Fig. 3.

Kinetic proofreading requires coupling of transcript initiation to activator binding; multiple proofreading steps improve fidelity. (A) Transition graph of Model 3. (B) Activator fidelity of Model 3 $\left(f_3\right)$ relative to the fidelity of Model 1 $\left(f_1\right)$, as a function of activator on-rate, $\kappa$; with $k_C=1$, $k_i=100$, α = $\beta =2$, and $\lambda =0$ (for $\lambda >0$, fidelities further decrease). (C) Transcription noise as a function of relative activator fidelity, $f\left(\kappa ,\mu \right)/f_0$, for Model 3 (yellow, 3), Model 4 (green, 4), and Model 1 (gray dashed line, 1). As in calculations for Fig. 2, we assumed $\delta =0.1$ and $v_C=5$; for Model 4 alone: $\lambda =0.1$ and $z,\zeta =10$ to reflect both active removal (by Mot1) and high concentration of TBP; all other parameters were as indicated above. Fano factor and fidelity were calculated as functions of the activator on-rate, κ, and the rate of transcription in the active state, $\mu$ (SI Appendix). (D) Transition graph of Model 4. (E) Activator fidelities of Model 4 (green, 4) and Model 2 (blue, 2) relative to fidelity for Model 1 as a function of $\alpha /\lambda$. For Model 4, we assumed $\alpha =\zeta$ (thus, both parameters are varied equally) and $\lambda ,\eta =0.1$. Other rate constants were $k_C=1$, $k_i=100$, $\beta =2$, and $z=10$. (For smaller $\lambda ,\hspace{0.17em}\eta ,\hspace{0.17em}\beta$, and z than assumed here, fidelity further increases; SI Appendix.)