Emergence of bimodality in the presence of extrinsic noise.

<p>(A) Qualitative representation of the miRNA production rate distribution. The black vertical line indicates the value of the miRNA transcription rate <i>k</i>_<i>S</i> = <i>αk</i>_<i>R</i> for different values of the target transcription rate <i>k</i>_<i>R</i>. The distributions represent the different conditions labelled from 1 to 4 shown in (B). The region of the distribution contributing to the repressed state is coloured in orange. (B) The amount of free mRNA molecules as a function of the target transcription rate <i>k</i>_<i>R</i>. Solid lines are analytic predictions while blue squares correspond to numerical simulations. (C) Free mRNA molecule distributions corresponding to the points highlighted in (B). Solid black lines correspond to numerical simulations while solid red lines are analytic predictions. The repressed region is coloured in orange. (D) Protein molecule distributions corresponding to the mRNA distributions in (C). Solid black lines correspond to numerical simulations while solid red lines are analytic predictions. The repressed region is coloured in orange. In (B) the parameters are <i>g</i>_<i>S</i> = 1.2 × 10⁻² min⁻¹, <i>g</i>_<i>R</i> = 2.4 × 10⁻² min⁻¹, <i>g</i> = 1.2 × 10² nM⁻¹ min⁻¹, <i>k</i>_<i>P</i> = 6.0 min⁻¹, <i>g</i>_<i>P</i> = 1.2 × 10⁻² min⁻¹, <i>α</i> = 0.5. <i>k</i>_<i>S</i> are picked from a gaussian distribution with mean and standard deviation <i>σ</i> = 4.8 × 10⁻⁴ nM min⁻¹. <i>k</i>_<i>R</i> ranges from 2.4 × 10⁻⁴ nM min⁻¹ to 5.2 × 10⁻³ nM min⁻¹. In (C) and (D) the parameters are the same as in (B) except for <i>k</i>_<i>R</i>, which is fixed for each distribution and for dashed lines from 1 to 4 takes the values <i>k</i>_<i>R</i> = 1.2 × 10⁻³ nM min⁻¹, 3.1 × 10⁻³ nM min⁻¹, 4.0 × 10⁻³ nM min⁻¹, 4.8 × 10⁻³ nM min⁻¹.