A rate-distortion theory for gene regulatory networks and its application to logic gate consistency

A gene regulatory network in which the modes (activation/inhibition) of the transcriptional regulations are known and in which gene expression assumes boolean values can be treated as a system of linear equations over a binary field, i.e. as a constraint satisfaction problem for an information code.

For currently available gene networks, we show in this article that the distortion associated with the corresponding information code is much lower than expected from null models, and that it is close to (when not lower than) the Shannon bound determined by the rate-distortion theorem. This corresponds to saying that the distribution of regulatory modes is highly atypical in the networks, and that this atypicality greatly helps in avoiding contradictory transcriptional actions. Choosing a boolean formalism to represent the gene networks, we also show how to formulate criteria for the selection of gates that maximize the compatibility with the empirical information available on the transcriptional regulatory modes. Proceeding in this way, we obtain in particular that non-canalizing gates are upper-bounded by the distortion, and hence that the boolean gene networks are more canalizing than expected from null models.