Cells send and receive signals through pathways that have been defined in great detail biochemically, and it is often presumed that the signals convey only level information. Cell signaling in the presence of noise is extensively studied but only rarely is the speed required to make a decision considered. However, in the immune system, rapidly developing embryos, and cellular response to stress, fast and accurate actions are required. Statistical theory under the rubric of "exploit-explore" quantifies trade-offs between decision speed and accuracy and supplies rigorous performance bounds and algorithms that realize them. We show that common protein phosphorylation networks can implement optimal decision theory algorithms and speculate that the ubiquitous chemical modifications to receptors during signaling actually perform analog computations. We quantify performance trade-offs when the cellular system has incomplete knowledge of the data model. For the problem of sensing the time when the composition of a ligand mixture changes, we find a nonanalytic dependence on relative concentrations and specify the number of parameters needed for near-optimal performance and how to adjust them. The algorithms specify the minimal computation that has to take place on a single receptor before the information is pooled across the cell.signal transduction | sequential probability ratio test T he exigencies of operations research during the second world war led to the following problem: Given a stream of data that is drawn from one of two prescribed models M1 or M2, what is the quickest way to decide between them subject to bounds on the errors? The solution found by Wald (1, 2) computes the ratio of two conditional probabilities using the data up to time t, RðtÞ ¼ Pðdataj M1Þ=Pðdataj M2Þ;[1]and calls M1 when R > H1 and M2 when R < H2 and waits for more data otherwise. The thresholds H control the errors; e.g., larger H1 decreases the odds of deciding M1 when the data come from M2. For the task of distinguishing two Gaussians with different means, the average decision time for Wald's algorithm is a factor two times shorter than using a fixed averaging time for the same error rate. This is a simple example of a general class of problems termed "exploit-explore"; i.e., either decide or accumulate more data (3, 4). They are used in medical statistics to decide when a clinical trial has generated enough data for a conclusion. For the problems that concern us, the next step in complexity was taken by Shiryaev (5-7), who considered the optimal detection of change points. A stream of data is presented and the model changes from M1 to M2 at an unknown time θ. The algorithm calls the change point at time t to minimize a linear combination of the false positive rate (e.g., t ≤ θ) and the decision time mean ðt − θÞ when t > θ. Again the algorithm "knows" the models M1, M2.Another step in complexity, about which we have little to say, corresponds to situations where the statistics of the hypotheses to be discriminated are not available or ...