How would you use readthrough as part of a genetic circuit design?
Readthrough has already been used to implement transcriptional NOR gates, wherein tandem input promoters express a repressor that represses an output promoter. (First time I recall here: 21150903, used widely here: 27034378, roadblocking modeled here: 32141239.) An advantage of this design is that the repressor need only be encoded in DNA once, which can significantly reduce the DNA footprint of the design and the likelihood of recombination if the repressor's DNA sequence is long (e.g., protein-based repressors). OR gates have similarly been implemented as two tandem promoters expressing a common output gene. (An alternative NOR design—which is common with repressors with short DNA sequences (e.g., sgRNAs)—is to duplicate the repressor and express it separately from both input promoters. This approach circumvents the roadblocking and input asymmetry that can occur with tandem promoters.)
Readthrough has also been used with antisense promoters to tune gene expression (see 26769567). In these designs, an input promoter must read through a downstream antisense promoter, and the strength of the antisense promoter can be used to tune the response of the input promoter.
Another application that comes to mind is encoding the relative ratio of expression of multiple genes by separating them with weak terminators (e.g., to achieve X-fold expression of the first gene relative to the second). This begins to evoke an operon, as jakebeal notes. The closest example I can think of comes from this paper: 23727987, although they actually used readthrough to address the inverse problem of characterizing terminator strength.