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A Simplified Model of Glycoprotein Production within Cell Culture

Lambert, AB; Smith, FT; Velayudhan, A; (2017) A Simplified Model of Glycoprotein Production within Cell Culture. European Journal of Applied Mathematics , 28 (4) pp. 535-561. 10.1017/S0956792516000437. Green open access

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Abstract

Complex biological products, such as those used to treat various forms of cancer, are typically produced by mammalian cells in bioreactors. The most important class of such biological medicines is proteins. These typically bind to sugars (glycans) in a process known as glycosylation, creating glycoproteins, which are more stable and effective medicines. The glycans are large polymers that are formed by a long sequence of enzyme catalysed reactions. This sequence is not always completed, thus leading to a heterogeneous glycoprotein distribution. A better comprehension of this distribution could lead to more efficient production of high quality drugs. To understand how the manufacturing process can affect the extent of glycosylation of protein, a non-linear ODE model of glycoprotein production is developed which describes the bioreactor configuration as well as the protein production and glycosylation reactions within the cell. The entire system evolves eventually to a stable steady state. The earlier evolution is critical however, as the amount of product produced and its quality varies over time. The model is considered as two coupled systems: the bioreactor submodel and the glycosylation submodel. To investigate the early time evolution within the bioreactor submodel, analytical and numerical properties are derived using matched asymptotic expansions and a finite difference scheme for a range of initial conditions. This leads to qualitatively different regimes for aglycosylated protein production, which affect the glycosylation submodel. The discrete glycoprotein distribution is approximated as continuous and written as a first-order PDE, with good agreement between the discrete and continuous models. The PDE is found to admit shocks, but the existence of these shocks is dependent on the early time evolution within the bioreactor submodel and leads to higher levels of glycosylation at early time. This suggests that changing the bioreactor configuration can lead to higher quality product at certain times.

Type: Article
Title: A Simplified Model of Glycoprotein Production within Cell Culture
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0956792516000437
Publisher version: http://doi.org/10.1017/S0956792516000437
Language: English
Additional information: Copyright © Cambridge University Press 2016. This article has been published in a revised form in the European Journal of Applied Mathematics [http://dx.doi.org/10.1017/S0956792516000437]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
Keywords: Mathematical Model, Glycosylation, Post-translational modification, Bioreactor
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Biochemical Engineering
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1522253
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