Kinetic characteristics of transcriptional bursting in a complex gene model with cyclic promoter structure

While transcription occurs often in a bursty manner, various possible regulations can lead to complex promoter patterns such as promoter cycles, giving rise to an important issue: How do promoter kinetics shape transcriptional bursting kinetics? Here we introduce and analyze a general model of the promoter cycle consisting of multi-OFF states and multi-ON states, focusing on the effects of multi-ON mechanisms on transcriptional bursting kinetics. The derived analytical results indicate that bust size follows a mixed geometric distribution rather than a single geometric distribution assumed in previous studies, and ON and OFF times obey their own mixed exponential distributions. In addition, we find that the multi-ON mechanism can lead to bimodal burst-size distribution, antagonistic timing of ON and OFF, and diverse burst frequencies, each further contributing to cell-to-cell variability in the mRNA expression level. These results not only reveal essential features of transcriptional bursting kinetics patterns shaped by multi-state mechanisms but also can be used to the inferences of transcriptional bursting kinetics and promoter structure based on experimental data.

Calculation of Free Energy Consumption in Gene Transcription with Complex Promoter Structure

From the viewpoint of thermodynamics, gene transcription necessarily consumes free energy due to nonequilibrium processes. On the other hand, regulatory molecules present on the core promoter of a gene interact often in a dynamic, highly combinatorial, and possibly energy-dependent manner, leading to a complex promoter structure. This raises the question of how gene transcription with general promoter topology consumes free energy. We propose a biophysically intuitive approach to calculate energy consumption (quantified by the production rate of entropy) of a gene transcription process. Then, we show that the numbers of the ON and OFF states of a promoter can reduce energy consumption of the gene system and the Fano factor of mRNA, and in contrast to other regulatory ways, the cooperative binding of transcription factors to DNA sites always reduces energy consumption but amplifies the mRNA noise. While our proposed approach is general, our obtained qualitative results can in turn be used to the inference of complex promoter structure.

Adaptive Dc Stabilizer with Reduced Dc System Application

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