Figure 2: Optimal dissociation rate of negative autoregulation.
From: Transcription factor binding kinetics constrain noise suppression via negative feedback
The left panel (a) displays the VMR as a function of the dissociation rates (kd), for various average amount (mp) of the regulated TF protein, TF association rate per operator (ka) and average numbers of TFs made per mRNA (b=ktranslation/kdecay). The solid lines are the analytical expressions given in the Supplementary Note 1. The crosses are measurements from stochastic simulations of fixed size cells where cell growth is approximated with protein decay. Circles are measurements from stochastic simulations of cells that are growing, replicating and dividing with measurements taken in the middle of the cell cycle. Rates are defined in terms of the generation time and TFs are only diluted by cell growth. In addition to the parameters given in the figure, the mRNA lifetime is 1/10 of the generation time. The dashed lines are VMR of unregulated synthesis. In the right panel (b), we display how the expression in Equation 3 for the optimal dissociation rate compares with that obtained from simulations of exponentially growing cells for specific parameter combinations (inset), each with three different mean protein copy numbers (20, 40 and 80). Note that the VMR is approximated in the middle of the cell cycle (see Supplementary Note 1).
