Power series solution of the inhomogeneous exclusion process

Molecular motor traffic with a slow binding site

We discuss how the presence of a slow binding site in molecular motor traffic gives rise to defect-induced "traffic jams" that have properties different from those of the well-studied boundary-induced jams that originate from an imbalance between initiation and termination. To this end we analyze in detail the stationary distribution of a lattice gas model for traffic of molecular motors with a defect. In particular, we obtain analytically the exact spatial distribution of motors, the probability distribution of the random position of the molecular traffic jam and we report unexpected spatial anticorrelations between local molecular motor densities near the defect.

EGGTART: A tool to visualize the dynamics of biophysical transport under the inhomogeneous l-TASEP

The totally asymmetric simple exclusion process (TASEP), which describes the stochastic dynamics of interacting particles on a lattice, has been actively studied over the past several decades and applied to model important biological transport processes. Here, we present a software package, called EGGTART (Extensive GUI gives TASEP-realization in Real Time), which quantifies and visualizes the dynamics associated with a generalized version of the TASEP with an extended particle size and heterogeneous jump rates. This computational tool is based on analytic formulas obtained from deriving and solving the hydrodynamic limit of the process. It allows an immediate quantification of the particle density, flux, and phase diagram, as a function of a few key parameters associated with the system, which would be difficult to achieve via conventional stochastic simulations. Our software should therefore be of interest to biophysicists studying general transport processes and can in particular be used in the context of gene expression to model and quantify mRNA translation of different coding sequences.

What determines eukaryotic translation elongation: recent molecular and quantitative analyses of protein synthesis

Protein synthesis from mRNA is an energy-intensive and tightly controlled cellular process. Translation elongation is a well-coordinated, multifactorial step in translation that undergoes dynamic regulation owing to cellular state and environmental determinants. Recent studies involving genome-wide approaches have uncovered some crucial aspects of translation elongation including the mRNA itself and the nascent polypeptide chain. Additionally, these studies have fuelled quantitative and mathematical modelling of translation elongation. In this review, we provide a comprehensive overview of the key determinants of translation elongation. We discuss consequences of ribosome stalling or collision, and how the cells regulate translation in case of such events. Next, we review theoretical approaches and widely used mathematical models that have become an essential ingredient to interpret complex molecular datasets and study translation dynamics quantitatively. Finally, we review recent advances in live-cell reporter and related analysis techniques, to monitor the translation dynamics of single cells and single-mRNA molecules in real time.

Inferring efficiency of translation initiation and elongation from ribosome profiling

One of the main goals of ribosome profiling is to quantify the rate of protein synthesis at the level of translation. Here, we develop a method for inferring translation elongation kinetics from ribosome profiling data using recent advances in mathematical modelling of mRNA translation. Our method distinguishes between the elongation rate intrinsic to the ribosome’s stepping cycle and the actual elongation rate that takes into account ribosome interference. This distinction allows us to quantify the extent of ribosomal collisions along the transcript and identify individual codons where ribosomal collisions are likely. When examining ribosome profiling in yeast, we observe that translation initiation and elongation are close to their optima and traffic is minimized at the beginning of the transcript to favour ribosome recruitment. However, we find many individual sites of congestion along the mRNAs where the probability of ribosome interference can reach \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$50\%$\end{document}. Our work provides new measures of translation initiation and elongation efficiencies, emphasizing the importance of rating these two stages of translation separately.

Current-density relation in the exclusion process with dynamic obstacles

We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of obstacles that dynamically bind and unbind from the lattice. The model is motivated by biological processes such as transcription in the presence of DNA-binding proteins. Similar models have been studied before using the mean-field approximation, but the exact relation between the particle current and density remains elusive. Here, we first show using extensive Monte Carlo simulations that the current-density relation in this model assumes a quasiparabolic form similar to that of the ordinary TASEP without obstacles. We then attempt to explain this relation using exact calculations in the limit of low and high density of particles. Our results suggest that the symmetric, quasiparabolic current-density relation arises through a nontrivial cancellation of higher-order terms, similarly as in the standard TASEP.

Dynamics of ribosomes in mRNA translation under steady- and nonsteady-state conditions

Recent advances in DNA sequencing and fluorescence imaging have made it possible to monitor the dynamics of ribosomes actively engaged in messenger RNA (mRNA) translation. Here, we model these experiments within the inhomogeneous totally asymmetric simple exclusion process (TASEP) using realistic kinetic parameters. In particular, we present analytic expressions to describe the following three cases: (a) translation of a newly transcribed mRNA, (b) translation in the steady state and, specifically, the dynamics of individual (tagged) ribosomes, and (c) runoff translation after inhibition of translation initiation. In cases (b) and (c) we develop an effective medium approximation to describe many-ribosome dynamics in terms of a single tagged ribosome in an effective medium. The predictions are in good agreement with stochastic simulations.

Power series method for solving TASEP-based models of mRNA translation

We develop a method for solving mathematical models of messenger RNA (mRNA) translation based on the totally asymmetric simple exclusion process (TASEP). Our main goal is to demonstrate that the method is versatile and applicable to realistic models of translation. To this end we consider the TASEP with codon-dependent elongation rates, premature termination due to ribosome drop-off and translation reinitiation due to circularisation of the mRNA. We apply the method to the model organism Saccharomyces cerevisiae under physiological conditions and find an excellent agreement with the results of stochastic simulations. Our findings suggest that the common view on translation as being rate-limited by initiation is oversimplistic. Instead we find theoretical evidence for ribosome interference and also theoretical support for the ramp hypothesis which argues that codons at the beginning of genes have slower elongation rates in order to reduce ribosome density and jamming.

Driven transport on a flexible polymer with particle recycling: A model inspired by transcription and translation

Many theoretical works have attempted to coarse grain gene expression at the level of transcription and translation via frameworks based on exclusion processes. Usually in these models the three-dimensional conformation of the substrates (DNA and mRNA) is neglected, and particles move on a static unidimensional lattice in contact to an infinite reservoir. In this work we generalize the paradigmatic exclusion process and study the transport of particles along a unidimensional polymerlike flexible lattice immersed in a three-dimensional particle reservoir. We study the recycling of particles in the reservoir, how the transport is influenced by the global conformation of the lattice, and, in turn, how particle density dictates the structure of the polymer.