Effective charge and free energy of DNA inside an ion channel

Translocation of a single stranded DNA (ssDNA) through an α -hemolysin channel in a lipid membrane driven by applied transmembrane voltage V was extensively studied recently. While the bare charge of the ssDNA piece inside the channel is approximately 12 (in units of electron charge) measurements of different effective charges resulted in values between one and two. We explain these challenging observations by a large self-energy of a charge in the narrow water filled gap between ssDNA and channel walls, related to large difference between dielectric constants of water and lipid, and calculate effective charges of ssDNA. We start from the most fundamental stall charge qs, which determines the force Fs = qs VL stalling DNA against the voltage V (L is the length of the channel). We show that the stall charge qs is proportional to the ion current blocked by DNA, which is small due to the self-energy barrier. Large voltage V reduces the capture barrier which DNA molecule should overcome in order to enter the channel by qc V, where qc is the effective capture charge. We expressed it through the stall charge qs. We also relate the stall charge qs to two other effective charges measured for ssDNA with a hairpin in the back end: the charge qu responsible for reduction of the barrier for unzipping of the hairpin and the charge qe responsible for DNA escape in the direction of hairpin against the voltage. At small V we explain reduction of the capture barrier with the salt concentration.