Structure-driven homology pairing of chromatin fibers: the role of electrostatics and protein-induced bridging.

Chromatin domains formed in vivo are characterized by different types of 3D organization of interconnected nucleosomes and architectural proteins. Here, we quantitatively test a hypothesis that the similarities in the structure of chromatin fibers (which we call "structural homology") can affect their mutual electrostatic and protein-mediated bridging interactions. For example, highly repetitive DNA sequences in heterochromatic regions can position nucleosomes so that preferred inter-nucleosomal distances are preserved on the surfaces of neighboring fibers. On the contrary, the segments of chromatin fiber formed on unrelated DNA sequences have different geometrical parameters and lack structural complementarity pivotal for stable association and cohesion. Furthermore, specific functional elements such as insulator regions, transcription start and termination sites, and replication origins are characterized by strong nucleosome ordering that might induce structure-driven iterations of chromatin fibers. We propose that shape-specific protein-bridging interactions facilitate long-range pairing of chromatin fragments, while for closely-juxtaposed fibers electrostatic forces can in addition yield fine-tuned structure-specific recognition and pairing. These pairing effects can account for some features observed for mitotic and inter-phase chromatins.

[Nucleosomes in gene regulation: theoretical approaches].

This work reviews current theoretical approaches of biophysics and bioinformatics for the description of nucleosome arrangement 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 mentioned. 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.

Long-range interactions between ligands bound to a DNA molecule give rise to adsorption with the character of phase transition of the first kind.

Influence of long-range interactions between ligands bound to DNA molecule on the character of their adsorption is studied using computer modeling. For this investigation, two calculation procedures are developed. They are based upon the method of the free energy minimum and on the partition function method. The both procedures demonstrate that in the case of a strong enough attraction between all the bound ligands their binding to DNA has the character of phase transition of the first kind. There is a break in the binding curve c(c0) where c - relative concentration of bound ligands, c0 - molar concentration of free ligands. The break occurs because there is an interval of central degrees of binding (approximately 50% of the maximum c value) that are prohibited for individual DNA molecules. Such a transition might be caused by some types of DNA condensation. Attraction between the neighboring ligands only, adjacent or/and separated by double helix regions, does not cause this effect.

[Calculation of DNA condensation, caused by adsorption of ligands]. / Raschet kondensatsii DNK, vyzvannoi adsorbtsiei ligandov.

A method for calculating the curves of DNA transition from linear to condensed state upon binding of condensing ligands has been developed. The character of the transition and ligand concentration necessary for condensation have been shown to be governed by the length of DNA molecule, energy and stoichiometry parameters of DNA-ligand complex (equilibrium constant between linear and condensed form in the absence of ligands, constants for ligand binding to linear and condensed forms, the number of base pairs covered by one ligand, etc.). The results of the calculations indicate that only slight difference in the free energies of these states in free DNA (less than 6 cal/mole(bp) for DNA of 500 bp long) is sufficient for the existence of stable linear state in the absence of ligands (in free DNA) and the formation of stable condensed state upon complexation.