The nuclei of eukaryotic cells house their DNA in a highly compact, yet incredibly dynamic chromatin structure. This non-uniform and dynamic structure enables many processes of biological relevance, such as gene expression. The motions of chromatin facilitate the process of bringing together protein components, such as those required for transcription, that are situated far apart along the DNA sequence. A complete account of the connection between the local features of DNA and protein and the global motions of chromatin is vital in understanding these processes.<br/><br/>Until now, the packing of nucleosomes, the fundamental structural unit of proteins and DNA in chromatin, has been studied physically via X-rays and cryogenic electron microscopy (cryo-EM), with few to little mathematical tools available. We have developed tools to quantitatively evaluate the amount of interaction between two nucleosomes on their faces and sides, as well as to give biological meaning to the regions of interaction. We apply our methods to X-ray crystal and cryo-EM structures, in the process confirming much of the existing observations while developing new insights into some atypical structures. We also deploy our algorithm to analyze configuration outputs from Markov Chain Monte Carlo (MCMC) simulations of precisely positioned nucleosome arrays. These structures, which we found to resemble those from cryo-EM and X-ray, differed in geometry based on the length of the linker DNA between the nucleosomes.

Using mathematical tools to characterize chromatin geometries in crystal, cryo-EM and simulated structures

255th National Meeting (2018)

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