Project
AA1-14
Development of an Ion-Channel Model-Framework for In-vitro Assisted Interpretation of Current Voltage Relations
Project Heads
Jürgen Fuhrmann, Manuel Landstorfer, Barbara Wagner
Project Members
Christine Keller
Project Duration
01.04.2022 − 31.03.2025
Located at
WIAS
Description
Within this project a PDE based model framework was developed to better understand how ion channels control the flow of charged particles such as sodium and potassium in and out of cells. These channels are crucial for many life processes, from nerve signaling to muscle contraction. The new model combines physics, electrochemistry and mathematics to explain how these channels selectively allow certain ions to pass through and block others. By including detailed effects such as the size of the ions and interactions with water, the model provides a clearer picture of how these microscopic gatekeepers work. This could help in the development of better medical treatments or advanced bioinspired technologies.
External Website
Related Publications
[1] J. Fuhrmann, “A numerical strategy for Nernst-Planck systems with solvation effect,” Fuel cells, vol. 16, no. 6, pp. 704–714, 2016. DOI: 10.1002/fuce.201500215.
[2] C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, and B. Gaudeul, “A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model,” IMA Journal of Numerical Analysis, vol. 41, no. 1, pp. 271–314, 2021. DOI: 10.1093/imanum/draa002.
[3] J. Fuhrmann, C. Guhlke, A. Linke, C. Merdon, and R. Müller, “Models and numerical methods for electrolyte flows,” in Topics in applied analysis and optimisation, 2019, pp. 183–209. DOI: 10.1007/978-3-030-33116-0_8.
[4] M. Landstorfer, C. Guhlke, and W. Dreyer, “Theory and structure of the metal-electrolyte interface incorporating adsorption and solvation effects,” Electrochimica Acta, vol. 201, pp. 187–219, 2016. DOI: 10.1016/j.electacta.2016.03.013.
[5] M. Landstorfer, “Boundary conditions for electrochemical interfaces,” Journal of The Electrochemical Society, vol. 164, no. 11, p. E3671, 2017. DOI: 10.1149/2.0641711jes.
[6] W. DREYER, C. GUHLKE, M. LANDSTORFER, and R. MÜLLER, “New insights on the interfacial tension of electrochemical interfaces and the lippmann equation,” European Journal of Applied Mathematics, vol. 29, no. 4, pp. 708–753, 2018. DOI: 10.1017/S0956792517000341.
[7] G. L. Celora, M. G. Hennessy, A. Münch, B. Wagner, and S. L. Waters, “A kinetic model of a polyelectrolyte gel undergoing phase separation.” WIAS Preprint 2802, 2020. DOI: 10.20347/WIAS.PREPRINT.2802.
[8] G. L. Celora, M. G. Hennessy, Münch, A., B. Wagner, and S. L. Waters, “A kinetic model of a polyelectrolyte gel undergoing phase separation.” WIAS Preprint 2731, 2020. DOI: 10.20347/WIAS.PREPRINT.2731.
[9] J.-L. Liu and B. Eisenberg, “Molecular mean-field theory of ionic solutions: A poisson-nernst-planck-bikerman model,” Entropy, vol. 22, no. 5, 2020. DOI: 10.3390/e22050550.
[10] D. Boda, M. Valiskó, D. Henderson, B. Eisenberg, D. Gillespie, and W. Nonner, “Ionic selectivity in L-type calcium channels by electrostatics and hard-core repulsion,” Journal of General Physiology, vol. 133, no. 5, pp. 497–509, Apr. 2009. DOI: 10.1085/jgp.200910211.
[11] Y. Wang, C. Liu, P. Liu, and B. Eisenberg, “Field theory of reaction-diffusion: Law of mass action with an energetic variational approach,” Phys. Rev. E, vol. 102, no. 6, p. 062147, 2020. DOI: 10.1103/PhysRevE.102.062147.
[12] J. Fuhrmann, B. Gaudeul, and Ch. Keller, “Two entropic finite volume schemes for a Nernst–Planck–Poisson system with ion volume constraints,” in Proc. Finite Volumes for Complex Applications X, 2023. DOI: 10.1007/978-3-031-40864-9_23.
[13] Ch. Keller, J. Fuhrmann, and M. Landstorfer, “A model framework for ion channels with selectivity filters based on continuum non-equilibrium thermodynamics,” WIAS Preprint 3072, 2023. DOI: 10.20347/WIAS.PREPRINT.3072.
[14] Ch. Keller, M. Landstorfer, J. Fuhrmann and B.Wagner. “A Model Framework for Ion Channels with Selectivity Filters Based on Non-Equilibrium Thermodynamics,” Entropy, 27(9), 981, 2025. DOI: 10.3390/e27090981.