Governing principles of transcriptional logic out of equilibrium

Cells face a myriad of environments and signaling cues. In order to survive, adapt, and desvelop, cells respond to external and internal stimuli, by tightly regulating transcription. Transcriptional regulation involves combinatorial binding of a repertoire of transcription factors (TFs) to DNA, which often results in switch-like binary outputs, akin to logic gates. Recent experimental studies have demonstrated that transcription factor binding to DNA often involves energy expenditure, thereby driving the system out of equilibrium. The governing mechanistic principles of transcriptional logic out of equilibrium remain elusive. To this end, we employ a simple two-input model of transcription that explicitly considers the non-equilibrium binding of TFs to DNA. This simple model can accommodate both equilibrium and non-equilibrium mechanisms and allows for a comparative study of logic operations obtained in the two regimes. We find that, out of equilibrium, the regulatory function of two transcription factors gets altered in a mutually exclusive manner. Such behavior allows non-equilibrium regimes to recreate all the logic operations seen in equilibrium and create new logic operations inaccessible in equilibrium. Our findings demonstrate that cells attain a wider range of decision-making abilities by expending energy.