We present a model to describe the on-off switching of transcriptional activity in a genetic assembly by considering the intrinsic characteristics of a giant genomic DNA molecule which can undergo a discrete structural transition between coiled and compact states. We propose a model in which the transition in the higher-order structure of DNA plays an essential role in regulating stable on-off switching and/or the oscillation of a large number of genes under the fluctuations in a living cell, where such a structural transition is caused by environmental factors. This model explains the rapid and broad transcriptional response in a genetic assembly as well as its robustness against fluctuations.