Analysis of the transcriptional logic governing differential spatial expression in Hh target genes
This work provides theoretical tools to analyse the transcriptional effects of certain biochemical mechanisms (i.e. affinity and cooperativity) that have been proposed in previous literature to explain the differential spatial expression of Hedgehog target genes involved in Drosophila development. Specifically we have focused on the expression of decapentaplegic and patched. The transcription of these genes is believed to be controlled by opposing gradients of the activator and repressor forms of the transcription factor Cubitus interruptus (Ci). This study is based on a thermodynamic approach, which provides expression rates for these genes. These expression rates are controlled by transcription factors which are competing and cooperating for common binding sites. We have made mathematical representations of the different expression rates which depend on multiple factors and variables. The expressions obtained with the model have been refined to produce simpler equivalent formulae which allow for their mathematical analysis. Thanks to this, we can evaluate the correlation between the different interactions involved in transcription and the biological features observed at tissular level. These mathematical models can be applied to other morphogenes to help understand the complex transcriptional logic of opposing activator and repressor gradients.\n\nAuthor summaryMorphogenic differentiation is a complex process that involves emission, reception and cellular response to different signals. It is well known that the same morphogenic signal can give rise to different cellular transcriptional responses that usually depend, among other factors, on transcription factors. In concordance with the activator threshold model, classically it has been distinguished between high and low threshold target genes in order to explain how cells receiving the same signal can activate different genes. However, in particular cases where the transcription is controlled by two opposing transcription factors, it has been tested that this logic is not valid. This motivates the necessity for describing new theoretical models in order to understand better these cellular responses. By a theoretical analysis we have deduced different versions of transcriptional logic that are significantly determined by how the opposing transcription factors cooperate between them in the transcription process. We have also tested these different scenarios focussing on the Drosophila Hh target genes, and we have reproduced similar conclusions to the ones obtained by other methodologies.