Monovalent and Divalent Salt Effects on Electrostatic Free Energies Defined by the Nonlinear Poisson−Boltzmann Equation:  Application to DNA Binding Reactions

Abstract

We have extended the finite-difference Poisson-Boltzmann (FDPB) equation method to incorporate the treatment of mixed salts (i.e. NaCl/MgCl 2 ). In this context, we have derived an expression for the total electrostatic free energy for mixed salt systems. We use the theory to study nonspecific mixed salt effects on the binding free energies of the minor groove binding antibiotic DAPI, and λ repressor, with DNA. We find that in a pure salt solution the electrostatic contribution to binding varies linearly with log[M n+ ], (where M n+ represents an n-valent cation) and that the effect is uncorrelated with either the valence of the binding ligand or the number of counterions in the binding site. In mixed salt solution, the monovalent and divalent counterions "compete" for the immediate vicinity of the DNA. As experimentally observed in mixed salt solutions, a pronounced curvature appears in the plot of the electrostatic binding free energy vs log[M n+ ]. The curvature for DAPI-DNA binding in mixed salts reflects the fact that divalent counterions interact with bound or free DNA molecules more strongly than monovalent counterions. However, the valence dependence of the electrostatic interaction between cations and negatively charged macromolecules is not solely responsible for the observed curvature. Rather anions, which can interact quite strongly with highly charged DNAbinding proteins, make a significant contribution to the observed salt effects. Our results support previous findings that treatments based on counterion condensation concepts break down for protein-DNA interactions; specifically, it is necessary to describe molecular structures in atomic detail if a realistic description of salt effects is to be obtained.

A thermodynamic framework for Mg 2+ binding to RNA

“…Details of the finite difference procedure to calculate electrostatic potentials and free energies with the NLPB equation in a mixed salt solution have been reported (2,32). The Na-and Mg-dependent contributions to the chemical potential of each RNA species were calculated by using a 65 3 lattice.…”

Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte

“…Specifically, we use the three-step focusing process. 47 In the first run, PB is solved on a large-scale grid. The size of the (cubic) cell of the first run relies on the salt concentration used.…”

Role and Applications of Electrostatic Effects on Nucleic Acid Conformational Transitions and Binding Processes

“…More recently, asymptotic solutions of the cylindrical PB equation for both high salt (κa ≥ 1, or more than 0.1 M univalent salt for B-DNA) (Shkel et al, 2000) and low salt (κa < 1, or less than 0.1 M 1:1 salt for B-DNA) (Shkel et al, 2002;Trizac & Téllez, 2007) (Koehl, 2006) for additional details), Poisson-Boltzmann analyses using detailed 3-D models have become widespread in the literature. Not surprisingly, NLPB calculations employing NA models with atomic resolution have come into vogue as well (Chen & Honig, 1997;Koehl, 2006;Misra et al, 1994;Sharp et al, 1995). With these developments, the minimum detail necessary to accurately describe experimentally relevant systems has come under debate.…”

“…With these developments, the minimum detail necessary to accurately describe experimentally relevant systems has come under debate. Proponents of highly detailed models have implied that such detail is necessary to predict phenomena accurately (Chen & Honig, 1997;Jayaram & Beveridge, 1996). Advocates of the "stripped down" (e.g., cylindrical) approach claim that simplified polyelectrolyte models capture the essence of thermodynamic phenomena under typical experimental conditions and often predict results with quantitative agreement to experiment.…”

“…NLPB calculations of small ligands binding to oligomers. Several NLPB analyses have considered antibiotic-DNA binding thermodynamics (Chen & Honig, 1997;Misra et al, 1994;Sharp et al, 1995). The interaction of the minor groove-binding antibiotic 4',6-diamidino-2-phenylindole (DAPI) with dsDNA exemplifies the debate on the existence of coulombic end effects.…”