Prediction of the effective force on DNA in a nanopore based on density functional theory

We consider voltage-driving DNA translocation through a nanopore in the present study. By assuming the DNA is coaxial with the cylindrical nanopore, a hydrodynamic model for determining effective force on a single DNA molecule in a nanopore was presented, in which density functional theory (DFT) combined with the continuum Navier-Stokes (NS) equations is utilized to investigate electro-osmotic flow and the viscous drag force acting on the DNA inside a nanopore. Surface charge on the walls of the nanopore is also taken into account in our model. The consistence between our calculation and the previous experimental measurement indicates that the present theoretical model is an effective tool to predict the hydrodynamic resistance on DNA. Results show that charge inversion, which cannot be obtained by the Poisson-Boltzmann (PB) model, will reduce electro-osmotic velocity, or even lead to flow reversal for higher salt concentration. This is helpful to raise the effective force profoundly in the overscreening region. Translocation of electrically driven single-stranded DNA and RNA molecules through an α –hemolysin channel of inside diameter of 2 nm was first demonstrated by Kasianowicz et al [1]. Each translocation through a nanopore can be detected by measuring variation of the ionic current caused by DNA blockage. This would provide a DNA sequencing method which is faster and cheaper than any previous one by many orders of magnitude. However, currently the translocation speed of individual polymer molecular is too fast for instruments to “read” each base signal: a single base pair transits the pore in about ~10s under typical experimental conditions in solid-state nanopores. To better understand and overcome this difficulty, it is indispensable to predict the effective force applied on DNA inside and outside the nanopore. In the DNA translocation process, the drag forces opposing electrical driving force can be divided into three components [2,3]: (1) the entropic force of DNA uncoiling/recoiling at the pore entrance/exits; (2) the hydrodynamic drag on untranslocated blob-like part of the DNA molecule outside the pore; (3) the electro-osmotic force acting on the linear DNA inside nanopore. Muthukumar et al [4] considered the entropic force arising from the conformational change of DNA molecule as the main factor determining the DNA translocation velocity. Storm et al. [5] evaluated the hydrodynamic drag acting on the blob-like DNA configuration outside the nanopore based on experimental parameters. His result yields a drag force of about 24pN when DNA’s translocation velocity is 10mm/s for 16.5 μm of double-stranded DNA. The magnitudes of these * Email: [email protected], corresponding author.