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Bursting on a two state stochastic model for gene transcription in Drosophila embryos

Recent experimental data on the transcription dynamics of eve gene stripe two formation of Drosophila melanogaster embryos occurs in bursts of multiple sizes and durations. That has motivated the proposition of a transcription model having multiple ON states for the promoter of the eve gene each of them characterized by different synthesis rate. To understand the role of multiple ON states on gene transcription we approach the exact solutions for a two state stochastic model for gene transcription in D. melanogaster embryos and derive its bursting limit. Simulations based on the Gillespie algorithm at the bursting limit show the occurrence of bursts of multiple sizes and durations. Based on our theoretical approach, we interpret the aforementioned experimental data as a demonstration of the intrinsic stochasticity of the transcriptional processes in fruit fly embryos. Then, we conceive the experimental arrangement to determine when gene transcription has multiple ON promoter state in a noisy environment.