(untitled) (CSIAM Transactions on Life Sciences, 2025)
Biological experiments have verified that chromatin organization has importance influence on gene expression, but the conventional models of gene expression neglect this influence, in particular the effect of enhancer-promoter (E-P) communication on gene expression. Here we first review properties of the classical Rouse model that is a quite accurate description of chromatin as confirmed by microscopy experiments. Second, we extend this model to the polymer models with long-range interactions so that they include E-P communications that are typically long-range interactions. We also carry out theoretical analysis for the extended models. Third, we establish mathematical models for the whole process of gene transcription, which consider connections between upstream chromatin dynamics and downstream promoter kinetics. These connections consider two possible ways of regulation: The one via E-P encounter probability and the other via E-P spatial distance, both supported by a different experimental measurement. These models lay solid foundations not only for the deep study of gene-expression dynamics but also for the statistical inference of experimental data.