General transfer matrix formalism to calculate DNA–protein–drug binding in gene regulation: application to OR operator of phage λ

The transfer matrix methodology is proposed as a systematic tool for the statistical–mechanical description of DNA–protein–drug binding involved in gene regulation. We show that a genetic system of several cis-regulatory modules is calculable using this method, considering explicitly the site-overlapping, competitive, cooperative binding of regulatory proteins, their multilayer assembly and DNA looping. In the methodological section, the matrix models are solved for the basic types of short- and long-range interactions between DNA-bound proteins, drugs and nucleosomes. We apply the matrix method to gene regulation at the OR operator of phage λ. The transfer matrix formalism allowed the description of the λ-switch at a single-nucleotide resolution, taking into account the effects of a range of inter-protein distances. Our calculations confirm previously established roles of the contact CI–Cro–RNAP interactions. Concerning long-range interactions, we show that while the DNA loop between the OR and OL operators is important at the lysogenic CI concentrations, the interference between the adjacent promoters PR and PRM becomes more important at small CI concentrations. A large change in the expression pattern may arise in this regime due to anticooperative interactions between DNA-bound RNA polymerases. The applicability of the matrix method to more complex systems is discussed

Nucleosomes in gene regulation: theoretical approaches

This work reviews current theoretical approaches of biophysics and bioinformatics for the description of nucleosome arrangements in chromatin and transcription factor binding to nucleosomal organized DNA. The role of nucleosomes in gene regulation is discussed from molecular-mechanistic and biological point of view. In addition to classical problems of this field, actual questions of epigenetic regulation are discussed. The authors selected for discussion what seem to be the most interesting concepts and hypotheses. Mathematical approaches are described in a simplified language to attract attention to the most important directions of this field