  Force-driven translocation of a macromolecule through a nanopore is
investigated by taking into account the monomer-pore friction as well as the
"crowding" of monomers on the {\it trans} - side of the membrane which
counterbalance the driving force acting in the pore. The set of governing
differential-algebraic equations for the translocation dynamics is derived and
solved numerically. The analysis of this solution shows that the crowding of
monomers on the trans side hardly affects the dynamics, but the monomer-pore
friction can substantially slow down the translocation process. Moreover, the
translocation exponent $\alpha$ in the translocation time - vs. - chain length
scaling law, $\tau \propto N^{\alpha}$, becomes smaller when monomer-pore
friction coefficient increases. This is most noticeable for relatively strong
forces. Our findings may explain the variety of $\alpha$ values which were
found in experiments and computer simulations.
