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Evaluation of Ion Binding to DNA Duplexes Using a Size-Modified Poisson-Boltzmann Theory

Vincent B. Chu ^*, Yu Bai  , Jan Lipfert , Daniel Herschlag   and Sebastian Doniach ^*  

^* Department of Applied Physics, Department of Biochemistry, Biophysics Program, and Department of Physics, Stanford University, California

Correspondence: Address reprint requests to Sebastian Doniach, Tel.: 650-723-4786; E-mail: doniach{at}drizzle.stanford.edu.

Poisson-Boltzmann (PB) theory is among the most widely applied electrostatic theories in biological and chemical science. Despite its reasonable success in explaining a wide variety of phenomena, it fails to incorporate two basic physical effects, ion size and ion-ion correlations, into its theoretical treatment. Recent experimental work has shown significant deviations from PB theory in competitive monovalent and divalent ion binding to a DNA duplex. The experimental data for monovalent binding are consistent with a hypothesis that attributes these deviations to counterion size. To model the observed differences, we have generalized an existing size-modified Poisson-Boltzmann (SMPB) theory and developed a new numerical implementation that solves the generalized theory around complex, atomistic representations of biological molecules. The results of our analysis show that good agreement to data at monovalent ion concentrations up to 150 mM can be attained by adjusting the ion-size parameters in the new size-modified theory. SMPB calculations employing calibrated ion-size parameters predict experimental observations for other nucleic acid structures and salt conditions, demonstrating that the theory is predictive. We are, however, unable to model the observed deviations in the divalent competition data with a theory that only accounts for size but neglects ion-ion correlations, highlighting the need for theoretical descriptions that further incorporate ion-ion correlations. The accompanying numerical solver has been released publicly, providing the general scientific community the ability to compute SMPB solutions around a variety of different biological structures with only modest computational resources.