能量消耗位置决定了动力学校正的深度
Where Energy Is Spent Sets the Depth of Kinetic Proofreading
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中文总结 AI 辅助
该研究表明动力学校正的能量消耗位置限制其准确性，推导了误差与驱动层、网络拓扑及驱动强度的关系，发现驱动最后一层会限制误差缩放，驱动位置对非平衡纠错有拓扑限制。
中文摘要 AI 辅助
动力学校正通过能量换取准确性，我们证明能量消耗的位置限制了其能达到的准确性。对于K级联检查点的第j层，当驱动该层时，误差永远不会低于ε^(K-j+1)，其中ε是相同网络在平衡态下达到的误差。该指数是下游子图的第一贝蒂数加1，用于计数其独立环的数量。驱动第一层可利用全部K个检查点，而驱动最后一层则将最佳缩放限制为ε²，与网络深度无关。我们还推导了误差对驱动强度的精确依赖关系，表明误差要么单调递减，要么存在唯一全局最小值，超过该值后更强的驱动会降低准确性。因此，驱动位置对非平衡纠错施加了拓扑限制。
英文摘要
Kinetic proofreading buys accuracy with energy. Where the energy is spent, we show, caps how much accuracy it can buy. Drive layer $j$ of a $K$-checkpoint cascade and the error never falls below $\eeq^{K-j+1}$, where $\eeq$ is the error the same network reaches at equilibrium. The exponent is one plus the first Betti number of the downstream subgraph, which counts its independent cycles. Driving the first layer can recruit all $K$ checkpoints, whereas driving the final layer restricts the best possible scaling to $\eeq^2$, independently of network depth. We also derive the exact dependence on driving strength and show that the error either decreases monotonically or has a unique global minimum, beyond which stronger driving worsens accuracy. Drive placement therefore imposes a topological limit on nonequilibrium error correction.
