Thermodynamic models of combinatorial gene regulation by distant enhancers.

The dynamical properties of distal and proximal gene regulatory elements are crucial to their functionality in gene regulatory networks. However, the multiplicity of regulatory interactions at control elements makes their theoretical and experimental characterisation difficult. Here a thermodynamic framework to describe gene regulation by distant enhancers via a chromatin mechanism is developed. In this mechanism transcription factors (TFs) modulate gene expression via shifts in the equilibrium between chromatin states. The designs of AND, OR, XOR and NAND two-input transcriptional gates for the chromatin mechanism are proposed and compared to similar gates based on the direct physical interactions of TFs with the transcriptional machinery. An algorithm is developed to estimate the thermodynamic parameters of chromatin mechanism gates from gene expression reporter data and applied to characterise the response function for the Gata2-3 enhancer in hematopoietic stem cells. In addition waiting-time distributions for transcriptionally active states were analysed to expose the biophysical differences between the contact and chromatin mechanisms. These differences can be experimentally observed in single-cell experiments and therefore can serve as a signature of the gene regulation mechanism. Taken together these results indicate the diverse functionality and unique features of the chromatin mechanism of combinatorial gene regulation.