our method, we extract, construct, and characterize 15 genetic reporters for the organophosphate malathion in the host bacterium \textit{Pseudomonas fluorescens} SBW25. Furthermore, we demonstrate how the distinct responses of each genetic reporter can be used to construct a single-input, single-output virtual sensor network, approximating a pair of reference trajectories. This library of living malathion sensors can be optimized for use in environmental diagnostics while the developed machine learning tool can be applied to discover genetic reporters in the compendium of host organisms and environmental conditions. Comparative time-series gene expression profiling analysis of RNA-seq data for the bacterium P. fluorescens SBW25 with and without induction of malathion.