# Impact of Residual Inducer on Titratable Expression Systems

## TL;DR

This paper shows how leftover inducer molecules in gene expression systems can change how well these systems work, affecting scientific experiments and genetic engineering.

## Contribution

The study introduces a mathematical model and experimental validation showing how residual inducers quantitatively alter inducible gene expression systems.

## Key findings

- Residual inducer reduces the apparent dynamic range of inducible systems.
- Activating systems are more sensitive to residual inducer than repressing systems.
- Residual inducer increases sensitivity in 'all-or-none' systems until full induction.

## Abstract

Inducible expression systems are widely employed for the titratable control of gene expression, yet molecules inadvertently present in the growth medium or synthesized by the host cells can alter the response profile of some of these systems. Here, we explored the quantitative impact of these residual inducers on the apparent response properties of inducible systems. Using a simple mathematical model, we found that the presence of residual inducer shrinks the apparent dynamic range and causes the apparent Hill coefficient to converge to one. We also found that activating systems were more sensitive than repressing systems to the presence of residual inducer and the response parameters were most heavily dependent on the original Hill coefficient. Experimental interrogation of common titratable systems based on an L-arabinose inducible promoter or a thiamine pyrophosphate-repressing riboswitch in Escherichia coli confirmed the predicted trends. We finally found that residual inducer had a distinct effect on “all-or-none” systems, which exhibited increased sensitivity to the added inducer until becoming fully induced. Our findings indicate that residual inducer or repressor alters the quantitative response properties of titratable systems, impacting their utility for scientific discovery and pathway engineering.