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The hierarchical packaging of DNA into chromatin within a eukaryotic nucleus plays a pivotal role in both the accessibility of genomic information and the dynamics of replication. Our work addresses the role of nanoscale physical and geometric properties in determining the structure of chromatin at the mesoscale level. We study the packaging of DNA in chromatin fibers by optimization of regular helical morphologies, considering the elasticity of the linker DNA as well as steric packing of the nucleosomes and linkers. Our model predicts a broad range of preferred helix structures for a fixed linker length of DNA; changing the linker length alters the predicted ensemble. Specifically, we find that the twist registry of the nucleosomes, as set by the internucleosome repeat length, determines the preferred angle between the nucleosomes and the fiber axis. For moderate to long linker lengths, we find a number of …