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Reliable information processing in cells requires high sensitivity to changes in the input signal but low sensitivity to random fluctuations in the transmitted signal. There are often many alternative biological circuits qualifying for this biological function. Distinguishing theses biological models and finding the most suitable one are essential, as such model ranking, by experimental evidence, will help to judge the support of the working hypotheses forming each model. Here, we employ the approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to search for biological circuits that can maintain signaling sensitivity while minimizing noise propagation, focusing on cases where the noise is characterized by rapid fluctuations. By systematically analyzing three-component circuits, we rank these biological circuits and identify three-basic-biological-motif buffering noise while maintaining sensitivity to long-term changes in input signals. We discuss in detail a particular implementation in control of nutrient homeostasis in yeast. The principal component analysis of the posterior provides insight into the nature of the reaction between nodes.