Solute transport with Michaelis-Menten kinetics for in vitro cell culture.

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2023-03-13 DOI:10.1093/imammb/dqac014
Lauren Hyndman, Sean McKee, Sean McGinty
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Abstract

A traditional method of in vitro cell culture involves a monolayer of cells at the base of a petri dish filled with culture medium. While the primary role of the culture medium is to supply nutrients to the cells, drug or other solutes may be added, depending on the purpose of the experiment. Metabolism by cells of oxygen, nutrients and drug is typically governed by Michaelis-Menten (M-M) kinetics. In this paper, a mathematical model of solute transport with M-M kinetics is developed. Upon non-dimensionalization, the reaction/diffusion system is re-characterized in terms of Volterra integral equations, where a parameter $\beta $, the ratio of the initial solute concentration to the M-M constant, proves important: $\beta \ll 1$ is relevant to drug metabolism for the liver, whereas $\beta \gg 1$ is more appropriate in the case of oxygen metabolism. Regular perturbation expansions for both cases are obtained. A small-time expansion and steady-state solution are also presented. All results are compared against the numerical solution of the Volterra integral equations, and excellent agreement is found. The utility of the model and analytical solutions are discussed in the context of assisting experimental researchers to better understand the environment within in vitro cell culture experiments.

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体外细胞培养中溶质运输的Michaelis-Menten动力学。
传统的体外细胞培养方法是在充满培养基的培养皿底部放置一层细胞。培养基的主要作用是为细胞提供营养,但根据实验目的,也可以添加药物或其他溶质。细胞对氧气、营养物质和药物的代谢通常受米切里斯-门腾(M-M)动力学控制。本文建立了溶质输运的M-M动力学数学模型。在非量纲化的情况下,反应/扩散系统用Volterra积分方程重新表征,其中参数$\beta $,即初始溶质浓度与M-M常数的比值,证明是重要的:$\beta \ll 1$与肝脏的药物代谢有关,而$\beta \gg 1$更适合于氧代谢的情况。得到了这两种情况的正则摄动展开式。给出了小时间展开式和稳态解。所有结果都与Volterra积分方程的数值解进行了比较,结果非常吻合。在帮助实验研究人员更好地了解体外细胞培养实验环境的背景下,讨论了模型和分析解决方案的实用性。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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