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Uncovering the basic principles that govern the three dimensional (3D) organization of genomes poses one of the main challenges in mathematical biology of the postgenomic era. In this talk I will show how geometric knot theory can reveal some such principles. Certain viruses and some organisms, such as trypanosomes, accommodate knotted or interlinked genomes. Others, such as bacteria, are known to have unknotted genomes. It remains to be determined if the genomes of higher organisms, such as humans, admit topologically complex forms. In their seminal paper Lieberman-Aiden et al. (2009) developed Hi-C, a novel experimental technique that helps identify genomic regions that are in close spatial proximity within the human cell. Using computer simulations of random and fractal globules, the authors argued that the human genome is not organized as a random globule and therefore cannot be knotted. We here introduce the BFACF globule and use it to determine whether the conclusion in Lieberman-Aiden et al. (2009) is adequate. The BFACF globule relies on the BFACF algorithm, a well-studied dynamic Monte Carlo method that generates an irreducible Markov chain for each knot type. We show that the BFACF globule is in agreement with Hi-C data, even when knotted globules are considered. Interestingly our results show that there is a limit to the knot complexity that the BFACF globule can hold while remaining consistent with the data.

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