First passage time properties of miRNA-mediated protein translation

An important function of microRNAs in gene regulation is to repress the protein synthesis in a multi-step process with implications in timing efficiency of the regulatory network. We propose a stochastic description of translation-initiation mechanism and solve for the steady state distribution of protein number in the linear regime. The time-dependent moments have been approximately calculated and the role of miRNAs in determining the First Passage Time (FPT) properties of protein dynamics has been established. We analytically show that the modulation of slow rates of the translation process will result in efficient and robust timing mechanism. For a general nonlinear model our numerical simulation results are in qualitative agreement with the linear model.