  The transport of polymers with folded configurations across membrane pores is
investigated theoretically by analyzing simple discrete stochastic models. The
translocation dynamics is viewed as a sequence of two events: motion of the
folded segment through the channel followed by the linear part of the polymer.
The transition rates vary for the folded and linear segments because of
different interactions between the polymer molecule and the pore. It is shown
that the translocation time depends non-monotonously on the length of the
folded segment for short polymers and weak external fields, while it becomes
monotonous for long molecules and large fields. Also, there is a critical
interaction between the polymers and the pore that separates two dynamic
regimes. For stronger interactions the folded polymer moves slower, while for
weaker interactions the linear chain translocation is the fastest. In addition,
our calculations show that the folding does not change the translocation
scaling properties of the polymer. These phenomena can be explained by the
interplay between the translocation distances and transition rates for the
folded and linear segments of the polymer. Theoretical results are applied for
analysis of experimental translocations through solid-state nanopores.
