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# Dynamical Response of Nanomechanical Resonators to Biomolecular Interactions

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We made a simple model for understanding the dynamic behavior of nanomechanical resonator in response to biomolecular interactions. Specifically, in our model, we considered the nanomechanical resonator, on whose surface the biomolecules (dsDNA) are adsorbed, such that Hamiltonian of the system consists of elastic bending energy of nanomechanical resonator and potential energy for biomolecular interaction (i.e. DNA-DNA interaction). It was shown that DNA-DNA interaction plays a role on the resonant frequency shift for nano-scale resonators. This work was accepted for publications at Physical Review B.

**Dynamical Response of Nanomechanical Resonators to Biomolecular Interactions**

**ABSTRACT**We studied the dynamical response of a nanomechanical resonator to biomolecular (e.g. DNA) adsorptions on a resonator’s surface by using theoretical model, which considers the Hamiltonian

*H*such that the potential energy consists of elastic bending energy of a resonator and the potential energy for biomolecular interactions. It was shown that the resonant frequency shift for a resonator due to biomolecular adsorption depends on not only the mass of adsorbed biomolecules but also the biomolecular interactions. Specifically, for dsDNA adsorption on a resonator’s surface, the resonant frequency shift is also dependent on the ionic strength of a solvent, implying the role of biomolecular interactions on the dynamic behavior of a resonator. This indicates that nanomechanical resonators may enable one to quantify the biomolecular mass, implying the enumeration of biomolecules, as well as gain insight into intermolecular interactions between adsorbed biomolecules on the surface.

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## Revised manuscript

I made a revision to the manuscript posted at http://www.imechanica.org/node/1620 for resubmission to journal based on a reviewer's comments. The revised manuscript is now available at http://arxiv.org/abs/0706.3743v2.

Abstract

We studied the dynamical response of a nanomechanical resonator to biomolecular (e.g. DNA) adsorptions on a resonator's surface by using a theoretical model, which considers the Hamiltonian H such that the potential energy consists of elastic bending energy of a resonator and the potential energy for biomolecular interactions. It was shown that the resonant frequency shift of a resonator due to biomolecular adsorption depends on not only the mass of adsorbed biomolecules but also the biomolecular interactions. Specifically, for dsDNA adsorption on a resonator's surface, the resonant frequency shift is also dependent on the ionic strength of a solvent, implying the role of molecular interactions on the dynamic behavior of a resonator. This indicates that nanomechanical resonators may enable one to quantify the biomolecular mass, implying the enumeration of biomolecules, as well as gain insight into intermolecular interactions between adsorbed biomolecules on the surface.