Calculations of the resonant response of carbon nanotubes to binding of DNA

We theoretically study the dynamical response of carbon nanotubes (CNTs) to the binding of DNA in an aqueous environment by considering two major interactions in DNA helical binding to the CNT side surface: adhesion between DNA nucleobases and CNT surfaces and electrostatic interactions between negative charges on DNA backbones. The equilibrium DNA helical wrapping angle is obtained using the minimum potential energy method. Our results show that the preferred DNA wrapping angle in the equilibrium binding to CNT is dependent on both DNA length and DNA base. The equilibrium wrapping angle for a poly(dT) chain is larger than a comparable poly(dA) chain as a result of dT in a homopolymer chain having a higher effective binding energy to CNT than dA. Our results also interestingly reveal a sharp transition in the wrapping angle-DNA length profile for both homopolymers, implying that the equilibrium helical wrapping configuration does not exist for a certain range of wrapping angles. Furthermore, the resonant response of the DNA-CNT complex is analysed based on the variational method with a Hamiltonian which takes into account the CNT bending energy as well as DNA-CNT interactions. The closed-form analytical solution for predicting the resonant frequency of the DNA-CNT complex is presented. Our results show that the hydrodynamic loading on the oscillating CNT in aqueous environments has profound impacts on the resonance behaviour of DNA-CNT complexes. Our results suggest that detection of DNA molecules using CNT resonators based on DNA-CNT interactions through frequency measurements should be conducted in media with low hydrodynamic loading on CNTs. Our theoretical framework provides a fundamental principle for label-free detection using CNT resonators based on DNA-CNT interactions.