  We explore and quantify the physical and biochemical mechanisms that may be
relevant in the regulation of translation. After elongation and detachment from
the 3' termination site of mRNA, parts of the ribosome machinery can diffuse
back to the initiation site, especially if it is held nearby, enhancing overall
translation rates. The elongation steps of the mRNA-bound ribosomes are modeled
using exact and asymptotic results of the totally asymmetric exclusion process
(TASEP).Since the ribosome injection rates of the TASEP depend on the local
concentrations at the initiation site, a source of ribosomes emanating from the
termination end can feed back to the initiation site, leading to a
self-consistent set of equations for the steady-state ribosome throughput.
Additional mRNA binding factors can also promote loop formation, or
cyclization, bringing the initiation and termination sites into close
proximity. The probability distribution of the distance between the initiation
and termination sites is described using simple noninteracting polymer models.
We find that the initiation, or initial ribosome adsorption binding required
for maximal throughput can vary dramatically depending on certain values of the
bulk ribosome concentration and diffusion constant. If cooperative interactions
among the loop-promoting proteins and the initiation/termination sites are
considered, the throughput can be further regulated in a nonmonotonic manner.
Potential experiments to test the hypothesized physical mechanisms are
discussed.
