Intrinsically disordered proteins (IDP) are a broad class of proteins with relatively flat energy landscapes showing a high level of functional promiscuity, which are frequently regulated through posttranslational covalent modifications. Histone tails, which are the terminal segments of the histone proteins, are prominent IDPs that are implicated in a variety of signaling processes, which control chromatin organization and dynamics. Although a large body of work has been done on elucidating the roles of posttranslational modifications in functional regulation of IDPs, molecular mechanisms behind the observed behaviors are not fully understood. Using extensive atomistic molecular dynamics simulations, we found in this work that H4 tail mono-acetylation at LYS-16, which is a key covalent modification, induces a significant reorganization of the tail's conformational landscape, inducing partial ordering and enhancing the propensity for alpha-helical segments. Furthermore, our calculations of the potentials of mean force between the H4 tail and a DNA fragment indicate that contrary to the expectations based on simple electrostatic reasoning, the Lys-16 mono-acetylated H4 tail binds to DNA stronger than the unacetylated protein. Based on these results, we propose a molecular mechanism for the way Lys-16 acetylation might lead to experimentally observed disruption of compact chromatin fibers.