细胞传感系统中时变信号的最佳检测理论
Theory for the optimal detection of time-varying signals in cellular sensing systems
摘要：
活细胞通常需要测量随时间变化的化学浓度。为此，它们部署了许多资源，例如受体、下游信号分子、时间和能量。在这里，我们提出了一个理论的最佳设计的一大类传感系统，需要检测时变信号，一个受体驱动的推挽网络。该理论基于动态输入-输出关系的概念，该关系描述了当前配体浓度与过去积分时间内的平均受体占有率之间的映射。这个概念是用来开发的想法，细胞采用其推拉网络来估计受体的占有率，然后使用这个估计来推断当前的配体浓度通过反转的动态输入-输出关系。理论表明，传感误差可以分解为两个方面：在估计的受体占有率和动态误差，因为在过去的积分时间的平均配体浓度可能不反映当前的配体浓度的采样误差。该理论概括了先前针对静态信号确定的最优资源分配的设计原理，该原理指出，在最优设计的传感系统中，受体的三个基本资源类别及其整合时间、读出分子和能量是同等限制的，从而不会浪费资源。然而，与静态信号相反，接收器和功率不能随时间自由地交易以达到期望的感测精度：存在最大化感测精度的最佳积分时间，其取决于接收器的数量、接收器相关时间以及输入信号的相关时间和方差。将我们的理论应用于大肠杆菌的趋化系统表明，这种细菌已经进化到最佳感浅梯度。
英文摘要：
Living cells often need to measure chemical concentrations that vary in time. To this end, they deploy many resources, e.g. receptors, downstream signaling molecules, time and energy. Here, we present a theory for the optimal design of a large class of sensing systems that need to detect time-varying signals, a receptor driving a push-pull network. The theory is based on the concept of the dynamic input-output relation, which describes the mapping between the current ligand concentration and the average receptor occupancy over the past integration time. This concept is used to develop the idea that the cell employs its push-pull network to estimate the receptor occupancy and then uses this estimate to infer the current ligand concentration by inverting the dynamic input-output relation. The theory reveals that the sensing error can be decomposed into two terms: the sampling error in the estimate of the receptor occupancy and the dynamical error that arises because the average ligand concentration over the past integration time may not reflect the current ligand concentration. The theory generalizes the design principle of optimal resource allocation previously identified for static signals, which states that in an optimally designed sensing system the three fundamental resource classes of receptors and their integration time, readout molecules, and energy are equally limiting so that no resource is wasted. However, in contrast to static signals, receptors and power cannot be traded freely against time to reach a desired sensing precision: there exists an optimal integration time that maximizes the sensing precision, which depends on the number of receptors, the receptor correlation time, and the correlation time and variance of the input signal. Applying our theory to the chemotaxis system of Escherichia coli indicates that this bacterium has evolved to optimally sense shallow gradients.
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