Basic, simple and extendable kinetic model of protein synthesis

Alexander N. Gorban; Annick Harel-Bellan; Nadya Morozova; Andrei Zinovyev; Alexander N. Gorban; Annick Harel-Bellan; Nadya Morozova; Andrei Zinovyev

doi:10.3934/mbe.2019329

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 6602-6622. doi: 10.3934/mbe.2019329

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Basic, simple and extendable kinetic model of protein synthesis

1.
University of Leicester, Center for Mathematical Modeling, Leicester, UK
2.
Lobachevsky University, Nizhny Novgorod, Russia
3.
Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, Université Paris-Saclay, Gif-sur-Yvette, France
4.
Institut des Hautes Etudes Scientiques, Bures-sur-Yvette, France
5.
Komarov Botanical Institute, Russian Academy of Sciences, Saint Petersburg, Russia
6.
Institut Curie, 26 rue d’Ulm, F-75248 Paris, France
7.
INSERM U900, France
8.
Mines PariTech, Fontainbleau, France

Received: 29 April 2019 Accepted: 18 June 2019 Published: 17 July 2019

Protein synthesis is one of the most fundamental biological processes. Despite existence of multiple mathematical models of translation, surprisingly, there is no basic and simple chemical kinetic model of this process, derived directly from the detailed kinetic scheme. One of the reasons for this is that the translation process is characterized by indefinite number of states, because of the structure of the polysome. We bypass this difficulty by applying lumping of multiple states of translated mRNA into few dynamical variables and by introducing a variable describing the pool of translating ribosomes. The simplest model can be solved analytically. The simplest model can be extended, if necessary, to take into account various phenomena such as the limited amount of ribosomal units or regulation of translation by microRNA. The introduced model is more suitable to describe the protein synthesis in eukaryotes but it can be extended to prokaryotes. The model can be used as a building block for more complex models of cellular processes. We demonstrate the utility of the model in two examples. First, we determine the critical parameters of the synthesis of a single protein for the case when the ribosomal units are abundant. Second, we demonstrate intrinsic bi-stability in the dynamics of the ribosomal protein turnover and predict that a minimal number of ribosomes should pre-exists in a living cell to sustain its protein synthesis machinery, even in the absence of proliferation.
- kinetic modeling,
- translation,
- protein,
- lumping,
- ribosomes
Citation: Alexander N. Gorban, Annick Harel-Bellan, Nadya Morozova, Andrei Zinovyev. Basic, simple and extendable kinetic model of protein synthesis[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6602-6622. doi: 10.3934/mbe.2019329

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Abstract

Protein synthesis is one of the most fundamental biological processes. Despite existence of multiple mathematical models of translation, surprisingly, there is no basic and simple chemical kinetic model of this process, derived directly from the detailed kinetic scheme. One of the reasons for this is that the translation process is characterized by indefinite number of states, because of the structure of the polysome. We bypass this difficulty by applying lumping of multiple states of translated mRNA into few dynamical variables and by introducing a variable describing the pool of translating ribosomes. The simplest model can be solved analytically. The simplest model can be extended, if necessary, to take into account various phenomena such as the limited amount of ribosomal units or regulation of translation by microRNA. The introduced model is more suitable to describe the protein synthesis in eukaryotes but it can be extended to prokaryotes. The model can be used as a building block for more complex models of cellular processes. We demonstrate the utility of the model in two examples. First, we determine the critical parameters of the synthesis of a single protein for the case when the ribosomal units are abundant. Second, we demonstrate intrinsic bi-stability in the dynamics of the ribosomal protein turnover and predict that a minimal number of ribosomes should pre-exists in a living cell to sustain its protein synthesis machinery, even in the absence of proliferation.

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