Characterizing the ionic distribution around chromatin is important for understanding the electrostatic forces governing chromatin structure and function. Here we develop an electrostatic model to handle multivalent ions and compute the ionic distribution around a mesoscale chromatin model as a function of conformation, number of nucleosome cores, and ionic strength and species using Poisson-Boltzmann theory. This approach enables us to visualize and measure the complex patterns of counterion condensation around chromatin by examining ionic densities, free energies, shielding charges, and correlations of shielding charges around the nucleosome core and various oligonucleosome conformations. We show that: Counterions, especially divalent cations, predominantly condense around the nucleosomal and linker DNA, unburied regions of histone tails, and exposed chromatin surfaces; ionic screening is sensitively influenced by local and global conformations, with a wide ranging net nucleosome core screening charge (56-100e); and screening charge correlations reveal conformational flexibility and interactions among chromatin subunits, especially between the histone tails and parental nucleosome cores. These results provide complementary and detailed views of ionic effects on chromatin structure for modest computational resources. The electrostatic model developed here is applicable to other coarse-grained macromolecular complexes.
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