October 13, 2009 | David F. Coppedge

DNA Organization Is Fractal

How would you pack spaghetti in a basketball (07/28/2004) such that you could get to any strand quickly?  You might try the “fractal globule” method.  You form little knots, or globules, on each strand.  These become like beads on a string.  Now you fold the beads into globules, and then fold those into higher-level globules.  A simple operation makes any spot in super-globule accessible without having to untie any knots.  The globule-of-globules-of-globules ordering of the material recalls those beautiful fractal patterns in geometry that keep repeating a design all the way down.
    A paper in Science suggested that this is how DNA is organized in the nucleus.1  DNA appears to be folded into “fractal globules” possessing a hierarchical organization.  Lieberman-Aiden et al explained:

Various authors have proposed that chromosomal regions can be modeled as an “equilibrium globule”: a compact, densely knotted configuration originally used to describe a polymer in a poor solvent at equilibrium…. Grosberg et al. proposed an alternative model, theorizing that polymers, including interphase DNA, can self-organize into a long-lived, nonequilibrium conformation that they described as a “fractal globule”.  This highly compact state is formed by an unentangled polymer when it crumples into a series of small globules in a “beads-on-a-string” configuration.  These beads serve as monomers in subsequent rounds of spontaneous crumpling until only a single globule-of-globules-of-globules remains.  The resulting structure resembles a Peano curve, a continuous fractal trajectory that densely fills 3D space without crossing itself.  Fractal globules are an attractive structure for chromatin segments because they lack knots and would facilitate unfolding and refolding, for example, during gene activation, gene repression, or the cell cycle.  In a fractal globule, contiguous regions of the genome tend to form spatial sectors whose size corresponds to the length of the original region (Fig. 4C).  In contrast, an equilibrium globule is highly knotted and lacks such sectors; instead, linear and spatial positions are largely decorrelated after, at most, a few megabases (Fig. 4C).  The fractal globule has not previously been observed.

At resolutions currently available, it was not possible to prove that DNA is organized in fractal globules: “We conclude that, at the scale of several megabases, the data are consistent with a fractal globule model for chromatin organization,” they said, adding: “Of course, we cannot rule out the possibility that other forms of regular organization might lead to similar findings.”  Measurements so far, however, are consistent with the fractal model and inconsistent with the equilibrium-globule model.  Their computational methods “confirm the presence of chromosome territories and the spatial proximity of small, gene-rich chromosomes,” they said.  This points to “an additional level of genome organization that is characterized by the spatial segregation of open and closed chromatin to form two genome-wide compartments.”  This is what is consistent with the “fractal globule, a knot-free, polymer conformation that enables maximally dense packing while preserving the ability to easily fold and unfold any genomic locus.”

1.  Lieberman-Aiden et al, “Comprehensive Mapping of Long-Range Interactions Reveals Folding Principles of the Human Genome,” Science, 9 October 2009: Vol. 326. no. 5950, pp. 289-293, DOI: 10.1126/science.1181369.

This is amazing and wonderful to consider.  Not only does DNA contain a vast library of genetic instructions, it is organized in a way that maximizes both packing and accessibility.  There are molecular machines that “know” how to pack DNA this way, but they themselves were coded in DNA.  The whole system is mechanized, optimized and integrated in levels we are only beginning to understand.  There was no mention of evolution in this paper (obviously).

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