Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their 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 forbidden in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here, we study the control of simple, ubiquitous gene regulatory networks to explore the consequences of departing equilibrium in transcription. Employing graph theory to model a set of especially common regulatory motifs, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor’s concentration. These features allow a single transcription factor to act as both a repressor and activator at different concentrations or achieve outputs with multiple concentration regimes of locally enhanced sensitivity. We systematically dissect how energetically driving individual transitions within regulatory networks, or pairs of transitions, generates a wide range of more adjustable and sensitive phenotypic responses than in equilibrium. These results generalize to more complex regulatory scenarios, including combinatorial control by multiple transcription factors, which we relate and often find collapse to simple mathematical behaviors. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors—feasibly accessed using biological energy budgets and rates—may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.

中文翻译：

---

基因调控失衡的灵活性和灵敏度


细胞通过控制蛋白质浓度及其在调节网络中的动力学来适应环境并调节基因表达。在真核生物和原核生物中，实验和理论越来越多地证明这些网络可以而且确实消耗生化能。这种耗散如何使细胞行为处于平衡状态？这个悬而未决的问题需要超越热力学平衡的定量模型。在这里，我们研究了简单、普遍存在的基因调控网络的控制，以探索在转录中脱离平衡的后果。采用图论对一组特别常见的调节基序进行建模，我们发现耗散释放了非单调性并增强了基因表达对转录因子浓度的敏感性。这些特性允许单个转录因子在不同浓度下同时充当阻遏因子和激活因子，或实现具有局部增强灵敏度的多个浓度方案的输出。我们系统地剖析了在调节网络或成对转换中充满活力地驱动个体转换如何产生比平衡时更可调和敏感的广泛表型反应。这些结果推广到更复杂的调控场景，包括多个转录因子的组合控制，我们将这些因素与简单的数学行为联系起来，并经常发现这些情况会崩溃。我们的研究结果量化了能量消耗的必要条件和可检测的后果。这些更丰富的数学行为——使用生物能量预算和速率可以实现——可能使细胞能够以比平衡时所需的结构更简单的架构完成复杂的调节。