Abstract
A ratiometric response gives an output that is proportional to the ratio between the magnitudes of two inputs. Ratio computation has been observed in nature and is also needed in the development of smart probiotics and organoids. Here, we achieve ratiometric gene expression response in bacteria Escherichia coli with the incoherent merger network. In this network, one input molecule activates expression of the output protein while the other molecule activates an intermediate protein that enhances the output's degradation. When degradation rate is first order and faster than dilution, the output responds linearly to the ratio between the input molecules' levels over a wide range with R2 close to 1. Response sensitivity can be quantitatively tuned by varying the output's translation rate. Furthermore, ratiometric responses are robust to global perturbations in cellular components that influence gene expression because such perturbations affect the output through an incoherent feedforward loop. This work demonstrates a new molecular signal processing mechanism for multiplexed sense-and-respond circuits that are robust to intra-cellular context.