  We study unbinding of multivalent cationic ligands from oppositely charged
polymeric binding sites sparsely grafted on a flat neutral substrate. Our
molecular dynamics (MD) simulations are suggested by single-molecule studies of
protein-DNA interactions. We consider univalent salt concentrations spanning
roughly a thousandfold range, together with various concentrations of excess
ligands in solution. To reveal the ionic effects on unbinding kinetics of
spontaneous and facilitated dissociation mechanisms, we treat electrostatic
interactions both at a Debye-H\"{u}ckel (DH, or `implicit' ions, i.e., use of
an electrostatic potential with a prescribed decay length) level, as well as by
the more precise approach of considering all ionic species explicitly in the
simulations. We find that the DH approach systematically overestimates
unbinding rates, relative to the calculations where all ion pairs are present
explicitly in solution, although many aspects of the two types of calculation
are qualitatively similar. For facilitated dissociation (FD, acceleration of
unbinding by free ligands in solution) explicit ion simulations lead to
unbinding at lower free ligand concentrations. Our simulations predict a
variety of FD regimes as a function of free ligand and ion concentrations; a
particularly interesting regime is at intermediate concentrations of ligands
where non-electrostatic binding strength controls FD. We conclude that
explicit-ion electrostatic modeling is an essential component to quantitatively
tackle problems in molecular ligand dissociation, including
nucleic-acid-binding proteins.
