Protein bursts cause peaks in protein time courses and skewed protein distributions.

<p>(A): mRNA (upper plots) and corresponding protein time courses (lower plots) of reaction systems without (left) and with (right) positive feedback. The average burst sizes and frequencies are identical in the two systems, but the transcription events are temporally clustered under positive feedback, leading to rare super-bursts. The functions used are <i>F</i>(<i>s</i>) = <i>a</i> + <i>v</i> ⋅ <i>s</i> and <i>G</i>(<i>m</i>) = <i>g</i> ⋅ <i>m</i> with <i>a</i> = 0.2 and <i>v</i> = 0 in the system without feedback and <i>a</i> = 0.05 and <i>v</i> = 0.075 in the system with feedback. In both cases, <i>g</i> = 10 and <i>ν</i> = 1. (B): The upper plot shows the graphical determination of the location of modes. Two modes are predicted in the monostable system (modes: rose diamonds, fixed point: green filled circles). The protein distribution in the lower figure shows that the prediction is exact. Here, , <i>G</i>(<i>m</i>) = 2000 ⋅ <i>m</i>, <i>ν</i> = 0.01.