Translocation of Gaussian polymers across a nanometric cylindrical channel

We present an analytical model to study translocation of Gaussian polymers across a cylindrical channel of nanometric size with a chemical potential inside the channel. Results show that polymer conformational entropy generates an entropic M-like free energy barrier for translocation. The presence of a small negative chemical potential reduces the entropic free energy barrier rendering the translocation time to follow a power law τ = A Nν as function of polymer size N. Power law exponents ν found here in varying the channel radius R, run from 1.525 to 1.999 for unforced translocation, and from 1.594 to 2.006 for translocation with small chemical potentials when R=1. Presence of large negative chemical potentials generate a free energy well rendering the translocation time to follow an exponential growth τ = A eα N. We show existence of a negative chemical potential μc that minimizes the translocation time due to an interplay of conformational entropy and channel-polymer interactions. The translocation time as function of channel length L grows exponentially as τ = A ecL, it runs from milliseconds up to decades in the range of lengths found in biological channels. Interestingly, small negative chemical potentials approaching μc overcome the effect of large channel lengths reducing the translocation time below seconds. Translocation speeds $<v(N)>$ show a maximum of micrometers per second then it decays with polymer size and channel length, the characteristic decay <v(N)>~ N⁻¹ has been observed in previous experiments of voltage-driven DNA translocation.