Figure 4.

Model calibration and prediction of the transcriptional activity as a function of the repressor concentration. The normalized transcription ($\overline{\Gamma }/{\Gamma }_{\max }$) was obtained for WT and seven mutants accounting for all the combinations of deletions of the three operators. For each of the eight cases, the results of the model (solid lines) as a function of the repressor concentration are compared with the experimental data from Oehler et al. (14) (squares). The particular set of WT or deleted operators is indicated for each curve; for instance, O₁-O₂-O₃ corresponds to the WT lac operon and O_1M-O_2M-O_3M to the mutant with all three operators deleted. The values of the experimental parameters used are c_L12 = 23.35 kcal/mol, c_L13 = 22.05 kcal/mol, c_L23 = 23.50 kcal/mol, and χ = 0.03. The PWM scores, S, for each site are as shown in Table 1. (A) Parameter values a = 1.387 kcal/mol and b = −9.064 kcal/mol, which connect interaction free energies with scores, e = aS + b, were obtained by fitting the model to all the experimental transcription data. (B) Parameter values a = 1.348 kcal/mol and b = −9.531 kcal/mol were obtained by fitting the model to the experimental data for operator configurations O₁-O₂-O₃ and O_1M-O₂-O₃. The model accurately predicts the normalized transcription for the other six operator configurations. (C) Only two experimental points (large gray circles) are used to obtain the parameter values a = 1.462 kcal/mol and b = −8.208 kcal/mol. The model is still able to accurately predict the normalized transcription for the remaining 20 experimental points.