Cell-Free Extract Data Variability Reduction in the Presence of Structural Non-Identifiability

The bottom up design of genetic circuits to control cellular behavior is one of the central objectives within Synthetic Biology. Performing design iterations on these circuits in vivo is often a time consuming process, which has led to E. coli cell extracts to be used as simplified circuit prototyping environments. Cell extracts, however, display large batch-to-batch variability in gene expression. In this paper, we develop the theoretical groundwork for a model based calibration methodology for correcting this variability. We also look at the interaction of this methodology with the phenomenon of parameter (structural) non-identifiability, which occurs when the parameter identification inverse problem has multiple solutions. In particular, we show that under certain consistency conditions on the sets of output-indistinguishable parameters, data variability reduction can still be performed, and when the parameter sets have a certain structural feature called covariation, our methodology may be modified in a particular way to still achieve the desired variability reduction.