Theory of DNA translocation through narrow ion channels and nanopores with charged walls

Translocation of a single stranded DNA through genetically engineered $\alpha$-hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from neutral wild type $\alpha$-hemolysin channel. We assume that the wall charges compensate the fraction $x$ of the bare charge $q_b$ of the DNA piece residing in the channel. Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with $x$. (ii) The effective charge $q$ of DNA piece, which is very small at $x=0$ (neutral channel) grows with $x$ and at $x=1$ reaches $q_b$. (iii) The rate of DNA capture by the channel exponentially grows with $x$. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.