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Mathematical Modelling of Cation Transport and Regulation in Yeast

Part of the Advances in Experimental Medicine and Biology book series (AEMB,volume 892)

Abstract

Mathematical modelling of ion transport is a strategy to understand the complex interplay between various ionic species and their transporters. Such models should provide new insights and suggest new interesting experiments. Two essential variables in models for ion transport and control are the membrane potential and the intracellular pH, which generates an additional layer of complexity absent from many other models of biochemical reaction pathways. The aim of this text is to introduce the reader to the basic principles and assumptions of modelling in this field. A simplified model of potassium transport will be used as an example and will be derived in a step by step manner. This forms the basis for understanding the advantages and limitations of more complex models. These are briefly reviewed at the end of this chapter.

Keywords

  • Systems biology
  • Mathematical modelling
  • Membrane potential
  • Ion homeostasis
  • Biological thermodynamics

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Fig. 12.1
Fig. 12.2

Notes

  1. 1.

    Mathematically, the buffering capacity is defined as \(\beta = \frac{d\left [H^{+}\right ]} {d(pH)}\).

  2. 2.

    This shape can be motivated by a simple two state model of voltage dependent switching, see e.g. for a derivation (Weiss 1996; Keener and Sneyd 2004).

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Acknowledgements

Maik Kschischo and Matthias Kahm were supported by BMBF grant 0315786C (SysMo2/Translucent 2). Both authors thank the members of the TRANSLUCENT consortium for helpful discussions.

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Correspondence to Maik Kschischo .

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Kahm, M., Kschischo, M. (2016). Mathematical Modelling of Cation Transport and Regulation in Yeast. In: Ramos, J., Sychrová, H., Kschischo, M. (eds) Yeast Membrane Transport. Advances in Experimental Medicine and Biology, vol 892. Springer, Cham. https://doi.org/10.1007/978-3-319-25304-6_12

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