Totally asymmetric exclusion process with extended objects: a model for protein synthesis

Hard rod gas with long-range interactions: Exact predictions for hydrodynamic properties of continuum systems from discrete models

One-dimensional hard rod gases are explicitly constructed as the limits of discrete systems: exclusion processes involving particles of arbitrary length. Those continuum many-body systems in general do not exhibit the same hydrodynamic properties as the underlying discrete models. Considering as examples a hard rod gas with additional long-range interaction and the generalized asymmetric exclusion process for extended particles, it is shown how a correspondence between continuous and discrete systems must be established instead. This opens up a possibility to exactly predict the hydrodynamic behavior of this continuum system under Eulerian scaling by solving its discrete counterpart with analytical or numerical tools. As an illustration, simulations of the totally asymmetric exclusion process are compared to analytical solutions of the model and applied to the corresponding hard rod gas. The case of short-range interaction is treated separately.

Steady-state properties of a totally asymmetric exclusion process with periodic structure

We study the steady-state behavior of totally asymmetric simple exclusion processes (TASEPs) that contain periodically varying movement rates. In this model, particles move to the right at one of two rates: p(2) if the particle occupies one of a periodically arranged set of lattice sites; p(1) otherwise. Approximate mean field approaches are used to study the steady-state currents and bulk densities of this model. These mean field methods are found to provide results in good agreement with data derived from Monte Carlo simulations. Finally, the condition for particle-hole symmetry in the TASEP with periodically varying movement rates is specified, and the changes in the locations of the boundary-limited to maximal-current transition lines due to symmetry violation are investigated.

Clustered bottlenecks in mRNA translation and protein synthesis

Using a model based on the totally asymmetric exclusion process, we investigate the effects of slow codons along messenger RNA. Ribosome density profiles near neighboring clusters of slow codons interact, enhancing suppression of ribosome throughput when such bottlenecks are closely spaced. Increasing the slow codon cluster size beyond approximately 3-4 codons does not significantly reduce the ribosome current. Our results are verified by both extensive Monte Carlo simulations and numerical calculation, and provide a biologically motivated explanation for the experimentally observed clustering of low-usage codons.

Totally asymmetric simple exclusion process with Langmuir kinetics

We discuss a class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting nonconserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high and low density phases, two and three phase coexistence regions, and a boundary independent "Meissner" phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert W functions. It allows one to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.

Mean-field approaches to the totally asymmetric exclusion process with quenched disorder and large particles

The process of protein synthesis in biological systems resembles a one-dimensional driven lattice gas in which the particles (ribosomes) have spatial extent, covering more than one lattice site. Realistic, nonuniform gene sequences lead to quenched disorder in the particle hopping rates. We study the totally asymmetric exclusion process with large particles and quenched disorder via several mean-field approaches and compare the mean-field results with Monte Carlo simulations. Mean-field equations obtained from the literature are found to be reasonably effective in describing this system. A numerical technique is developed for computing the particle current rapidly. The mean-field approach is extended to include two-point correlations between adjacent sites. The two-point results are found to match Monte Carlo simulations more closely.

Engineering HlyA hypersecretion inEscherichia coli based on proteomic and microarray analyses

Escherichia coli is a common host for recombinant protein production for biotechnology applications. Secretion to the extracellular media has the potential to reduce protein aggregation and to simplify downstream purification. However, the complexity of the mechanisms of protein secretion has confounded prior attempts to engineer enhanced secretion phenotypes. Here, mutagenesis was used to perturb E. coli W3110 cells secreting HlyA via a Type I pathway. An activity assay identified a mutant secreting fourfold more active alpha-hemolysin than the parent strain. The mutant was characterized using both high-density microarrays for mRNA profiling and a proteomics strategy for protein expression. The relative mRNA and protein expression levels of tRNA-synthetases were decreased in the mutant compared to the parent. A mathematical model of prokaryotic translation was used to design a variant of the hlyA gene that encodes the same amino acid sequence but uses rare codons to slow the rate of translation by altering five bases. Analysis of the parent strain transformed with a plasmid containing this variant gene resulted in the recovery of, and further improvement upon, the selected hypersecretion phenotype. These results present one of the first successful metabolic engineering attempts based on molecular information provided by mRNA and protein expression profiling approaches and resulting in a phenotype useful to the biotechnology community.