We conducted molecular dynamics computer simulations of charged histone tail-DNA interactions in systems mimicking nucleosome core particles (NCP) . In a coarse-grained model, the NCP is modeled as a negatively charged spherical particle with flexible polycationic histone tails attached to it in a dielectric continuum with explicit mobile counterions and added salt. The size, charge, and distribution of the tails relative to the core were built to mimick real NCP. In this way, we incorporate attractive ion-ion correlation effects due to fluctuations in the ion cloud and the attractive entropic and energetic tail-bridging effects. In agreement with experimental data, increase of monovalent salt content from salt-free to physiological concentration leads to the formation of NCP aggregates; likewise, in the presence of MgCl2, the NCPs form condensed systems via histone-tail bridging and accumulation of counterions. More detailed mechanisms of the histone tail-DNA interactions and dynamics have been obtained from all-atom molecular dynamics simulations (including water), comprising three DNA 22-mers and 14 short fragments of the H4 histone tail (amino acids 5-12) carrying three positive charges on lysine+ interacting with DNA. We found correlation of the DNA-DNA distance with the presence and association of the histone tail between the DNA molecules.