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Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments
R. K. P. Zia, J. J. Dong, B. Schmittmann
TL;DR
The paper asks how protein production can be modeled with TASEP while retaining useful biological structure and tractable mathematics. It presents a tutorial and examines finite cellular resources, extended particles, and inhomogeneous hopping rates. The reported developments include a reliable linear relation between simulated currents and the minimum effective hopping rate across silent mutations, while the analysis remains a simplified and approximate treatment of complex systems.
Problem
The paper addresses how protein production rates relate to sequence information while biological translation involves complex processes and cellular resource constraints.
Method
The paper combines a biological and mathematical tutorial with generalized TASEP models for translation, including extended particles, finite particle reservoirs, and inhomogeneous hopping rates.
Results
A reliable linear relation was found between currents and K12,min across 5000 randomly selected silent mutations in 10 proteins, with a proportionality constant appearing common across the proteins studied.
Takeaways & Limitations
TASEP provides a framework for summarizing translation dynamics while incorporating limited ribosome supplies and sequence-dependent hopping rates.
Takeaways & Limitations
The treatment is not comprehensive, and estimating inhomogeneous currents remains uncertain because aggregate rate statistics do not encode the locations of slow sites.
Abstract
from arXiv · showhide
The phenomenon of protein synthesis has been modeled in terms of totally asymmetric simple exclusion processes (TASEP) since 1968. In this article, we provide a tutorial of the biological and mathematical aspects of this approach. We also summarize several new results, concerned with limited resources in the cell and simple estimates for the current (protein production rate) of a TASEP with inhomogeneous hopping rates, reflecting the characteristics of real genes.
1 Introduction
The paper uses TASEP as a simple model for connecting protein synthesis with nonequilibrium statistical physics. It combines a tutorial on biology and TASEP with recent developments involving resource limits and model generalizations.
- Nonequilibrium statistical physics studies open many-particle systems sustaining nontrivial currents and applies naturally to biological transport.
- The paper contrasts detailed biological models, which enable quantitative comparison with experiments, with simple models that make generic characteristics easier to identify.
- Protein synthesis is modeled using the totally asymmetric exclusion process, linking a complex biological process to a simple statistical-physics model.
- The article provides a tutorial on protein synthesis and translation, alongside a review of the simplest TASEP and translation-relevant generalizations.
- Recent developments include competition between multiple TASEPs and a quenched distribution of distributions motivated by silent mutations.
2 Rudiments of protein synthesis
Protein synthesis transfers DNA sequence information through transcription and translation, with ribosomes moving along mRNA and selecting amino acids via tRNAs. Translation rates depend on sequence-related factors including unequal aa-tRNA availability, while the paper deliberately focuses on simplified models.
- Protein synthesis has two stages: transcription from DNA to mRNA and translation from mRNA to proteins through ribosome translocation.
- In bacterial translation, mRNA provides the template, ribosomes provide the assembly machinery, and charged aa-tRNAs provide amino acids.
- The mRNA encodes information in 64 codons, including three stop codons and 61 codons specifying 20 amino acids.
- Ribosomes contain A, P, and E sites for aa-tRNA docking, peptide transfer, and tRNA release, respectively.
- Translation proceeds through initiation, elongation, and termination as ribosomes move along mRNA without backtracking.
- Aa-tRNA concentrations in E. coli can differ by a factor of 15, and elongation rates are believed to correlate with aa-tRNA availability.
- The article focuses on a few key ingredients and simplest models, leaving prokaryote-eukaryote differences, regulation, wobbling, and other biological subtleties beyond scope.
3 The TASEP and its generalizations
The TASEP models translation as particles moving unidirectionally along an open lattice with exclusion, entry, exit, and hopping rules. Its extensions address extended ribosomes, inhomogeneous rates, and finite-resource effects, while revealing phase behavior and unresolved analytical problems.
- Proto model: The proto TASEP represents particles on a one-dimensional lattice that hop forward only when the next site is empty, with entry rate α, exit rate β, and hopping probability γ.The open model uses L+1 update attempts per Monte Carlo step and is emphasized because it resembles protein synthesis.
- Proto model: The open TASEP has maximal-current, high-density, and low-density phases controlled by α and β.With γ set to unity, the maximal-current phase is half-filled, while the phase structure is represented in the α-β plane.
- Proto model: Transitions from maximal-current to high- or low-density phases are continuous, whereas the high-density–low-density transition is discontinuous and supports shock-separated coexistence.The shock is a microscopic interface separating macroscopic high- and low-density regions.
- Generalizations of TASEP: Extended particles model ribosomes covering ℓ≥1 sites, requiring complete entry and incremental exit rules tied to the reader position.The first ℓ sites must be empty for entry, while the last ℓ codons can be traversed without hindrance when the ribosome is last.
- Generalizations of TASEP: For extended particles, particle density and coverage density differ, and although the phase diagram and current-density relation remain qualitatively similar, exact stationary solutions remain elusive.On a homogeneous ring, an exact current-density relation can nevertheless be derived; stationary profiles are especially affected in the high-density phase.
- Generalizations of TASEP: Inhomogeneous hopping rates motivated by non-uniform tRNA abundance produce a current-density plateau and soften otherwise sharp phase transitions.The plateau near overall density 1/2 depends on the variance of inverse rates, while the resulting phases still resemble maximal-current, high-density, and low-density phases.
4 Some recent developments
The paper develops finite-resource competition models and a simple current estimate for inhomogeneous TASEPs motivated by translation. Simulations show structured current behavior across competing lattices and synonymous gene sequences, while the proposed estimate is useful but remains approximate.
- 4.1 Competition for ribosomes: TASEP with finite particle reservoirs: The LD-HD crossover spans a discontinuous boundary and produces a response analogous to a first-order transition, with feedback localizing the shock.The average density follows a linear section, while the density profile resembles a stationary shock rather than the profile of an unconstrained TASEP.
- 4.1 Competition for ribosomes: TASEP with finite particle reservoirs: Finite particle pools couple multiple TASEPs, producing density crossovers and shock behavior that generalized domain wall theory captures successfully.For two lattices, anti-correlated shock motion keeps the pool population essentially fixed; three-lattice systems show additional features when lengths differ widely.
- 4.2 A simple estimate for currents in the inhomogeneous TASEP: Inhomogeneous hopping rates reflect codon-dependent aa-tRNA abundances, making exact prediction of the current difficult for realistic gene sequences.The paper therefore seeks a quick estimate for J(α, β, {γi}, ℓ), while noting that existing estimates work mainly for severe bottlenecks or neglect slow-site locations.
- 4.2 A simple estimate for currents in the inhomogeneous TASEP: 5000 randomly generated synonymous sequences for each of 10 E. coli proteins produced current distributions with means of 1.00-1.25 for 100 × J and standard deviations of 0.05-0.10.The distributions appeared approximately normal, while most wild-type sequences lay above the random-sequence clusters; five were more than 6.5 standard deviations above the mean.
- 4.2 A simple estimate for currents in the inhomogeneous TASEP: Across the 10 proteins, average currents and K12,min values each varied by 25%, but their ratio was essentially constant.This stability motivated defining a coefficient A from the average ratio across proteins.
5 Conclusions and outlook
The article connects nonequilibrium steady states with quantitative protein-production modeling through generalized TASEP models. It develops resource-limited and inhomogeneous-rate extensions, including current estimates, while identifying major open questions about model stability and biological rate limitations.
- The standard TASEP has three phases and exact results, whereas extended particles and inhomogeneous hopping rates generally require simulations or approximate mean-field methods.
- Generalized TASEP models represent mRNA as a one-dimensional lattice, ribosomes as extended particles, codons as sites, and particle current as protein production rate.Non-uniform hopping rates reflect variability in aa-tRNA concentrations across codons.
- Finite particle reservoirs produce multiple density-profile regimes and shock localization when one or several TASEPs compete for limited ribosomes.This resource limitation is motivated by the high cellular cost of synthesizing ribosomes.
- For 5000 randomly selected silent mutations across 10 proteins, K12,min showed a reliable linear relation with simulated currents, and the wild type followed the same relation.K12,min is the lowest coarse-grained hopping rate in a sequence and provides a current estimate.
- Open questions include steady-state stability under microscopic model changes and whether aa-tRNA concentrations, intrinsic rates, initiation, or secondary structures limit protein production.