Boolean composition restricts biological logics.

Networks of gene regulation determine cell identity and regulate cell function, but little is known about which logics are biologically favored. We show that, remarkably, the number of logical dependencies that a gene can have on others is severely restricted. This is because genes interact via transcription factors but only gene-gene interactions are observed. We enumerate the number of biologically permitted logics by mapping the problem onto the composition of Boolean functions, and confirm our predictions computationally. This is a key insight into how information is processed at the genetic level.