Clumped-MCEM: Inference for multistep transcriptional processes.

Many biochemical events involve multistep reactions. Among them, an important biological process that involves multistep reaction is the transcriptional process. A widely used approach for simplifying multistep reactions is the delayed reaction method. In this work, we devise a model reduction strategy that represents several OFF states by a single state, accompanied by specifying a time delay for burst frequency. Using this model reduction, we develop Clumped-MCEM which enables simulation and parameter inference. We apply this method to time-series data of endogenous mouse glutaminase promoter, to validate the model assumptions and infer the kinetic parameters. Further, we compare efficiency of Clumped-MCEM with state-of-the-art methods - Bursty MCEM and delay Bursty MCEM. Simulation results show that Clumped-MCEM inference is more efficient for time-series data and is able to produce similar numerical accuracy as state-of-the-art methods - Bursty MCEM and delay Bursty MCEM in less time. Clumped-MCEM reduces computational cost by 57.58% when compared with Bursty MCEM and 32.19% when compared with delay Bursty MCEM.