Electrostatic energy barriers from dielectric membranes upon approach of translocating DNA molecules

We probe the electrostatic cost associated with the approach phase of DNA translocation events. Within an analytical theory at the Debye-Hückel level, we calculate the electrostatic energy of a rigid DNA molecule interacting with a dielectric membrane. For carbon or silicon based low permittivity neutral membranes, the DNA molecule experiences a repulsive energy barrier between 10 k(B)T and 100 k(B)T. In the case of engineered membranes with high dielectric permittivities, the membrane surface attracts the DNA with an energy of the same magnitude. Both the repulsive and attractive interactions result from image-charge effects and their magnitude survive even for the thinnest graphene-based membranes of size d ≈ 6 Å. For weakly charged membranes, the electrostatic energy is always attractive at large separation distances but switches to repulsive close to the membrane surface. We also characterise the polymer length dependence of the interaction energy. For specific values of the membrane charge density, low permittivity membranes repel short polymers but attract long polymers. Our results can be used to control the strong electrostatic energy of DNA-membrane interactions prior to translocation events by chemical engineering of the relevant system parameters.