AI 中文总结
该研究针对细胞感知化学浓度的精度限制，推导出最优空间加权的无偏估计器，发现最优权重集中于监测区域边界，可降低浓度与梯度感知的不确定性，且结果适用于任意几何和维度。
AI 中文摘要
细胞常仅通过少量扩散分子估计化学浓度，分子的随机运动限制了感知精度。我们考虑一种完美监测仪器，它记录有限区域内的瞬时分子密度，且不扰动浓度场、不区分分子身份。标准Berg-Purcell估计器对所有位置均匀加权，本文在一大类无偏估计器中推导了浓度与梯度感知的最优空间加权，方差最小化可映射为静电问题。令人惊讶的是，尽管仪器监测整个体积，最优估计器却将所有权重分配到其边界，降低了浓度与梯度感知的不确定性，我们将结果扩展到任意几何形状和空间维度。
英文摘要
Cells often estimate chemical concentrations from only a few diffusing molecules, whose stochastic motion limits sensing precision. We consider a perfect monitoring instrument that records the instantaneous molecular density throughout a finite region without perturbing the concentration field or distinguishing molecular identities. The standard Berg-Purcell estimator weights all positions uniformly. Here we derive the optimal spatial weighting within a large class of unbiased estimators for both concentration and gradient sensing. Variance minimization maps to an electrostatic problem. Surprisingly, although the instrument monitors the entire volume, the optimal estimator assigns all weight to its boundary, reducing the uncertainty in both concentration and gradient sensing. We extend the results to arbitrary geometries and spatial dimensions.
