Mathematical Models for Sensing Devices Constructed out of Artificial Cell Membranes

• Autorzy: William Hoiles , Vikram Krishnamurthy , Bruce Cornell
• Języki publikacji: EN

Abstrakty

EN

This paper presents a review of ion channel based biosensors with a focus on the mathematical modeling of the stateof- the-art ion channel switch (ICS) biosensor and the novel cation specific (CS) sensor. The characteristics of the analyte present in the electrolyte, the ionic transport of chemical species, and the bioelectronic interface present in the ICS biosensor and CS sensor are modeled using ordinary and partial differential equations. The methodologies presented are important for modeling similar bioelectronic devices. Biosensors have applications in the fields of medicine, engineering, and biology. The recent emergence of biomimetically engineered nanomachine devices capable of measuring femto-molar concentrations of chemical species and the detection of channelopathies (ion channel disorders) makes them an attractive tool due to their high sensitivity and rapid detection rates. Beyond the continuum models used for the ICS and CS sensors, we present methods by which firstprinciple approaches such as molecular dynamics combined with stochastic methodologies can be used to obtain macrolevel parameters such as conductance and chemical reaction rates.

Słowa kluczowe

EN

Ion Channel Biosensors; Molecular Dynamics; Stochastic Dynamics; Poisson-Nernst-Planck; Disease Diagnosis and Medicine

Kategorie tematyczne

• 93C20: Systems governed by partial differential equations
• 65N06: Finite difference methods
• 93C70: Time-scale analysis and singular perturbations
• 34L30: Nonlinear ordinary differential operators

• Wydawca: De Gruyter Open
• Czasopismo: Nanoscale Systems: Mathematical Modeling, Theory and Applications
• Rocznik: 2012
• Tom: 1
• Strony: 143-171

Daty

otrzymano

2012-10-29

poprawiono

2012-12-06

zaakceptowano

2012-12-09

online

2012-12-28

Twórcy

autor

William Hoiles

• Department of Electrical and Computer Engineering,
  University of British Columbia, 5500-2332 Main Mall,
  V6T 1Z4 Vancouver, Canada

autor

Vikram Krishnamurthy

• Department of Electrical and Computer Engineering,
  University of British Columbia, 5500-2332 Main Mall,
  V6T 1Z4 Vancouver, Canada

autor

Bruce Cornell

• DSurgical Diagnostics Ltd.,
  St. Leonards, NSW 2065 Melbourne, Australia

Bibliografia

• M. Ahrens, P. Bertin, A. Gaustad, D. Georganopoulou, M. Wunder, G. Blackburn, and et al. Spectroscopic and redox properties of amine-functionalized K2[OsII(bpy)(CN)4] complexes. Dalton Trans. 40, 1732 (2011).
• T. Allen, O. Andersen, and B. Roux. Molecular dynamics - potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels. Biophysical Chemistry 124, 251 (2006).
• P. Amestoy, I. Duff, and J. L’Excellent. Multifrontal parallel distributed symmetric and unsymmetric solvers. Computer Methods in Applied Mechanics and Engineering 184, 501 (2000).
• S. Barnes. Handbook of biological effects of electromagnetic fields. Biological and medical aspects of electromagnetic fields. CRC Press (2007).
• S. Berneche and B. Roux. A microscopic view of ion conduction through the K+ channel. Proceedings of the National Academy of Science of the United States of America 100, 8644 (2003).
• P. Bertin, M. Ahrens, K. Bhavsar, D. Georganopoulou, M. Wunder, G. Blackburn, and et al. Ferrocene and Maleimidefunctionalized disulfide scaffolds for self-assembled monolayers on gold. Organic Letters 12, 3372 (2010). [Crossref][PubMed]
• J. Brody, P. Yager, R. Goldstein, and R. Austin. Biotechnology at low Reynolds numbers. Biophysical Journal 71, 3430 (1996).
• J. Bufler, S. Kahlert, S. Tzartos, A. Maelicke, and C. Franke. Activation and blockade of mouse muscle nicotinic channels by antibodies directed against the binding site of the acetylcholine receptor. Journal of Physiology-London 492 (1996).
• R. Coalson and M. Kurnikova. Poisson-Nernst-Planck theory of ion permeation through biological channels. In S. H. Chung, O. Andersen, and V. Krishnamurthy, editors, Biological Membrane Ion Channels, 449, New York, Springer-Verlag (2007).
• B. Cornell. Membrane-based biosensors. In Frances S. Ligler and Chris A. Rowe Taitt, editors, Optical Biosensors Present and Future, Chapter 15, pages 457–495, Elsevier (2002).
• B. Cornell, V. Braach-Maksvytis, L. King, P. Osman, B. Raguse, L. Wieczorek, and et al. A biosensor that uses ion-channel switches. Letters to Nature 387, 580 (1997).
• B. Cornell, G. Krishna, P. Osman, R. Pace, and L. Wieczorek. Tethered bilayer lipid membranes as a support for membrane-active peptides. Biochemical Society Transactions 29, 613 (2001). [Crossref][PubMed]
• B. Corry, S. Kuyucak, and S. Chung. Dielectric self-energy in Poisson-Boltzmann and Poisson-Nernst-Planck models of ion channels. Biophysical Journal 84, 3594 (2003). [PubMed][Crossref]
• J. Elliott, D. Needham, J. Dilger, and D. Haydon. The effects of bilayer thickness and tension on gramicidin singlechannel lifetime. Biochimica et Biophysica Acta (BBA) - Biomembranes 735, 95 (1983).
• P. Fromherz. Neuroelectronics interfacing: Semiconductor chips with ion channels, nerve cells and brain. In R. Weise, editor, Nanoelectronics and Information Technology, pages 781–810, Wiley-VCH, Berlin (2003).
• D. Georganopoulou. Reagentless electrochemical biosensors for clinical diagnostics. In 41st Annual Oak Ridge Conference, Baltimore, April 2009. Frontiers in Clinical Diagnostics.
• D. Gordon, V. Krishnamurthy, and S. Chung. Generalized Langevin models of molecular dynamics simulations, with applications to ion channels. Journal of Chemical Physics 131, 111 (2009).
• P. Graf, M. Kurnikova, R. Coalson, and A. Nitzan. Comparison of dynamic lattice Monte Carlo simulations and the dielectric self-energy Poisson-Nernst-Planck continuum theory for model ion channels. The Journal of Physical Chemistry B 108, 2006 (2004). [Crossref]
• G. Harms, G. Orr, M. Montal, B. Thrall, S. Colson, and H. Lu. Probing conformational changes of gramicidin ion channels by single-molecule Patch-Clamp Fluorescence microscopy. Biophysical Journal 85, 1826 (2003). [Crossref][PubMed]
• S. Heysel, H. Vogel, M. Sanger, and H. Sigrist. Covalent attachment of functionalized lipid bilayers to planar waveguides for measuring protein binding to biomimetic membranes. Protein Science 4, 2532 (1995). [Crossref]
• B. Hille. Ion Channels of Excitable Membranes. Sinauer Associates, Sunderland, MA (2001).
• T. Horng, T. Lin, C. Liu, and B. Eisenberg. Pnp equations with steric effects: A model of ion flow through channels. The Journal of Physical Chemistry B 116, 11422 (2012). [Crossref]
• S. Howorka, J. Nam, H. Bayley, and D. Kahne. Stochastic detection of monovalent and bivalent protein-ligand interactions. Angew. Chem. Int. Ed. 43, 842 (2004). [Crossref]
• W. Im and B. Roux. Ion permeation and selectivity of OmpF Porin: A theoretical study based on molecular dynamics, Brownian Dynamics, and continuum electrodiffusion theory. Journal of Molecular Biology 322, 851 (2002).
• M. Kato. Numerical analysis of the Nernst-Planck-Poisson system. Journal of Theoretical Biology 177, 299 (1995).
• H. Khalil. Nonlinear Systems. Prentice Hall (2002).
• M. Kilic, M. Bazant, and A. Ajdari. Steric effects in the dynamics of electrolytes at large applied voltages. I. double-layer charging. Phys. Rev. E 75, 021502 (2007).
• M. Kilic, M. Bazant, and A. Ajdari. Steric effects in the dynamics of electrolytes at large applied voltages. II. modified Poisson-Nernst-Planck equations. Phys. Rev. E 75, 021503, (2007).
• T. Kok, L. Mickan, and C. Burrell. Routine diagnosis of seven respiratory viruses and Mycoplasma pneumoniae by enzyme immunoassay. Journal of Virological Methods 50, 87 (1994).
• V. Krishanmurthy, S. Monfared, and B. Cornell. Ion-channel biosensors - Part I: Construction, operation and clinical studies. IEEE Transactions Nanotechnology, (Special Issue on Nanoelectronic Interface to Biomolecules and Cells) 9 303 (2010).
• V. Krishanmurthy, S. Monfared, and B. Cornell. Ion-channel biosensors - Part II: Dynamic modeling, analysis and statistical signal processing. IEEE Transactions Nanotechnology, (Special Issue on Nanoelectronic Interface to Biomolecules and Cells) 9, 313 (2010). [Crossref]
• V. Krishnamurthy and B. Cornell. Engineering aspects of biological ion channels-from biosensors to computational models for permeation. Protoplasma 249, 3 (2012).
• M. Kurnikova, R. Coalson, P. Graf, and A. Nitzan. A lattice relaxation algorithm for three-dimensional Poisson- Nernst-Planck theory with application to ion transport through the gramicidin A channel. Biophysical Journal 76, 642 (1999). [PubMed][Crossref]
• R. Levine. Molecular reaction dynamics. Cambridge University Press (2005).
• K. Lieberman, G. Cherf, M. Doody, F. Olasagasti, Y. Kolodji, and M. Akeson. Processive replication of single DNA molecules in a nanopore catalyzed by phi29 DNA Polymerase. Journal of the American Chemical Society 132, 17961 (2010).
• F. Ligler, T. Fare, E. Seib, J. Smuda, A. Singh, P. Ahl, and et al. Fabrication of key components of a receptor-based biosensor. Med. Instrumentation 22, 247 (1988).
• F. Ligler, G. Anderson, P. Davidson, R. Foch, J. Ives, K. King, and et al. Remote sensing using an airborne biosensor. Environmental Science & Technology 32, 2461 (1998). [Crossref]
• A. Liu, Q. Zhao, and X. Guan. Stochastic nanopore sensors for the detection of terrorist agents: Current status and challenges. Analytica Chimica Acta 675, 106 (2010).
• A. Lomize, V. Orekhov, and A. Arsen’ev. Refinement of the spatial structure of the gramicidin a ion channel. Bioorg Khim 18, 182 (1992).
• A. Lopatin, E. Makhina, and C. Nichols. The mechanism of inward rectification of potassium channels: long-pore plugging by cytoplasmic polyamines. Journal of General Physiology 106, 923 (1995). [Crossref]
• C. Lopreore, T. Bartol, J. Coggan, D. Keller, G. Sosinsky, M. Ellisman, and et al. Computational modeling of threedimensional electrodiffusion in biological systems: Application to the node of Ranvier. Biophysical Journal 95, 2624 (2008). [Crossref]
• B. Lu, Y. Zhou, G. Huber, S. Bond, M. Holst, and J. McCammon. Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution. The Journal of Chemical Physics 127.
• B. Lu, M. Holst, J. McCammon, and Y. Zhou. Poisson-Nernst-Planck equations for simulating biomolecular diffusionreaction processes I: Finite element solutions. Journal of Computational Physics 229, 6979 (2010).
• H. Lu. Probing single-molecule protein conformational dynamics. Accounts of Chemical Research 38, 557 (2005). [PubMed][Crossref]
• X. Lu, A. Ottova, and H. Tien. Biophysical aspects of agar-gel supported bilayer lipid membranes: a new method for forming and studying planar bilayer lipid membranes. Bioelectrochemistry and Bioenergetics 39, 285 (1996). [Crossref]
• A. MacGillivray. Nernst-Planck equations and the electroneutrality and Donnan equilibrium assumptions. Journal of Chemical Physics 48, 2903 (1967).
• A. MacGillivray and D. Hare. Applicability of Goldman’s constant field assumption to biological systems. Journal of Theoretical Biology 25, 113 (1969). [Crossref]
• C. Maffeo, S. Bhattacharya, J. Yoo, D. Wells, and A. Aksimentiev. Modeling and simulation of ion channels. Chemical Reviews, Accepted (2012).
• A. Mamonov, R. Coalson, A. Nitzan, and M. Kurnikova. The role of the dielectric barrier in narrow biological channels: A novel composite approach to modeling single-channel currents. Biophysical Journal 84, 3646 (2003). [Crossref][PubMed]
• A. Mamonov, M. Kurnikova, and R. Coalson. Diffusion constant of K+ inside gramicidin A: A comparative study of four computational methods. Biophysical Chemistry 124, 268 (2006).
• G. Miloshevsky and P. Jordan. Gating gramicidin channels in lipid bilayers: Reaction coordinates and the mechanism of dissociation. Biophysical Journal 86, 92 (2004). [PubMed][Crossref]
• G. Miloshevsky and P. Jordan. The open state gating mechanism of gramicidin a requires relative opposed monomer rotation and simultaneous lateral displacement. Structure 14, 1241 (2006). [Crossref][PubMed]
• N. Modi, M. Winterhalter, and U. Kleinekathofer. Computational modeling of ion transport through nanopores Nanoscale 4, 6166 (2012). [PubMed]
• S. Monfared, V. Krishnamurthy, and B. Cornell. A molecular machine biosensor: Construction, predictive models, and experimental studies. Biosensors and Bioelectronics 34, 261 (2012). [Crossref]
• Y. Mori and C. Peskin. A numerical method for cellular electrophysiology based on the electrodiffusion equations with internal boundary conditions at internal membranes. Communications in Applied Mathematics and Computational Science 4, 85 (2009).
• Y. Mori, J. Jerome, and C. Peskin. A three-dimensional model of cellular electrical activity. Bulletin of the Institute of Mathematics, Academia Sinica 2, 367 (2007).
• C. Naumann, W. Knoll, and C. Frank. Hindered diffusion in polymer-tethered membranes: A monolayer study at the air-water interface. Biomacromolecules 2, 1097 (2001). [Crossref][PubMed]
• R. Naumann, E. Schmidt, A. Jonczyk, K. Fendler, B. Kadenbach, T. Liebermann, and et al. The peptide-tethered lipid membrane as a biomimetic system to incorporate cytochrome c oxidase in a functionally active form. Biosensors and Bioelectronics 14, 651 (1999). [Crossref]
• E. Neher. Molecular biology meets microelectronics. Nature Biotechnology 19, (2001). [PubMed][Crossref]
• F. Olasagasti, K. Lieberman, S. Benner, G. Cherf, J. Dahl, D. Deamer, and et al. Replication of individual DNA molecules under electronic control using a protein nanopore. Nature Nanotechnology 5, 798 (2010). [Crossref][PubMed]
• M. Pabst, G. Wrobel, S. Ingebrandt, F. Sommerhage, and A. Offenhäusser. Solution of the Poisson-Nernst-Planck equations in the cell-substrate interface. The European Physical Journal E: Soft Matter and Biological Physics 24, 1 (2007). [Crossref]
• M. Peterman, J. Ziebarth, O. Braha, H. Bayley, H. Fishman, and D. Bloom. Ion channels and lipid bilayer membranes under high potentials using microfabricated apertures. Biomedical Microdevices 4, 236 (2002).
• A. Plant. Supported hybrid bilayer membranes as rugged cell membrane mimics. Langmuir 15, 5128 (1999). [Crossref]
• A. Ramos, A. Raizer, and J. Marques. A new computational approach for electrical analysis of biological tissues. Bioelectrochemistry 59, 73 (2003).
• A. Ring. Influence of ion occupancy and membrane deformation on gramicidin a channel stability in lipid membranes. Biophysical Journal 61, 1306 (1992). [Crossref][PubMed]
• B. Roux, T. Allen, S. Bemeche, and W. Im. Theoretical and computational models of biological ion channels. Quarterly Reviews of Biophysics 37, 15 (2004). [PubMed][Crossref]
• I. Rubinstein. Electrodiffusion of Ions. SIAM Studies in Applied Mathematics (1990).
• E. Sackmann. Supported membranes: Scientific and practical applications. Science 271, 43 (1996).
• J. Sandblom, J. Galvanovskis, and B. Jilderos. Voltage-dependent formation of gramicidin channels in lipid bilayers. Biophysical Journal 81, 827 (2001). [Crossref][PubMed]
• M. Schumaker, R. Pomes, and B. Roux. Framework model for single proton conduction through gramicidin. Biophysical Journal 80, 12 (2001). [Crossref][PubMed]
• Z. Schuss, B. Nadler, and R. S. Eisenberg. Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model. Phys. Rev. E 64, 036116 (2001).
• Z. Schuss, B. Nadler, and S. Eisenberg. Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model. Phys. Rev. E 64, 036116 (2001).
• S. Selberherr. Analysis and simulation of semiconductor devices. New York: Springer-Verlag (1984).
• F. Separovic and B. Cornell. Gated ion channel-based biosensor device. In S. H. Chung, O. Andersen, and V. Krishnamurthy, editors, Biological Membrane Ion Channels, pages 595–621. New York: Springer-Verlag (2007).
• J. Silva, H. Pan, D. Wu, A. Nekouzadeh, K. Decker, J. Cui, and et al. A multiscale model linking ion-channel molecular dynamics and electrostatics to the cardiac action potential. Proceedings of the National Academy of Science of the United States of America 106, 11102 (2009).
• C. Song and B. Corry. Testing the applicability of Nernst-Planck theory in ion channels: Comparisons with Brownian Dynamics simulations. PLoS ONE 6, e21204 (2011).
• C. Steinem, A. Janshoff, W. Ulrich, M. Sieber, and H. Galla. Impedance analysis of supported lipid bilayer membranes: a scrutiny of different preparation techniques. Biochimica et Biophysica Acta. 1279, 169 (1996).
• D. Stoddart, A. Heron, J. Klingelhoefer, E. Mikhailova, G. Maglia, and H. Bayley. Nucleobase recognition in ssDNA at the central constriction of the α-Hemolysin Pore. Nano Letters 10, 3633 (2010). [PubMed][Crossref]
• B. Stone, J. Burrows, S. Schepetiuk, G. Higgins, A. Hampson, R. Shaw, and et al. Rapid detection and simultaneous subtype differentiation of influenza a viruses by real time pcr. Journal of Virological Methods 117, 103 (2004). [PubMed][Crossref]
• T. Stora, J. Lakey, and H. Vogel. Ion-channel gating in transmembrane receptor proteins: Functional activity in tethered lipid membranes. Angewandte Chemie International Edition 38, 389 (1999). [Crossref]
• E. Toro-Goyco, A. Rodriguez, and J. Castillo. Detection of anti-insulin antibodies with a new electrical technique: Lipid membrane conductometry. Biochemical and Biophysical Research Communications 23, 341 (1966). [Crossref]
• S. Wanasundara, V. Krishnamurthy, and S. Chung. Free energy calculations of gramicidin dimer dissociation. The Journal of Physical Chemistry B 115, 3765 (2011).
• G. Woodhouse, L. King, L. Wieczorek, P. Osman, and B. Cornell. The ion channel switch biosensor. Journal of Molecular Recognition 12, 328 (1999). [Crossref]
• P. Yager. Development of membrane-based biosensors: measurement of current from photocycling bacteriorhodopsin on patch clamp electrodes. Biotechnological Applications of Lipid Microstructures, 238.
• S. Zaˇitsev, S. Dzekhitser, and V. Zubov. Polymer monolayers with immobilized bacteriorhodopsin. Bioorg. Khim. 14, 850 (1988).
• Q. Zheng and G. Wei. Poisson-Boltzmann-Nernst-Planck model. The Journal of Chemical Physics 134, 17 (2011).
• Q. Zheng, D. Chen, and G. Wei. Second-order Poisson-Nernst-Planck solver for ion transport. Journal of Computational Physics 230, 5239 (2011).

Identyfikatory

DOI

10.2478/nsmmt-2012-0009