A mathematical modelling framework for elucidating the role of feedback control in translation termination

Origins of robustness in translational control via eukaryotic translation initiation factor (eIF) 2

Phosphorylation of eukaryotic translation initiation factor 2 (eIF2) is one of the best studied and most widely used means for regulating protein synthesis activity in eukaryotic cells. This pathway regulates protein synthesis in response to stresses, viral infections, and nutrient depletion, among others. We present analyses of an ordinary differential equation-based model of this pathway, which aim to identify its principal robustness-conferring features. Our analyses indicate that robustness is a distributed property, rather than arising from the properties of any one individual pathway species. However, robustness-conferring properties are unevenly distributed between the different species, and we identify a guanine nucleotide dissociation inhibitor (GDI) complex as a species that likely contributes strongly to the robustness of the pathway. Our analyses make further predictions on the dynamic response to different types of kinases that impinge on eIF2.

Probabilistic Boolean Network Modelling and Analysis Framework for mRNA Translation

mRNA translation is a complex process involving the progression of ribosomes on the mRNA, resulting in the synthesis of proteins, and is subject to multiple layers of regulation. This process has been modelled using different formalisms, both stochastic and deterministic. Recently, we introduced a Probabilistic Boolean modelling framework for mRNA translation, which possesses the advantage of tools for numerically exact computation of steady state probability distribution, without requiring simulation. Here, we extend this model to incorporate both random sequential and parallel update rules, and demonstrate its effectiveness in various settings, including its flexibility in accommodating additional static and dynamic biological complexities and its role in parameter sensitivity analysis. In these applications, the results from the model analysis match those of TASEP model simulations. Importantly, the proposed modelling framework maintains the stochastic aspects of mRNA translation and provides a way to exactly calculate probability distributions, providing additional tools of analysis in this context. Finally, the proposed modelling methodology provides an alternative approach to the understanding of the mRNA translation process, by bridging the gap between existing approaches, providing new analysis tools, and contributing to a more robust platform for modelling and understanding translation.

Toxin effect on protein biosynthesis in eukaryotic cells: a simple kinetic model

A model for toxin inhibition of protein synthesis inside eukaryotic cells is presented. Mitigation of this effect by introduction of an antibody is also studied. Antibody and toxin (ricin) initially are delivered outside the cell. The model describes toxin internalization from the extracellular into the intracellular domain, its transport to the endoplasmic reticulum (ER) and the cleavage inside the ER into the RTA and RTB chains, the release of RTA into the cytosol, inactivation (depurination) of ribosomes, and the effect on translation. The model consists of a set of ODEs which are solved numerically. Numerical results are illustrated by figures and discussed.

mRNA translation and protein synthesis: an analysis of different modelling methodologies and a new PBN based approach

Background

mRNA translation involves simultaneous movement of multiple ribosomes on the mRNA and is also subject to regulatory mechanisms at different stages. Translation can be described by various codon-based models, including ODE, TASEP, and Petri net models. Although such models have been extensively used, the overlap and differences between these models and the implications of the assumptions of each model has not been systematically elucidated. The selection of the most appropriate modelling framework, and the most appropriate way to develop coarse-grained/fine-grained models in different contexts is not clear.

Results

We systematically analyze and compare how different modelling methodologies can be used to describe translation. We define various statistically equivalent codon-based simulation algorithms and analyze the importance of the update rule in determining the steady state, an aspect often neglected. Then a novel probabilistic Boolean network (PBN) model is proposed for modelling translation, which enjoys an exact numerical solution. This solution matches those of numerical simulation from other methods and acts as a complementary tool to analytical approximations and simulations. The advantages and limitations of various codon-based models are compared, and illustrated by examples with real biological complexities such as slow codons, premature termination and feedback regulation. Our studies reveal that while different models gives broadly similiar trends in many cases, important differences also arise and can be clearly seen, in the dependence of the translation rate on different parameters. Furthermore, the update rule affects the steady state solution.

Conclusions

The codon-based models are based on different levels of abstraction. Our analysis suggests that a multiple model approach to understanding translation allows one to ascertain which aspects of the conclusions are robust with respect to the choice of modelling methodology, and when (and why) important differences may arise. This approach also allows for an optimal use of analysis tools, which is especially important when additional complexities or regulatory mechanisms are included. This approach can provide a robust platform for dissecting translation, and results in an improved predictive framework for applications in systems and synthetic biology.

Regulation of release factor expression using a translational negative feedback loop: a systems analysis

The essential eukaryote release factor eRF1, encoded by the yeast SUP45 gene, recognizes stop codons during ribosomal translation. SUP45 nonsense alleles are, however, viable due to the establishment of feedback-regulated readthrough of the premature termination codon; reductions in full-length eRF1 promote tRNA-mediated stop codon readthrough, which, in turn, drives partial production of full-length eRF1. A deterministic mathematical model of this eRF1 feedback loop was developed using a staged increase in model complexity. Model predictions matched the experimental observation that strains carrying the mutant SUQ5 tRNA (a weak UAA suppressor) in combination with any of the tested sup45(UAA) nonsense alleles exhibit threefold more stop codon readthrough than that of an SUQ5 yeast strain. The model also successfully predicted that eRF1 feedback control in an SUQ5 sup45(UAA) mutant would resist, but not completely prevent, imposed changes in eRF1 expression. In these experiments, the introduction of a plasmid-borne SUQ5 copy into a sup45(UAA) SUQ5 mutant directed additional readthrough and full-length eRF1 expression, despite feedback. Secondly, induction of additional sup45(UAA) mRNA expression in a sup45(UAA) SUQ5 strain also directed increased full-length eRF1 expression. The autogenous sup45 control mechanism therefore acts not to precisely control eRF1 expression, but rather as a damping mechanism that only partially resists changes in release factor expression level. The validated model predicts that the degree of feedback damping (i.e., control precision) is proportional to eRF1 affinity for the premature stop codon. The validated model represents an important tool to analyze this and other translational negative feedback loops.

Mathematical and Computational Modelling of Ribosomal Movement and Protein Synthesis: an overview

Translation or protein synthesis consists of a complex system of chemical reactions, which ultimately result in decoding of the mRNA and the production of a protein. The complexity of this reaction system makes it difficult to quantitatively connect its input parameters (such as translation factor or ribosome concentrations, codon composition of the mRNA, or energy availability) to output parameters (such as protein synthesis rates or ribosome densities on mRNAs). Mathematical and computational models of translation have now been used for nearly five decades to investigate translation, and to shed light on the relationship between the different reactions in the system. This review gives an overview over the principal approaches used in the modelling efforts, and summarises some of the major findings that were made.

A systems view of the protein expression process

Many biological processes are regulated by changing the concentration and activity of proteins. The presence of a protein at a given subcellular location at a given time with a certain conformation is the result of an apparently sequential process. The rate of protein formation is influenced by chromatin state, and the rates of transcription, translation, and degradation. There is an exquisite control system where each stage of the process is controlled both by seemingly unregulated proteins as well as through feedbacks mediated by RNA and protein products. Here we review the biological facts and mathematical models for each stage of the protein production process. We conclude that advances in experimental techniques leading to a detailed description of the process have not been matched by mathematical models that represent the details of the process and facilitate analysis. Such an exercise is the first step towards development of a framework for a systems biology analysis of the protein production process.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-011-9088-1) contains supplementary material, which is available to authorized users.

Autoregulatory systems controlling translation factor expression: thermostat-like control of translational accuracy

In both prokaryotes and eukaryotes, the expression of a large number of genes is controlled by negative feedback, in some cases operating at the level of translation of the mRNA transcript. Of particular interest are those cases where the proteins concerned have cell-wide function in recognizing a particular codon or RNA sequence. Examples include the bacterial translation termination release factor RF2, initiation factor IF3, and eukaryote poly(A) binding protein. The regulatory loops that control their synthesis establish a negative feedback control mechanism based upon that protein's RNA sequence recognition function in translation (for example, stop codon recognition) without compromising the accurate recognition of that codon, or sequence during general, cell-wide translation. Here, the bacterial release factor RF2 and initiation factor IF3 negative feedback loops are reviewed and compared with similar negative feedback loops that regulate the levels of the eukaryote release factor, eRF1, established artificially by mutation. The control properties of such negative feedback loops are discussed as well as their evolution. The role of negative feedback to control translation factor expression is considered in the context of a growing body of evidence that both IF3 and RF2 can play a role in stimulating stalled ribosomes to abandon translation in response to amino acid starvation. Here, we make the case that negative feedback control serves primarily to limit the overexpression of these translation factors, preventing the loss of fitness resulting from an unregulated increase in the frequency of ribosome drop-off.