The concept of activation in transcriptional regulation is based on the assumption that product mRNA increases monotonically as a function of regulator concentration. We analyze the Shea-Ackers model of transcription and find this assumption to be correct only for the simplest of promoters. We define a new regulatory constant that is a nonlinear combination of association and transcription initiation constants characterizing activation and repression for more complicated promoters. Our results

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... an guide the synthesis of new promoters and lead to a deeper understanding of the constraints guiding the natural promoters evolution. Using a validated mathematical model based on the Shea-Ackers transcription rate function, we then show that two modes of upregulation have very different effects on the function of promoter PRM in phage lambda. We predict that if CI2 bound to OR2 produced equal increase in RNAP-DNA binding constant (compared to wild-type increase in the closed-open transition probability), the lysogen would be significantly less stable. We then focus on the promoter clearance process during transcription initiation. Our work builds upon an initial sequence-dependent three-pathway model proposed by Xue et al. After making several modifications to this model and not being able to satisfactorily match experimental data, we introduce a new parameter to the model: the possible formation of secondary structure in the single stranded scrunched DNA accumulated before RNA polymerase is able to escape the promoter .