# After 20 years the concept of ‘fractal globule’ is experimentally verified in genomics

In the paper “Comprehensive Mapping of Long-Range Interactions Reveals Folding Principles of the Human Genome” (Science **326**, 289 (2009)), a team of US authors has reported the existence of a new structural organization of a DNA chain in the human genome in the form of a "fractal globule". This first direct experimental observation of the fractal globule by means of the so-called Hi-C method (genome-wide chromosome conformation capture method) has answered many important questions concerning the functioning and packing of DNA in a chromosome. The concept of fractal globule is currently becoming the new paradigm in genomics. For example this concept has explained why the parts of DNA in the dense globular state can be easily folded out and then retracted back.

The observed fractal ("crumpled") globule has been theoretically predicted more than 20 years ago in a theoretical work by A. Grosberg, S. Nechaev and E. Schakhnovich "The role of topological constraints in the kinetics of collapse of macromolecules" (J. Physique, **49**, 2095 (1988)). So, after 20 years this theoretical prediction has found an experimental verification in genomics. The theoretical investigation of the fractal globule was one of the main topics of Sergei Nechaev (LPTMS) during the last decade. In particular, Sergei Nechaev and Oleg Vasilyev have considered the "topological correlations" in unknotted polymer chains in collapsed (globular) phase using methods of algebraic topology, and have proved that due to the topological constraints the trajectory of the chain looks like a statistical Peano curve densely filling the volume on different scales in the 3-dimensional space (S. Nechaev, O. Vasilyev, "On topological correlations in trivial knots: From Brownian bridges to crumpled globules" Journal of Knot Theory and Its Ramifications, **14**, 243 (2005)). The works on this subject have been reviewed in: S. Nechaev, O. Vasilyev, "Thermodynamics and topology of disordered knots: Correlations in trivial lattice knot diagrams", in ”Physical and Numerical Models in Knot Theory”, chapter 22, pp. 421-472, Series on Knots and Everything, (WSPC: Singapore, 2005).

The recently developed Hi-C method provides a comprehensive map of spatial contacts between every accessible genomic region of the genome. A map of genomic contacts gives a wealth of information about genome organization in 3D. However inference of the actual 3D conformation (or ensemble of such conformations) and physical principles that govern its folding are challenging problems that is under current investigation by Leonid Mirny Lab (MIT, USA) and Sergei Nechaev group (LPTMS, France). The progress in elucidating principles of 3D genome folding requires deeper understanding of the interplay between topological and physical properties of polymers and connection of these properties to quantities measured by the Hi-C method.

Maps of the genomic contact frequencies obtained by the Hi-C method show several specific features that suggest a possible hierarchical folding of the genome organization. Such hierarchical organization can be revealed by analysis developed in the field of random hierarchical matrices proposed by Sergei Nechaev, Vladik Avetisov et al in the work "On scale free and poly-scale behaviors of random hierarchical networks" (J. Stat. Mech.: Theory and Experiment, 2009: P07008). The mathematical connection between topology and fractal properties of polymers implies new principles of genome organization in 3D.

The digests of Harvard and MIT devoted to the experimental observation of fractal globule can be found here:

http://news.harvard.edu/gazette/tag/fractal-globule

http://web.mit.edu/newsoffice/2009/3d-genome.html