Analysing disturbance response of cell-to-cell communication systems: a case study for activator-repressor-diffuser motif

In biomolecular communication networks, bacterial cells communicate with each other using a cell-to-cell communication mechanism mediated by diffusible signaling molecules. The dynamics of molecular concentrations in such systems are approximately modeled by reaction-diffusion equations. In this paper, we analyse the ability of cell-to-cell communication systems to attenuate impulsive disturbances with various spatial frequency profiles by computing the integrated squared concentration of molecules. In particular, we perform in-depth study of disturbance responses for an activator-repressor-diffuser biocircuit in the spatial frequency domain to characterize its spatial frequency gain.