The pH-dependent electrical potential and elastic modulus of a nanoscale DNA film and the resultant bending signal for a microcantilever biosensor

Abstract

This paper devotes to formulating several multiscale models to study the effect of pH-dependent ionic inhomogeneity on the electrical potential distributions and the graded elastic properties of a nanoscale DNA film and the related bending deflections of a microcantilever biosensor. First, the Langmuir isotherm was used to improve the classical Poisson-Boltzmann equation for polyelectrolyte solutions by introducing a new solution parameters to consider the effect of the inhomogeneous distribution of hydrogen ions on the electrical potential. Second, inspired by the Parsegian's mesoscopic attraction potential for cation condensed DNAs, the graded distribution properties of the particles were taken in the construction of an alternative interaction potential for both attraction-dominated and repulsion-dominated films. The new model parameters were obtained by curve fitting with the bending deflection experiments of a microcantilever done by Arroyo-Hernandez et al. Third, by the improved interaction potential and the thought experiment about the compression of a DNA bar in the context of macroscopic continuum mechanics, we investigated the diversity of elastic properties of single-stranded DNA (ssDNA) films due to the self-adaptability of its microstructures and constituents to the pH value, salt concentration and cation valence. Numerical results show that electronegative DNA could be overcharged with a positive electrical potential when the particle distribution conforms with the condition that the sign of the new introduced solution parameter is negative. There exists a transition from the pH-sensitive interval to pH-insensitive one for bending signals and elastic moduli. Negative elastic modulus is first revealed in the attraction-dominated ssDNA film constrained on the Au-layer of a microcantilever biosensor.