Paper Title
Mathematical Modeling of Microcantielver Interaction with DNA Molecules

Abstract
Here we mathematically modeled the interaction of DNA and microcantilever in which we propose a more accurate model for modeling the adsorption of biomolecules on the microcantilever surface. To do so, we modeled the elastic energy of microcantilever and also the intermolecular bonding energy of DNA molecules with the assumption that they are adsorbed on the surface of the microcantilever. For modeling, the microcantilever elastic energy a new deformation beam theory including of two unknown functions with taking into account shear deformations is proposed for the static and dynamic analysis of microcantilever. Based on this deformation beam theory and using the modified couple stress analysis, the governing equations and the related boundary conditions are derived using the principle of the minimum total potential energy. The energy of the system is consist of the energy of intermolecular interaction and also the elastic potential of microcantilever that altogether makes the Hamiltonian of the system. Then by taking the variation of this system the equation of motion for cantilever is derived. Having the equation of motion will enable us for studying the response of the microsensor for various amount of DNA adsorption on the surface of the microcantilever. In the cantilever model, we also took into account the effects of shear stress on the overall deformation of microcantilever for more accurate measuring. We only studied the static deformation in this report. This study shows how we can model the mechanical biosensor when we can describe the intermolecular interaction mathematically. Keywords- Microcantilever, biosensors, nanomechanics, DNA, multiscale modeling, couple-stress theory, surface stress