Decoding frequency-modulated signals increases information entropy in bacterial second messenger networks

Bacterial second messenger networks transmit environmental information through both amplitude and frequency modulation strategies. However, the mechanisms by which cells decode frequency-encoded signals remain poorly understood. By reconstructing the cAMP second messenger system in Pseudomonas aeruginosa, we demonstrate that frequency-to-amplitude signal conversion (FAC) emerges through three distinct filtering modules that decode frequency-encoded signals into gene expression patterns. Our mathematical framework predicts high-pass and low-pass regimes controlled by a dimensionless threshold parameter, validated using synthetic circuits and an automated experimental platform. Quantitative analysis reveals that, under the given parameter conditions, frequency modulation enables higher information entropy compared to amplitude modulation, with states scaling proportionally to n^2.03 versus n^0.78 with the number of regulated genes (n). This results in approximately two additional bits of information entropy in three-gene systems when utilizing frequency-based control. Our findings establish fundamental principles of frequency-based signal processing in bacterial second messenger networks, revealing how cells exploit temporal dynamics to regulate multiple genes and expand accessible state spaces. This provides insights into both cellular information physics and design principles for synthetic biology.