Time and Length Scales of Incomplete Translocation through Nanopores

Polymer translocation is utilized by cells, for example in mitochondrial import and protein degradation, and used in sensing and sequencing nanotechnologies. A polymer entering a nanopore from one side can either complete its translocation emerging on the other side or fail by returning to the same side where it has started. Motivated by recent experimental advances that succeeded in differentiating between such failed and successful translocation events, here we focus on the former. Using a model which views translocation as one-dimensional diffusive dynamics in an effective potential and describes the polymer escape into the bulk using radiation boundary conditions at the pore's entrance and exit, we derive analytical expressions for the distribution of the "span" of the incomplete translocation events (describing how far the system advances through the pore before turning back) and the average temporal duration of such events, both unconditional and conditional on its span.