Determining the Radial Modulus of DNA Measured by VPSFM

Mechanical properties of DNA, for example the elastic modulus, are of vital importance for its biological function. Previously, the modulus is mainly obtained by bending, stretching and twisting DNA using various techniques and tools. By applying vibrating mode scanning polarization force microscopy (VPSFM), deformations of DNA under ultra-small indentation forces can be measured and so the radial modulus can be computed. In this paper, modeling of the VPSFM measuring system is presented. The system is modeled as a spring-mass-damper oscillator under various force fields, such as van der Waals force, attractive electrical force and repulsive interactions between the tip and sample. The electrical polarization force is described by using uniformly charged line model and the DNA is considered to be a simple elastic rod. By numerically integrating the equation of tip motion, the contact force and the radial modulus of DNA under different deformation can be calculated. We found that in measuring radial modulus of DNA, the existence of substrate cannot be neglected, especially when the relative large deformation is reached.