Nanomechanical behaviors of microcantilever-based single-stranded DNA chips induced by counterion osmotic effects

Experiments show that deflections of microcantilever-DNA chip can be induced by many factors, such as grafting density, hybridization efficiency, concentration, length and sequence of DNA molecules, buffer salt concentration, time, and temperature variation. However, there are few theoretical works on microcantilever-DNA chips. The present paper is aimed to study the influence of counterion effects of single-stranded DNA (ssDNA) polyelectrolyte solution on the nanomechanical behaviors of microcantilever-based ssDNA chips during packing process. First, the effect of osmotic pressure induced by ingress of counterions into DNA brush structures is studied with Hagan's model for a cylindrical polyelectrolyte brush system on the basis of Poisson-Boltzmann distribution hypothesis. Second, Zhang's two-variable method for a laminated cantilever is used to formulate a four-layer energy model for ssDNA chips with weak interactions. Third, the influence of grafting density, ssDNA chain length, and salt concentration on packing deflection is investigated using the principle of minimum energy. The predictive tendency is qualitatively similar to those observed in some related ssDNA chip experiments. The difference between the four-layer model and the simplified two-layer model for ssDNA chips is also discussed.