你尚未目睹，却已预见：未来生化浓度可被惊人高精度预测
You ain't seen nothing, and yet: Future biochemical concentrations can be predicted with surprisingly high accuracy
AI总结：
利用浓度剖面的先验知识，通过贝叶斯推断框架，MAP估计可超越经典伯格-珀塞尔极限，实现精度δc/c=1/√(a²N)，其中a>1。
摘要：
精确感知化学浓度对众多生物过程至关重要。对于少量分子，这种感知的精度受限于散粒噪声。在准静态和随机波动浓度的背景下，作为感知持续时间函数的相应理论极限已得到充分研究。然而，在发育过程中以及许多其他情况下，浓度剖面并非随机，而是表现出可预测的时空模式。我们提出，利用这些结构化剖面的先验知识，可以通过利用当前分子结合事件的信息来预测未来浓度，从而改善并加速浓度感知。通过将受约束的感知问题视为对允许的时空剖面类别进行贝叶斯推断，我们推导出感知精度的新理论极限。我们的分析表明，最大后验（MAP）估计可以超越经典的Berg-Purcell和最大似然（泊松计数）极限，实现感知精度δc/c = 1/√(a²N)，其中N是结合事件的数量，在某些情况下a > 1。因此，对浓度剖面统计结构的了解增强了感知精度，为发育过程中观察到的快速且高度准确的细胞命运决定提供了潜在解释。
英文摘要：
Accurate sensing of chemical concentrations is essential for numerous biological processes. The accuracy of this sensing, for small numbers of molecules, is limited by shot noise. Corresponding theoretical limits on sensing precision, as a function of sensing duration, have been well-studied in the context of quasi-static and randomly fluctuating concentrations. However, during development and in many other cases, concentration profiles are not random but exhibit predictable spatiotemporal patterns. We propose that leveraging prior knowledge of these structured profiles can improve and accelerate concentration sensing by utilizing information from current molecular binding events to predict future concentrations. By framing the constrained sensing problem as Bayesian inference over an allowed class of spatiotemporal profiles, we derive new theoretical limits on sensing accuracy. Our analysis reveals that maximum a posteriori (MAP) estimation can outperform the classical Berg-Purcell and maximum-likelihood (Poisson counting) limits, achieving a sensing precision of $δc/c = 1/\sqrt{a^2N}$, where $N$ is the number of binding events, and $a > 1$ in certain cases. Thus knowledge of the statistical structure of concentration profiles enhances sensing precision, providing a potential explanation for the rapid yet highly accurate cell fate decisions observed during development.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
