scholarly journals Theoretical analysis of the distribution of isolated particles in the TASEP: Application to mRNA translation rate estimation

2017 ◽  
Author(s):  
Khanh Dao Duc ◽  
Zain H. Saleem ◽  
Yun S. Song
Keyword(s):  
Theoretical Analysis ◽  
Nearest Neighbor ◽  
Average Distance ◽  
Mean Field ◽  
Exclusion Process ◽  
Mrna Translation ◽  
Ribosome Profiling ◽  
Asymmetric Exclusion Process ◽  
Initiation Rate ◽  
Translation Rate

AbstractThe Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the mRNA during translation. Although this model has been widely studied in the past, the extent of collision between particles and the average distance between a particle to its nearest neighbor have not been quantified explicitly. We provide here a theoretical analysis of such quantities via the distribution of isolated particles. In the classical form of the model in which each particle occupies only a single site, we obtain an exact analytic solution using the Matrix Ansatz. We then employ a refined mean field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from S. cerevisiae suggests a potential bias against the detection of nearby ribosomes with gap distance less than ~ 3 codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate associated with collisions can be robustly estimated, and show that approximately 1% of the translating ribosomes get obstructed.

scholarly journals Random Walks Reaching Against all Odds the other Side of the Quarter Plane

2013 ◽  
Vol 50 (1) ◽  
pp. 85-102 ◽  
Author(s):  
Johan S. H. van Leeuwaarden ◽  
Kilian Raschel
Keyword(s):  
Random Walk ◽  
Integral Representation ◽  
Nearest Neighbor ◽  
Asymptotic Expression ◽  
Exclusion Process ◽  
Vertical Axis ◽  
The Other ◽  
Asymmetric Exclusion Process ◽  
Quarter Plane ◽  
Asymptotic Evaluation

For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state (i0,j0), we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive a certain integral representation for the probability of this event, and an asymptotic expression for the case when i0 becomes large, a situation in which the event becomes highly unlikely. The integral representation follows from the solution of a boundary value problem and involves a conformal gluing function. The asymptotic expression follows from the asymptotic evaluation of this integral. Our results find applications in a model for nucleosome shifting, the voter model, and the asymmetric exclusion process.

ASYMMETRIC EXCLUSION PROCESS WITH CONSTRAINED HOPPING AND PARALLEL DYNAMICS AT A JUNCTION

2011 ◽  
Vol 25 (25) ◽  
pp. 2011-2020 ◽  
Author(s):  
MINGZHE LIU ◽  
XIANGUO TUO ◽  
ZHE LI ◽  
JIANBO YANG
Keyword(s):  
Stationary Phases ◽  
Mean Field ◽  
Exclusion Process ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Asymmetric Exclusion Process ◽  
Traffic Light ◽  
Congested Traffic ◽  
Parallel Dynamics ◽  
The Right

In this article totally asymmetric simple exclusion process (TASEP) with constrained hopping and parallel dynamics at a junction is investigated using a mean-field approximation and Monte Carlo simulations. The constrained particle hopping probability r (r ≤ 1) at a junction may correspond to a delay caused by a driver choosing the right direction or a delay waiting for green traffic light in the real world. There are six stationary phases in the system, which can reflect free flow and congested traffic situations. Correlations at the junction point are investigated via simulations. It is observed that small r leads to stronger correlations. The theoretical results are agreement with computer simulations well.

Theoretical analysis and simulation for a facilitated asymmetric exclusion process

2016 ◽  
Vol 94 (2) ◽  
Author(s):  
Qing-Yi Hao ◽  
Zhe Chen ◽  
Xiao-Yan Sun ◽  
Bing-Bing Liu ◽  
Chao-Yun Wu
Keyword(s):  
Theoretical Analysis ◽  
Exclusion Process ◽  
Asymmetric Exclusion Process ◽  
Asymmetric Exclusion

TWO-SPECIES ASYMMETRIC EXCLUSION PROCESS WITH SITE SHARING

2010 ◽  
Vol 24 (08) ◽  
pp. 707-716 ◽  
Author(s):  
MINGZHE LIU ◽  
SONG XIAO ◽  
RUILI WANG
Keyword(s):  
Current Density ◽  
Mean Field ◽  
Exclusion Process ◽  
Asymmetric Exclusion Process ◽  
Field Calculation ◽  
Simple Exclusion Process ◽  
Asymmetric Case ◽  
Density Relationship ◽  
Asymmetric Simple Exclusion ◽  
A Site

This letter investigates the two-species asymmetric simple exclusion process (ASEP) with site sharing on a ring. The contribution of this study as compared to previous two-species ASEP models is that the oppositely moving particles do not pass each other by an exchanging mechanism but by sharing a site (characterized by sharing probability q). The model is investigated under random update and with periodic boundary conditions using Monte Carlo simulations and a cluster-based mean-field calculation. In the symmetric case (densities of two-species particles are equal), the simulation results show that there is a plateau in the current–density relationship for intermediate particle densities. The plateau corresponds to the maximal current and the plateau region shrinks with the increase of q. In the asymmetric case, the plateau is not observed. For comparison we examine the site-exchanging model which means that two-species particles can exchange their positions with a certain probability. The site-exchanging model does not exhibit such a plateau in the current–density relationship.

The Heisenberg Chain as a Dynamical Model for Protein Synthesis - Some Theoretical and Experimental Results

1997 ◽  
Vol 11 (01n02) ◽  
pp. 197-202 ◽  
Author(s):  
Gunter M. Schütz
Keyword(s):  
Exact Solution ◽  
Protein Synthesis ◽  
Lattice Gas ◽  
Mean Field ◽  
Exclusion Process ◽  
Open Boundary ◽  
Asymmetric Exclusion Process ◽  
Open Boundary Conditions ◽  
Heisenberg Chain ◽  
Boundary Fields

The integrable Heisenberg quantum chain with certain non-diagonal boundary fields is the generator of a Markov process known as asymmetric exclusion process with open boundary conditions. This is a driven lattice gas where particles hop randomly along a one-dimensional chain and are injected and absorbed at the boundaries. This model has been suggested in 1968 by MacDonald, Gibbs and Pipkin as a model for the kinetics of protein synthesis on nucleic acid templates. The exact solution of the steady state of the system (corresponding to the exact ground state of the Heisenberg chain) which was obtained recently is shown to be in qualitative agreement with experimental data. The exact solution supports some of the original conclusions drawn from a mean field treatment by MacDonald et al. but gives deeper insight into one important aspect.

scholarly journals Random Walks Reaching Against all Odds the other Side of the Quarter Plane

2013 ◽  
Vol 50 (01) ◽  
pp. 85-102 ◽  
Author(s):  
Johan S. H. van Leeuwaarden ◽  
Kilian Raschel
Keyword(s):  
Random Walk ◽  
Integral Representation ◽  
Nearest Neighbor ◽  
Asymptotic Expression ◽  
Exclusion Process ◽  
Vertical Axis ◽  
The Other ◽  
Asymmetric Exclusion Process ◽  
Quarter Plane ◽  
Asymptotic Evaluation

For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state (i0,j0), we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive a certain integral representation for the probability of this event, and an asymptotic expression for the case wheni0becomes large, a situation in which the event becomes highly unlikely. The integral representation follows from the solution of a boundary value problem and involves a conformal gluing function. The asymptotic expression follows from the asymptotic evaluation of this integral. Our results find applications in a model for nucleosome shifting, the voter model, and the asymmetric exclusion process.

scholarly journals The key parameters that govern translation efficiency

2018 ◽  
Author(s):  
Dan D. Erdmann-Pham ◽  
Khanh Dao Duc ◽  
Yun S. Song
Keyword(s):  
Particle System ◽  
Mean Field ◽  
Exclusion Process ◽  
Design Principles ◽  
Complete Characterization ◽  
Ribosome Profiling ◽  
Translation System ◽  
Translation Efficiency ◽  
Complex Biological Process ◽  
Asymmetric Simple Exclusion

AbstractTranslation of mRNA into protein is a fundamental yet complex biological process with multiple factors that can potentially affect its efficiency. In particular, different genes can have quite different initiation rates, while site-specific elongation rates can vary substantially along a given transcript. Here, we analyze a stochastic model of translation dynamics to identify the key parameters that govern the overall rate of protein synthesis and the efficiency of ribosome usage. The mathematical model we study is an interacting particle system that generalizes the Totally Asymmetric Simple Exclusion Process (TASEP), where particles correspond to ribosomes. While the TASEP and its variants have been studied for the past several decades through simulations and mean field approximations, a general analytic solution has remained challenging to obtain. By analyzing the so-called hydrodynamic limit, we here obtain exact closed-form expressions for stationary currents and particle densities that agree well with Monte Carlo simulations. In addition, we provide a complete characterization of phase transitions in the system. Surprisingly, phase boundaries depend on only four parameters: the particle size, and the first, last and minimum particle jump rates. Relating these theoretical results to translation, we formulate four design principles that detail how to tune these parameters to optimize translation efficiency in terms of protein production rate and resource usage. We then analyze ribosome profiling data of S. cerevisiae and demonstrate that its translation system is generally efficient, consistent with the design principles we found. We discuss implications of our findings on evolutionary constraints and codon usage bias.

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