论文标题
使用基于转录的检测器效仿基于顺序概率比率检测器的行为
Using transcription-based detectors to emulate the behaviour of sequential probability ratio-based concentration detectors
论文作者
论文摘要
已知来自统计数据的顺序概率比测试（SPRT）与给定错误率的其他顺序或固定时间测试相比，平均决策时间最小。在某些情况下，细胞需要准确，快速做出决策，因此建议将SPRT用于了解细胞决策中的速度准确性权衡。通常认为，为了使用SPRT，有必要找到可以计算SPRT所需的对数可能比率的生化回路。但是，本文采用了不同的方法。我们认识到，SPRT的高级行为是由其正检测或命中率定义的，而对数可能性比率的计算只是实现这种行为的一种方法。在本文中，我们将提出一种使用基于转录的检测器模拟SPRT的命中率的方法，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并快速检测转录因子的浓度是否高于目标水平的问题。我们表明，可以找到转录因子与启动子的结合位点的结合和解关率，以便产生的mRNA量高于阈值的概率大约等于SPRT检测器的命中率。此外，我们表明，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的平均时间。我们指出，最后一个陈述并不与Wald的最佳结果相矛盾，因为我们的基于转录的检测器使用开放式测试。
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.
