DNA-Dendrimer Nano-Cluster Electrostatics Prediction with the Nonlinear Poission - Boltzmann Equation

Abstract

A DNA-dendronized polymer nano-cluster (or inclusion aggregate) is generally formed by wrapping the DNA around a dendronized polymer which has a cylindrical shape. The electrostatic free energy in terms of different contributions of fixed and mobile charges and the entropic free energy of mixing of mobile species and solvent have been determined by solving the nonlinear Poisson-Boltzmann equation. The electrostatic potential generated around the nano-cluster, which plays a central role in biological systems, is determined by a finite-difference method. Thermodynamics of fixed ions, mobile ions, solvent and total system is considered for several conformations in different ionic strengths. It is shown that in a series of conformations at constant temperature and constant ionic strength, the electrostatic and entropic free energies primarily decrease sharply and then smoothly increase with increment of the wrapped DNA pitches. This indicates that the average concentrations of positive and negative mobile ions have been increased and decreased, respectively in these conformations.