The tri-frame model

A priori, de novo mathematical exploration of gene expression mechanism via regression viewpoint with briefly cataloged modeling antiquity

Various algorithms have been devised to mathematically model the dynamic mechanism of the gene expression data. Gillespie’s stochastic simulation (GSSA) has been exceptionally primal for chemical reaction synthesis with future ameliorations. Several other mathematical techniques such as differential equations, thermodynamic models and Boolean models have been implemented to optimally and effectively represent the gene functioning. We present a novel mathematical framework of gene expression, undertaking the mathematical modeling of the transcription and translation phases, which is a detour from conventional modeling approaches. These subprocesses are inherent to every gene expression, which is implicitly an experimental outcome. As we foresee, there can be modeled a generality about some basal translation or transcription values that correspond to a particular assay.

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.

A stochastic model of translation with -1 programmed ribosomal frameshifting

Many viruses produce multiple proteins from a single mRNA sequence by encoding overlapping genes. One mechanism to decode both genes, which reside in alternate reading frames, is -1 programmed ribosomal frameshifting. Although recognized for over 25 years, the molecular and physical mechanism of -1 frameshifting remains poorly understood. We have developed a mathematical model that treats mRNA translation and associated -1 frameshifting as a stochastic process in which the transition probabilities are based on the energetics of local molecular interactions. The model predicts both the location and efficiency of -1 frameshift events in HIV-1. Moreover, we compute -1 frameshift efficiencies upon mutations in the viral mRNA sequence and variations in relative tRNA abundances, predictions that are directly testable in experiment.

Transimulation - protein biosynthesis web service

Although translation is the key step during gene expression, it remains poorly characterized at the level of individual genes. For this reason, we developed Transimulation – a web service measuring translational activity of genes in three model organisms: Escherichia coli, Saccharomyces cerevisiae and Homo sapiens. The calculations are based on our previous computational model of translation and experimental data sets. Transimulation quantifies mean translation initiation and elongation time (expressed in SI units), and the number of proteins produced per transcript. It also approximates the number of ribosomes that typically occupy a transcript during translation, and simulates their propagation. The simulation of ribosomes’ movement is interactive and allows modifying the coding sequence on the fly. It also enables uploading any coding sequence and simulating its translation in one of three model organisms. In such a case, ribosomes propagate according to mean codon elongation times of the host organism, which may prove useful for heterologous expression. Transimulation was used to examine evolutionary conservation of translational parameters of orthologous genes. Transimulation may be accessed at http://nexus.ibb.waw.pl/Transimulation (requires Java version 1.7 or higher). Its manual and source code, distributed under the GPL-2.0 license, is freely available at the website.

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.

Natural selection retains overrepresented out-of-frame stop codons against frameshift peptides in prokaryotes

Background

Out-of-frame stop codons (OSCs) occur naturally in coding sequences of all organisms, providing a mechanism of early termination of translation in incorrect reading frame so that the metabolic cost associated with frameshift events can be reduced. Given such a functional significance, we expect statistically overrepresented OSCs in coding sequences as a result of a widespread selection. Accordingly, we examined available prokaryotic genomes to look for evidence of this selection.

Results

The complete genome sequences of 990 prokaryotes were obtained from NCBI GenBank. We found that low G+C content coding sequences contain significantly more OSCs and G+C content at specific codon positions were the principal determinants of OSC usage bias in the different reading frames. To investigate if there is overrepresentation of OSCs, we modeled the trinucleotide and hexanucleotide biases of the coding sequences using Markov models, and calculated the expected OSC frequencies for each organism using a Monte Carlo approach. More than 93% of 342 phylogenetically representative prokaryotic genomes contain excess OSCs. Interestingly the degree of OSC overrepresentation correlates positively with G+C content, which may represent a compensatory mechanism for the negative correlation of OSC frequency with G+C content. We extended the analysis using additional compositional bias models and showed that lower-order bias like codon usage and dipeptide bias could not explain the OSC overrepresentation. The degree of OSC overrepresentation was found to correlate negatively with the optimal growth temperature of the organism after correcting for the G+C% and AT skew of the coding sequence.

Conclusions

The present study uses approaches with statistical rigor to show that OSC overrepresentation is a widespread phenomenon among prokaryotes. Our results support the hypothesis that OSCs carry functional significance and have been selected in the course of genome evolution to act against unintended frameshift occurrences. Some results also hint that OSC overrepresentation being a compensatory mechanism to make up for the decrease in OSCs in high G+C organisms, thus revealing the interplay between two different determinants of OSC frequency.

A comprehensive, quantitative, and genome-wide model of translation

Translation is still poorly characterised at the level of individual proteins and its role in regulation of gene expression has been constantly underestimated. To better understand the process of protein synthesis we developed a comprehensive and quantitative model of translation, characterising protein synthesis separately for individual genes. The main advantage of the model is that basing it on only a few datasets and general assumptions allows the calculation of many important translational parameters, which are extremely difficult to measure experimentally. In the model, each gene is attributed with a set of translational parameters, namely the absolute number of transcripts, ribosome density, mean codon translation time, total transcript translation time, total time required for translation initiation and elongation, translation initiation rate, mean mRNA lifetime, and absolute number of proteins produced by gene transcripts. Most parameters were calculated based on only one experimental dataset of genome-wide ribosome profiling. The model was implemented in Saccharomyces cerevisiae, and its results were compared with available data, yielding reasonably good correlations. The calculated coefficients were used to perform a global analysis of translation in yeast, revealing some interesting aspects of the process. We have shown that two commonly used measures of translation efficiency – ribosome density and number of protein molecules produced – are affected by two distinct factors. High values of both measures are caused, i.a., by very short times of translation initiation, however, the origins of initiation time reduction are completely different in both cases. The model is universal and can be applied to any organism, if the necessary input data are available. The model allows us to better integrate transcriptomic and proteomic data. A few other possibilities of the model utilisation are discussed concerning the example of the yeast system.

Translation is the production of proteins by decoding mRNA produced in transcription, and is a part of the overall process of gene expression. Although the general theoretical background of translation is known, the process is still poorly characterised at the level of individual proteins. In particular, the quantitative parameters of translation, such as time required to complete it or the number of protein molecules produced from a transcript during its lifetime, are extremely difficult to measure experimentally. To overcome this problem, we developed a computational model that, on the basis of only few datasets and general assumptions, measures quantitatively the translational activity at the level of individual genes. We discussed it concerning the example of the yeast system; however, it can be applied to any organism of known genome. We used the obtained results to study the general characteristics of the yeast translational system, revealing the diversity of strategies of gene expression regulation. We exemplified and discussed other possible ways of model utilisation, as it may help in examining protein-protein interactions, metabolic pathways, gene annotation, ribosome queueing, protein folding, and translation initiation. It also may be crucial for better integration of cell-wide, high-throughput experiments.