One of the important challenges in the emerging field of synthetic biology is designing artificial networks that achieve coordinated behavior in cell communities. Here we present a synthetic multicellular bacterial system where receiver cells exhibit transient gene expression in response to a long-lasting signal from neighboring sender cells. The engineered sender cells synthesize an inducer, an acyl-homoserine lactone (AHL), which freely diffuses to spatially proximate receiver cells. The receiver cells contain a pulse-generator circuit that incorporates a feed-forward regulatory motif. The circuit responds to a long-lasting increase in the level of AHL by transiently activating, and then repressing, the expression of a GFP. Based on simulation models, we engineered variants of the pulse-generator circuit that exhibit different quantitative responses such as increased duration and intensity of the pulse. As shown by our models and experiments, the maximum amplitude and timing of the pulse depend not only on the final inducer concentration, but also on its rate of increase. The ability to differentiate between various rates of increase in inducer concentrations affords the system a unique spatiotemporal behavior for cells grown on solid media. Specifically, receiver cells can respond to communication from nearby sender cells while completely ignoring communication from senders cells further away, despite the fact that AHL concentrations eventually reach high levels everywhere. Because of the resemblance to naturally occurring feed-forward motifs, the pulse generator can serve as a model to improve our understanding of such systems.