| Circadian clock is an internal timekeeping system for organism adapts to changes of the environment, which is found in all kingdoms of life. The circadian cycle is about 24 h. Recent study indicates that nearly half of all the protein coding genes present circadian rhythm in mouse.E-box is a cis-element who plays an important role in regulating the transcription of clock-controlled genes. The BMAL1_CLOCK promotes the transcription of clock-controlled genes by binding to their E-box, PER_CRY further inhibits BMAL1_CLOCK transcriptional activity. However, the detailed regulatory mechanism of E-box remains unclear. There are two alternative regulatory models of E-box have been proposed. Model 1 suggests that the heterodimer PER_CRY binds to BMAL1_CLOCK to inhibit the transcription of clock-controlled genes. By contrast, model 2 hypothesizes that the complex PER_CRY displaces BMAL1_CLOCK from E-box to suppress the transcription.The following are the main results and contributions:(1) It has been observed that Dbp gene has different E-boxes. These differ-ent E-boxes exhibit different patterns in some aspects, including phase. We build a more reasonable model of the regulatory mechanism of E-box, particularly, model 1 and model 2 are the special cases of the new model. In addition, the new model not only explains the function mechanism of E-box in biology, but also provides the basic formula of E-box for future modeling work in mathematics.(2) The new model reproduces the dynamics of different E-boxes of Dbp. Also, the simulation results are consistent with the experiments about knocking out Fbxl3. Therefore, the model is validated by experimental results.(3) We further analyze the stability of the new model and the properties of E_BC and E_BC_PC. Quasi steady state predicts that the binding ability of PER_CRY determines the phase of E-box. Reflect to the parameters, any single parameter is not enough to impact on the E-box phase, while parameters combination may alter phase. |
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