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

Abstract

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.