Basic, simple and extendable kinetic model of protein synthesis (original) (raw)
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Basic and simple mathematical model of coupled transcription, translation and degradation
Synthesis of proteins is one of the most fundamental biological processes, which consumes a significant amount of cellular resources. Despite many efforts to produce detailed mechanistic mathematical models of translation, no basic and simple kinetic model of mRNA lifecycle (transcription, translation and degradation) exists. We build such a model by lumping multiple states of translated mRNA into few dynamical variables and introducing a pool of translating ribosomes. The basic and simple model can be extended, if necessary, to take into account various phenomena such as the interaction between translating ribosomes or regulation of translation by microRNA. The model can be used as a building block (translation module) for more complex models of cellular processes.
Semi-Markov models of mRNA-translation
2011
Translation is the cellular process in which ribosomes make proteins from information encoded on messenger RNA (mRNA). We model translation with an exclusion process taking into account the experimentally determined, non-exponential, waiting time between steps of a ribosome. From numerical simulations using realistic parameter values, we determine the distribution P(E) of the number of proteins E produced by one mRNA. We find that for small E this distribution is not geometric. We present a simplified and analytically solvable semi-Markov model that relates P(E) to the distributions of the times to produce the first E proteins.
A max-plus model of ribosome dynamics during mRNA translation
Journal of Theoretical Biology, 2012
We examine the dynamics of the translation stage of cellular protein production, in which ribosomes move uni-directionally along mRNA strands building an amino acid chain as they go. We describe the system using a timed event graph-a class of Petri net useful for studying discrete events which take a finite time. We use max-plus algebra to describe a deterministic version of the model, calculating the protein production rate and density of ribosomes on the mRNA. We find exact agreement between these analytical results and numerical simulations of the deterministic case.
A quantitative model for mRNA translation in Saccharomyces cerevisiae
Yeast (Chichester, England), 2010
Messenger RNA (mRNA) translation is an essential step in eukaryotic gene expression that contributes to the regulation of this process. We describe a deterministic model based on ordinary differential equations that describe mRNA translation in Saccharomyces cerevisiae. This model, which was parameterized using published data, was developed to examine the kinetic behaviour of translation initiation factors in response to amino acid availability. The model predicts that the abundance of the eIF1-eIF3-eIF5 complex increases under amino acid starvation conditions, suggesting a possible auxiliary role for these factors in modulating translation initiation in addition to the known mechanisms involving eIF2. Our analyses of the robustness of the mRNA translation model suggest that individual cells within a randomly generated population are sensitive to external perturbations (such as changes in amino acid availability) through Gcn2 signalling. However, the model predicts that individual c...
Dynamical modeling of microRNA action on the protein translation process
BMC systems …, 2010
Background: Protein translation is a multistep process which can be represented as a cascade of biochemical reactions (initiation, ribosome assembly, elongation, etc.), the rate of which can be regulated by small non-coding microRNAs through multiple mechanisms. It remains unclear what mechanisms of microRNA action are the most dominant: moreover, many experimental reports deliver controversial messages on what is the concrete mechanism actually observed in the experiment. Nissan and Parker have recently demonstrated that it might be impossible to distinguish alternative biological hypotheses using the steady state data on the rate of protein synthesis. For their analysis they used two simple kinetic models of protein translation. Results: In contrary to the study by Nissan and Parker, we show that dynamical data allow discriminating some of the mechanisms of microRNA action. We demonstrate this using the same models as developed by Nissan and Parker for the sake of comparison but the methods developed (asymptotology of biochemical networks) can be used for other models. We formulate a hypothesis that the effect of microRNA action is measurable and observable only if it affects the dominant system (generalization of the limiting step notion for complex networks) of the protein translation machinery. The dominant system can vary in different experimental conditions that can partially explain the existing controversy of some of the experimental data.
IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2000
Gene translation is a central stage in the intra-cellular process of protein synthesis. Gene translation proceeds in three major stages: initiation, elongation, and termination. During the elongation step ribosomes (intra cellular macro-molecules) link amino acids together in the order specified by messenger RNA (mRNA) molecules. The homogeneous ribosome flow model (HRFM) is a mathematical model of translation-elongation under the assumption of constant elongation rate along the mRNA sequence. The HRFM includes n first-order nonlinear ordinary differential equations, where n represents the length of the mRNA sequence, and two positive parameters: ribosomal initiation rate and the (constant) elongation rate.
2020
We derive phenomenological models of gene expression from a mechanistic description of chemical reactions using an automated model reduction method. Using this method, we get analytical descriptions and computational performance guarantees to compare the reduced dynamics with the full models. We develop a new two-state model with the dynamics of the available free ribosomes in the system and the protein concentration. We show that this new two-state model captures the detailed mass-action kinetics of the chemical reaction network under various biologically plausible conditions on model parameters. On comparing the performance of this model with the commonly used mRNA transcript-protein dynamical model for gene expression, we analytically show that the free ribosome and protein model has superior error and robustness performance.
Stochastic theory of protein synthesis and polysome: Ribosome profile on a single mRNA transcript
Journal of Theoretical Biology, 2011
The process of polymerizing a protein by a ribosome, using a messenger RNA (mRNA) as the corresponding template, is called translation. Ribosome may be regarded as a molecular motor for which the mRNA template serves also as the track. Often several ribosomes may translate the same (mRNA) simultaneously. The ribosomes bound simultaneously to a single mRNA transcript are the members of a polyribosome (or, simply, polysome). Experimentally measured polysome profile gives the distribution of polysome sizes. Recently a breakthrough in determining the instantaneous positions of the ribosomes on a given mRNA track has been achieved and the technique is called ribosome profiling [1, 2]. Motivated by the success of these techniques, we have studied the spatio-temporal organization of ribosomes by extending a theoretical model that we have reported elsewhere . This extended version of our model incorporates not only (i) mechano-chemical cycle of individual ribomes, and (ii) their steric interactions, but also (iii) the effects of (a) kinetic proofreading, (b) translational infidelity, (c) ribosome recycling, and (d) sequence inhomogeneities. The theoretical framework developed here will serve in guiding further experiments and in analyzing the data to gain deep insight into various kinetic processes involved in translation.
Modeling of ribosome dynamics on a ds-mRNA under an external load
Protein molecules in cells are synthesized by macromolecular machines called ibosomes. According to the recent experimental data, we reduce the complexity of the ribosome and propose a model to express its activity in six main states. Using our model, we study the translation rate in different biological relevant situations in the presence of external force and the translation through the RNA double stranded region in the absence or presence of the external force. In the present study, we give a quantitative theory for translation rate and show that the ribosome behaves more like a Brownian Ratchet motor. Our findings could shed some light on understanding behaviors of the ribosome in biological conditions.