It is well known that synthetic gene expression is highly sensitive to how genetic elements (promoter structure, spacing regions between promoter and coding sequences, ribosome binding sites, etc.) are spatially configured. An important topic that has received far less attention is how the compositional context, or spatial arrangement, of entire genes within a synthetic gene network affects their individual expression levels. In this paper we show, both quantitatively and qualitatively, that compositional context significantly alters transcription levels in synthetic gene networks. We demonstrate that key characteristics of gene induction, such as ultra-sensitivity and dynamic range, strongly depend on compositional context. We postulate that supercoiling can be used to explain this interference and validate this hypothesis through modeling and a series of in vitro supercoiling relaxation experiments. This compositional interference enables a novel form of feedback in synthetic gene networks. We illustrate the use of this feedback by redesigning the toggle switch to incorporate compositional context. We show the context-optimized toggle switch has improved threshold detection and memory properties.