  How fast a post-translational nascent protein escapes from the ribosomal exit
tunnel is relevant to its folding and protection against aggregation. Here, by
using Langevin molecular dynamics, we show that non-local native interactions
help decreasing the escape time, and foldable proteins generally escape much
faster than same-length self-repulsive homopolymers at low temperatures. The
escape process, however, is slowed down by the local interactions that
stabilize the {\alpha}-helices. The escape time is found to increase with both
the tunnel length and the concentration of macromolecular crowders outside the
tunnel. We show that a simple diffusion model described by the Smoluchowski
equation with an effective linear potential can be used to map out the escape
time distribution for various tunnel lengths and various crowder
concentrations. The consistency between the simulation data and the diffusion
model however is found only for the tunnel length smaller than a cross-over
length of 90 {\AA} to 110 {\AA}, above which the escape time increases much
faster with the tunnel length. It is suggested that the length of ribosomal
exit tunnel has been selected by evolution to facilitate both the efficient
folding and efficient escape of single domain proteins. We show that
macromolecular crowders lead to an increase of the escape time, and attractive
crowders are unfavorable for the folding of nascent polypeptide.
