Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125.
Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125.
Proc Natl Acad Sci U S A. 2024 Nov 12;121(46):e2411395121. doi: 10.1073/pnas.2411395121. Epub 2024 Nov 5.
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.
细胞通过控制调控网络中蛋白质的浓度及其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，实验和理论越来越证明这些网络可以而且确实会消耗生化能量。这种耗散如何使细胞行为在平衡时无法实现？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，我们研究了简单的、普遍存在的基因调控网络的控制，以探索转录中偏离平衡的后果。我们运用图论来模拟一组特别常见的调控基序，发现耗散会解锁非单调和基因表达对转录因子浓度的增强敏感性。这些特征允许单个转录因子在不同浓度下既作为抑制剂又作为激活剂，或者在局部增强敏感性的多个浓度范围内实现输出。我们系统地剖析了在调控网络中驱动单个转变或对转变的组合如何产生比平衡时更广泛的、更可调的和更敏感的表型反应。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，我们将其关联并经常发现可以简化为简单的数学行为。我们的发现量化了能量消耗的必要条件和可检测后果。这些更丰富的数学行为——可以使用生物能量预算和速率来实现——可能使细胞能够用比平衡时更简单的结构来完成复杂的调控。
