Inhomogeneous Totally Asymmetric Simple Exclusion Processes: Simulations, Theory and Application to Protein Synthesis

In the process of translation, ribosomes, a type of macromolecules, read the genetic code on a messenger RNA template (mRNA) and assemble amino acids into a polypeptide chain which folds into a functioning protein product. The ribosomes perform discrete directed motion that is well modeled by a totally asymmetric simple exclusion process (TASEP) with open boundaries. We incorporate the essential components of the translation process: Ribosomes, cognate tRNA concentrations, and mRNA templates correspond to particles (covering ell > 1 sites), hopping rates, and the underlying lattice, respectively.

As the hopping rates in an mRNA are given by its sequence (in the unit of codons), we are especially interested in the effects of a finite number of slow codons to the overall stationary current. To study this matter systematically, we first explore the effects of local inhomogeneities, i.e., one or two slow sites of hopping rate q<1 in TASEP for particles of size ell > 1(in the unit of lattice site) using Monte Carlo simulation. We compare the results of ell =1 and ell >1 and notice that the existence of local defects has qualitatively similar effects to the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the location of the slow site for both ell =1 and ell >1 cases. In particular, we notice a novel "edge" effect, i.e., the interaction of a single slow codon with the system boundary. When two slow sites are introduced, more intriguing phenomena such as dramatic decreases in the current when the two are close together emerge. We analyze the simulation results using several different levels of mean-field theory. A finite-segment mean-field approximation is especially successful in understanding the "edge effect."

If we consider the systems with finite defects as "contrived mRNA's", the real mRNA's are of more biological significance. Inspired by the previous results, we study several mRNA sequences from Escherichia coli. We argue that an effective translation rate including the context of each codon needs to be taken into consideration when seeking an efficient strategy to optimize the protein production.