  Chaperone-assisted biopolymer translocation is the main model proposed for
translocation \textit{in vivo}. A dynamical Monte Carlo method is used to
simulate the translocation of a stiff homopolymer through a nanopore driven by
chaperones. Chaperones are proteins that bind to the polymer near the wall and
prevent its backsliding through Cis side. The important parameters include
binding energy, size and the local concentration of the chaperones. The profile
of these local concentrations, build up the chaperones distribution. Here we
investigate the effects of binding energy, size and the exponential
distribution of chaperones in their equilibration in each step of the polymer
translocation needed for stable translocation time. The simulation results show
that in case of chaperones with the size of a monomer ($\lambda=1$) and/or
positive effective binding energy and/or uniform distribution, the chaperones
binding equilibration rate/frequency is less than $5$ times per monomer.
However, in some special cases in the exponential distribution of chaperones
with size $\lambda>1$ and negative effective binding energy the equilibration
rate will diverge to more than $20$ times per monomer. We show that this
non-equilibrium effect results in supper diffusion, seen before. Moreover, we
confirm the equilibration process theoretically.
