Predicting concentration changes via discrete sampling

Age J. Tjalma, Pieter Rein ten Wolde
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Abstract

To successfully navigate chemical gradients, microorganisms need to predict how the ligand concentration changes in space. Due to their limited size, they do not take a spatial derivative over their body length but rather a temporal derivative, comparing the current signal with that in the recent past, over the so-called adaptation time. This strategy is pervasive in biology, but it remains unclear what determines the accuracy of such measurements. Using a generalized version of the previously established sampling framework, we investigate how resource limitations and the statistics of the input signal set the optimal design of a well-characterized network that measures temporal concentration changes: the Escherichia coli chemotaxis network. Our results show how an optimal adaptation time arises from the trade-off between the sampling error, caused by the stochastic nature of the network, and the dynamical error, caused by uninformative fluctuations in the input. A larger resource availability reduces the sampling error, which allows for a smaller adaptation time, thereby simultaneously decreasing the dynamical error. Similarly, we find that the optimal adaptation time scales inversely with the gradient steepness, because steeper gradients lift the signal above the noise and reduce the sampling error. These findings shed light on the principles that govern the optimal design of the E. coli chemotaxis network specifically, and any system measuring temporal changes more broadly.
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通过离散采样预测浓度变化
要成功驾驭化学梯度,微生物需要预测配体浓度在空间中的变化。由于微生物的体型有限,它们不会对其体长进行空间导数计算,而是进行时间导数计算,将当前信号与近期信号进行比较,即所谓的适应时间。这种策略在生物学中非常普遍,但目前还不清楚是什么决定了这种测量的准确性。利用以前建立的采样框架的广义版本,我们研究了资源限制和输入信号的统计量如何决定了一个特性良好的测量时间浓度变化的网络(大肠杆菌趋化网络)的最佳设计。我们的研究结果表明,最佳适应时间是如何从网络随机性引起的采样误差和输入中无信息波动引起的动态误差之间的权衡中产生的。同样,我们发现最佳适应时间与梯度陡度成反比,因为较陡的梯度能将信号提升到噪声之上并减少采样误差。这些发现揭示了大肠杆菌趋化网络以及任何测量时间变化的系统的优化设计原则。
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