Mean protein numbers as a function of upstream transcription rate. The different curves show how threshold expression depends on the strength of miRNA/mRNA association rate. Mean protein expression shows a crossover regime from low expression to linear expression with increasing transcription rate. As the strength of miRNA/mRNA association, κ, increases, the threshold becomes sharper. The solid curve is a perfect threshold-linear behavior. The parameters are set as γm = γμ = 0.01, γp = 0.002, σ = 0.5, kp = 0.1, kd = 200.0.