Adaptability and sensitivity in gene regulatory responses out of equilibrium

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins (and their associated kinetics) in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume biochemical energy. How does this dissipation enable cellular behaviors? This open question demands quantitative models that transcend thermodynamic equilibrium. Here we study the control of a simple, ubiquitous gene regulatory motif to explore the consequences of departing equilibrium in kinetic cycles. Employing graph theory, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a variable that tunes transition rates (like a transcription factor). For example, these features allow a single transcription factor to act as both a repressor and activator at different levels or achieve multimodal outputs. We systematically dissect how energetically-driving individual transitions, or pairs of transitions, generates exceptional phenotypic responses. Our work quantifies necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors may empower cells (existing in nature or designed in tomorrow's synthetic biology) to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.