A stochastic model of the formation of the molecular configuration of an enhancer site

Abstract

Various molecular configurations can be formed by combinations of free and occupied transcription-factor binding sites at an enhancer site that regulates the transcriptional activity of a target gene. Thermodynamic models of gene expression enable the calculation of the probability of transcriptional activation of a target gene using the probabilities that correspond to specific molecular configurations of an enhancer. A simple stochastic model for the formation of such configurations is presented in this study. The processes of the non-specific binding of transcription factors to DNA, the sliding of proteins along DNA, and energetically favorable binding to specific sites are taken into account in the model, which has been used to investigate the properties of molecular configurations of the regulatory site of the knirps gene, which is expressed during early embryonic development of Drosophila in a manner that is dependent on the activity of the Hunchback and Bicoid transcription factors. The assumptions that are included in the model allowed for discrimination between three successive dynamic stages that are characterized by different binding rates. Transcription-factor binding sites could be divided into three groups according to the degree of occupancy. The probability of occupation that was calculated for the sites in a quasi-equilibrium state was substantially different from the distribution that was predicted using the assumption of thermodynamic equilibrium that is employed in thermodynamic models of expression. These results can serve as the first step towards the refinement of expression models based on more detailed information on the regulatory regions of target genes.