使用基于转录的检测器来模拟基于顺序概率比的浓度检测器的行为
Using transcription-based detectors to emulate the behaviour of sequential probability ratio-based concentration detectors
摘要：
序贯概率比检验（SPRT）是统计学中已知的具有最小的平均决策时间相比，其他顺序或固定时间的测试给定的错误率。在某些情况下，小区需要准确和快速地做出决策，因此已经建议SPRT可以用于理解蜂窝决策中的速度-准确性权衡。一般认为，为了使细胞利用SPRT，有必要找到可以计算SPRT所需的对数似然比的生化电路。然而，本文采取了不同的方法。我们认识到，SPRT的高级行为是由其阳性检测或命中率定义的，对数似然比的计算只是实现这种行为的一种方式。在本文中，我们将提出一种方法，它使用一个基于转录的检测器来模拟SPRT的命中率，而无需计算精确的对数似然比。我们考虑使用具有多个结合位点的启动子来准确和快速地检测转录因子的浓度是否高于目标水平的问题。我们表明，它是可能的，以找到的转录因子的启动子的结合位点的结合和未结合率，使产生的mRNA的量将高于阈值的概率约等于SPRT检测器的命中率。此外，我们表明，这种基于转录的检测器需要进行阳性检测的平均时间小于或等于SPRT的浓度范围很广。我们注意到，最后一句话并不矛盾沃尔德的最优性结果，因为我们的基于转录的检测器使用开放式测试。
英文摘要：
The sequential probability ratio test (SPRT) from statistics is known to have the least mean decision time compared to other sequential or fixed-time tests for given error rates. In some circumstances, cells need to make decisions accurately and quickly, therefore it has been suggested the SPRT may be used to understand the speed-accuracy tradeoff in cellular decision making. It is generally thought that in order for cells to make use of the SPRT, it is necessary to find biochemical circuits that can compute the log-likelihood ratio needed for the SPRT. However, this paper takes a different approach. We recognise that the high-level behaviour of the SPRT is defined by its positive detection or hit rate, and the computation of the log-likelihood ratio is just one way to realise this behaviour. In this paper, we will present a method which uses a transcription-based detector to emulate the hit rate of the SPRT without computing the exact log-likelihood ratio. We consider the problem of using a promoter with multiple binding sites to accurately and quickly detect whether the concentration of a transcription factor is above a target level. We show that it is possible to find binding and unbinding rates of the transcription factor to the promoter's binding sites so that the probability that the amount of mRNA produced will be higher than a threshold is approximately equal to the hit rate of the SPRT detector. Moreover, we show that the average time that this transcription-based detector needs to make a positive detection is less than or equal to that of the SPRT for a wide range of concentrations. We remark that the last statement does not contradict Wald's optimality result because our transcription-based detector uses an open-ended test.
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