To survive, adapt, and develop, cells respond to external and internal stimuli by tightly regulating transcription. Transcriptional regulation involves the combinatorial binding of a repertoire of transcription factors to DNA, which often results in switch-like binary outputs akin to Boolean logic gates. Recent experimental studies have demonstrated that in eukaryotes, transcription factor binding to DNA often involves energy expenditure, thereby driving the system out of equilibrium. The governing principles of transcriptional logic operations out of equilibrium remain unexplored. Here, we employ a simple two-input, single-locus model of transcription that can accommodate both equilibrium and nonequilibrium mechanisms. Using this model, we find that nonequilibrium regimes can give rise to all the logic operations accessible in equilibrium. Strikingly, energy expenditure alters the regulatory function of the two transcription factors in a mutually exclusive manner. This allows for the emergence of new logic operations that are inaccessible in equilibrium. Overall, our results show that energy expenditure can expand the range of cellular decision-making without the need for more complex promoter architectures.

中文翻译：

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转录逻辑失衡的控制原则

为了生存、适应和发育，细胞通过严格调节转录来响应外部和内部刺激。转录调控涉及一系列转录因子与 DNA 的组合结合，这通常会产生类似于布尔逻辑门的开关式二进制输出。最近的实验研究表明，在真核生物中，转录因子与DNA的结合常常涉及能量消耗，从而使系统失去平衡。不平衡的转录逻辑运算的控制原理仍未被探索。在这里，我们采用了一个简单的双输入、单基因座转录模型，可以适应平衡和非平衡机制。使用这个模型，我们发现非平衡状态可以产生平衡状态下可以进行的所有逻辑运算。引人注目的是，能量消耗以相互排斥的方式改变了两种转录因子的调节功能。这允许出现在平衡状态下无法访问的新逻辑运算。总的来说，我们的结果表明，能量消耗可以扩大细胞决策的范围，而不需要更复杂的启动子结构。