Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels

Riccardo Sacco; Fabio Manganini; Joseph W. Jerome

Molecular Based Mathematical Biology (2015)

  • Volume: 3, Issue: 1
  • ISSN: 2299-3266

Abstract

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In this articlewe address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the well-known velocity-extended Poisson-Nernst-Planck (vPNP) electrodiffusion model. Two extensions of the vPNP system are proposed: the velocity-extended Thermo-Hydrodynamic model (vTHD) and the velocity-extended Electro-Thermal model (vET). Both formulations are based on the principles of conservation of mass, momentum and energy, and collapse into the vPNP model under thermodynamical equilibrium conditions. Upon introducing a suitable one-dimensional geometrical representation of the channel,we discuss appropriate boundary conditions that depend only on effectively accessible measurable quantities. Then, we describe the novel models, the solution map used to iteratively solve them, and the mixed-hybrid flux-conservative stabilized finite element scheme used to discretize the linearized equations. Finally,we successfully apply our computational algorithms to the simulation of two different realistic biological channels: 1) the Gramicidin-A channel considered in [12]; and 2) the bipolar nanofluidic diode considered in [45].

How to cite

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Riccardo Sacco, Fabio Manganini, and Joseph W. Jerome. "Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels." Molecular Based Mathematical Biology 3.1 (2015): null. <http://eudml.org/doc/275855>.

@article{RiccardoSacco2015,
abstract = {In this articlewe address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the well-known velocity-extended Poisson-Nernst-Planck (vPNP) electrodiffusion model. Two extensions of the vPNP system are proposed: the velocity-extended Thermo-Hydrodynamic model (vTHD) and the velocity-extended Electro-Thermal model (vET). Both formulations are based on the principles of conservation of mass, momentum and energy, and collapse into the vPNP model under thermodynamical equilibrium conditions. Upon introducing a suitable one-dimensional geometrical representation of the channel,we discuss appropriate boundary conditions that depend only on effectively accessible measurable quantities. Then, we describe the novel models, the solution map used to iteratively solve them, and the mixed-hybrid flux-conservative stabilized finite element scheme used to discretize the linearized equations. Finally,we successfully apply our computational algorithms to the simulation of two different realistic biological channels: 1) the Gramicidin-A channel considered in [12]; and 2) the bipolar nanofluidic diode considered in [45].},
author = {Riccardo Sacco, Fabio Manganini, Joseph W. Jerome},
journal = {Molecular Based Mathematical Biology},
language = {eng},
number = {1},
pages = {null},
title = {Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels},
url = {http://eudml.org/doc/275855},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Riccardo Sacco
AU - Fabio Manganini
AU - Joseph W. Jerome
TI - Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels
JO - Molecular Based Mathematical Biology
PY - 2015
VL - 3
IS - 1
SP - null
AB - In this articlewe address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the well-known velocity-extended Poisson-Nernst-Planck (vPNP) electrodiffusion model. Two extensions of the vPNP system are proposed: the velocity-extended Thermo-Hydrodynamic model (vTHD) and the velocity-extended Electro-Thermal model (vET). Both formulations are based on the principles of conservation of mass, momentum and energy, and collapse into the vPNP model under thermodynamical equilibrium conditions. Upon introducing a suitable one-dimensional geometrical representation of the channel,we discuss appropriate boundary conditions that depend only on effectively accessible measurable quantities. Then, we describe the novel models, the solution map used to iteratively solve them, and the mixed-hybrid flux-conservative stabilized finite element scheme used to discretize the linearized equations. Finally,we successfully apply our computational algorithms to the simulation of two different realistic biological channels: 1) the Gramicidin-A channel considered in [12]; and 2) the bipolar nanofluidic diode considered in [45].
LA - eng
UR - http://eudml.org/doc/275855
ER -

References

top
  1.  
  2. [1] A. Abramo, R. Brunetti, C. Fiegna, C. Jacoboni, B. Riccò, E. Sangiorgi, and F. Venturi. Monte Carlo simulation of silicon devices. In G. Baccarani, editor, Process and Device Modeling for Microelectronics, chapter 2, pages 155–216. Elsevier, 1993. 
  3. [2] P. Airoldi, A. G. Mauri, R. Sacco, and J. W. Jerome. Three-dimensional numerical simulation of ion nanochannels. Journal of Coupled Systems and Multiscale Dynamics, 3(1):57–65, 2015-04-01T00:00:00. 
  4. [3] T. Arbogast and Z. Chen. On the implementation of mixed methods as nonconforming methods for second-order elliptic problems. Math. Comput., 64(211):943–972, July 1995. Zbl0829.65127
  5. [4] D.N Arnold and F. Brezzi. Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates. Math. Modeling and Numer. Anal., 19(1):7–32, 1985. Zbl0567.65078
  6. [5] G. Baccarani, M. Rudan, R. Guerrieri, and P. Ciampolini. Process and device modeling. chapter Physical models for numerical device simulation, pages 107–158. North-Holland Publishing Co., Amsterdam, The Netherlands, The Netherlands, 1986. 
  7. [6] D. Boda, M. Valiskó, D. Henderson, R.S. Eisenberg, D. Gillespie, and W. Nonner. Ionic selectivity in L-type calcium channels by electrostatics and hard-core repulsion. J. Ge, Physiol., 133(5):497–509, 2009. [WoS] 
  8. [7] F. Brezzi and M. Fortin. Mixed and Hybrid Finite Element Methods. Springer Verlag, New York, 1991. Zbl0788.73002
  9. [8] A. N. Brooks and T. J.R. Hughes. Streamline Upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 32(1˘20133):199 – 259, 1982. [Crossref] Zbl0497.76041
  10. [9] M. J. Caterina, M. A. Schumacher, M. Tominaga, T. A. Rosen, J. D. Levine, and D. Julius. The capsaicin receptor: a heatactivated ion channel in the pain pathway. Nature, 389(6653):816–824, October 1997. 
  11. [10] D. P. Chen and R. S. Eisenberg. Charges, currents, and potentials in ionic channels of one conformation. Biophysical journal, 64(5):1405–1421, 1993. [Crossref] 
  12. [11] D. P. Chen and R. S. Eisenberg. Flux, coupling, and selectivity in ionic channels of one conformation. Biophysical journal, 65:727–746, 1993. [Crossref] 
  13. [12] D.P. Chen, R.S. Eisenberg, J.W. Jerome, and C.W. Shu. Hydrodynamic model of temperature change in open ionic channels. Biophysical Journal, 69(6):2304 – 2322, 1995. [Crossref] 
  14. [13] J Douglas and J. E. Roberts. Global estimates for mixed methods for second order elliptic equations. Math. Comp., 44:39–52, 1985. Zbl0624.65109
  15. [14] R. S. Eisenberg. Ions in fluctuating channels: transistors alive. Fluctuations and Noise Letters, 11:76–96, 2005. 
  16. [15] G. B. Ermentrout and D. H. Terman. Mathematical Foundations of Neuroscience. Springer, 2010. Zbl1320.92002
  17. [16] H. L. Fields. Pain. McGraw-Hill, New York, 1987. 
  18. [17] K. Hess, U. Ravaioli, N.R. Aluru, M. Gupta, and R.S. Eisenberg. Simulation of biological ionic channels by technology computer-aided design. In Computational Electronics, 2000. Book of Abstracts. IWCE Glasgow 2000. 7th InternationalWorkshop on, pages 70–, May 2000. 
  19. [18] K. Hess, U. Ravaioli, M. Gupta, N. Aluru, van der Straaten, and R. S. Eisenberg. Simulation of biological ionic channels by technology computer-aided design. VLSI Design, 13(1-4):179–187, 2001. [Crossref] 
  20. [19] B. Hille. Ionic Channels of Excitable Membranes. Sinauer Associates, Inc., Sunderland, MA, 2001. 
  21. [20] A.L. Hodgkin and A.F. Huxley. Currents carried by sodium and potassium ions through the membrane of the giant axon of loligo. Journal of Physiology, 116:449–472, 1952. [Crossref] 
  22. [21] A.L. Hodgkin and A.F. Huxley. A quantitative description of membrane current’and its application to conduction and excitation in nerve. Journal of Physiology, 117:500–544, 1952. [Crossref] 
  23. [22] S. Hu and K. Hess. An application of the recombination and generation theory by Shockley, Read and Hall to biological ion channels. Journal of Computational Electronics, 4(1-2):153–156, 2005. [Crossref] 
  24. [23] J.W. Jerome. Analysis of charge transport. Springer-Verlag, 1996. 
  25. [24] J.W. Jerome. Analytical approaches to charge transport in a moving medium. Transport Theory and Statistical Physics, 31:333–366, 2002. Zbl1032.35166
  26. [25] J.W. Jerome and R. Sacco. Global weak solutions for an incompressible charged fluid with multi-scale couplings: Initialboundary value problem. Nonlinear Analysis, 71:e2487–e2497, 2009. 
  27. [26] A. Juengel. Transport Equations for Semiconductors. Number 773 in Lecture Notes in Physics. Springer, Berlin, 2009. 
  28. [27] J. P. Keener and J. Sneyd. Mathematical Physiology. Springer, New York, 1998. Zbl0913.92009
  29. [28] T. Kerkhoven and Y. Saad. On acceleration methods for coupled nonlinear elliptic systems. Numerische Mathematik, 60:525–548, 1992. [Crossref] Zbl0724.65095
  30. [29] F.Manganini. Thermo-electro-chemical modeling and simulation of ion transport in nanochannels. Master’s thesis, Politecnico di Milano, 2013. https://www.politesi.polimi.it/bitstream/10589/88365/1/Tesi_LM_770306_Fabio_Manganini.pdf. 
  31. [30] P.A. Markowich. The Stationary Semiconductor Device Equations. Computational Microelectronics. Springer-Verlag, 1986. 
  32. [31] P.A. Markowich, C.A. Ringhofer, and C. Schmeiser. Semiconductor Equations. Springer-Verlag, 1990. Zbl0765.35001
  33. [32] R.S. Muller and T.I. Kamins. Device Electronics for Integrated Circuits. Wiley, 2002. 
  34. [33] S. Pandey, A. Bortei-Doku, and M. H. White. Simulation of biological ion channels with technology computer-aided design. Computer Methods and Programs in Biomedicine, 85(1):1 – 7, 2007. 
  35. [34] J.E. Roberts and J.M. Thomas. Mixed and hybrid methods. In P.G. Ciarlet and J.L. Lions, editors, Finite Element Methods, Part I. North-Holland, Amsterdam, 1991. Vol.2. Zbl0875.65090
  36. [35] H. G. Roos, M. Stynes, and L. Tobiska. Robust Numerical Methods for Singularly Perturbed Differential Equations. Springer- Verlag Berlin Heidelberg, 2008. Zbl1155.65087
  37. [36] I. Rubinstein. Electrodiffusion of Ions. SIAM, Philadelphia, PA, 1990. 
  38. [37] M. Rudan, A. Gnudi, and W. Quade. A generalized approach to the hydrodynamic model of semiconductor equations. In G. Baccarani, editor, Process and Device Modeling for Microelectronics, chapter 2, pages 109–154. Elsevier, 1993. 
  39. [38] R. Sacco and F. Saleri. Stabilized mixed finite volume methods for convection-diffusion problems. East West J. Numer.Math., 5(4):291–311, 1997. Zbl0895.65050
  40. [39] D.L. Scharfetter and H.K. Gummel. Large signal analysis of a silicon Read diode oscillator. IEEE Trans. Electron Devices, ED-16(1):64–77, 1969. [Crossref] 
  41. [40] M. Schmuck. Analysis of the Navier-Stokes-Nernst-Planck-Poisson system. Mathematical Models and Methods in Applied Sciences, 19(6):993–1015, 2009. Zbl1229.35215
  42. [41] S. Selberherr. Analysis and Simulation of Semiconductor Devices. Springer-Verlag, 1984. 
  43. [42] C.W. Shu and S. Osher. Eflcient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics, 77(2):439 – 471, 1988. [Crossref] Zbl0653.65072
  44. [43] C.W. Shu and S. Osher. Eflcient implementation of essentially non-oscillatory shock-capturing schemes, {II}. Journal of Computational Physics, 83(1):32 – 78, 1989. [Crossref] Zbl0674.65061
  45. [44] L. Vay, C. Gu, and P.A. McNaughton. The thermo-trp ion channel family: properties and therapeutic implications. British Journal of Pharmacology, 165(4):787–801, 2012. [WoS][Crossref] 
  46. [45] I. Vlassiouk, S. Smirnov, and Z.S. Siwy. Nanofluidic ionic diodes. comparison of analytical and numerical solutions. ACS Nano, 2(8):1589–1602, 2008. [WoS][Crossref] 
  47. [46] T. Voets, G. Droogmans, U. Wissenbach, A. Janssens, V. Flockerzi, and B. Nilius. The principle of temperature-dependent gating in cold- and heat-sensitive TRP channels. Nature, 430(7001):748–754, 2004. 

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