Controlling gene expression timing through gene regulatory architecture
Fig 2
Effect of TF-binding affinity on MFPT for auto-regulated genes without any competing binding sites.
(A, D) MFPT as a function of off-rate (binding affinity) of auto-activated gene and auto-repressed gene. Each curve (blue, red, yellow) is generated by keeping the transcription rate (r0) and translation rate (b) fixed and varying only the binding affinity through koff. Dashed curves correspond to doubling the translation rate (2b). Black dashed lines correspond to MFPT of a constitutive gene of transcription rate r0. (B, E) MFPT as a function of TF-promoter occupancy. Solid and dashed curves are for translation rates b and 2b, respectively. (C,F) Scaled steady state TF expression (SSE) and inverse of production rate (1/R) as a function of off-rate. The ratio of SSE and R (black curve) qualitatively predicts the behavior of the MFPT as a function of off-rate. For auto-activation we use r0 = 0.0025 s−1, b = 0.025 s−1mRNA−1; for auto-repression r0 = 0.05 s−1, b = 0.1 s−1mRNA−1. The protein and mRNA degradation rates are γ = 0.0003 s−1 and γm = 0.011 s−1 per molecule, all additional parameter values listed in the Materials and methods.