[1] Abidor, I., Arakelyan, V., Chernomordik, L., Chizmadzhev, Y., Pastushenko, V., and Tarasevich, M. 1979. Electric breakdown of bilayer lipid membranes: I. The main experimental facts and their qualitative discussion. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 104, 37–52.CrossRefGoogle Scholar

[2] Abolfath-Beygi, M., and Krishnamurthy, V. 2014. Biosensor arrays for estimating molecular concentration in fluid flows. IEEE Transactions on Signal Processing, 62(1), 239–251.CrossRefGoogle Scholar

[3] Abolfath-Beygi, M., Krishnamurthy, V., and Cornell, B. 2013. Multiple surface-based biosensors for enhanced molecular detection in fluid flow systems. IEEE Sensors Journal, 13(4), 1265–1273.CrossRefGoogle Scholar

[4] Ackerberg, R., Patel, R., and Gupta, S. 1978. The heat/mass transfer to a finite strip at small Péclet numbers. Journal of Fluid Mechanics, 86(1), 49–65.CrossRefGoogle Scholar

[5] Adamczyk, Z., and Warszyński, P. 1996. Role of electrostatic interactions in particle adsorption. Advances in Colloid and Interface Science, 63, 41–149.CrossRefGoogle Scholar

[6] Aernouts, J., Couckuyt, I., Crombecq, K., and Dirckx, J. 2010. Elastic characterization of membranes with a complex shape using point indentation measurements and inverse modelling. International Journal of Engineering Science, 48(6), 599–611.CrossRefGoogle Scholar

[7] Afonin, S., Grage, S., Ieronimo, M., Wadhwani, P., and Ulrich, A. 2008. Temperaturedependent transmembrane insertion of the amphiphilic peptide PGLa in lipid bilayers observed by solid state 19F NMR spectroscopy. Journal of the American Chemical Society, 130(49), 16512–16514.CrossRefGoogle Scholar

[8] Aguilella-Arzo, M., Aguilella, V., and Eisenberg, R. 2005. Computing numerically the access resistance of a pore. European Biophysics Journal, 34(4), 314–322.CrossRefGoogle ScholarPubMed

[9] Al-Sakere, B., André, F., Bernat, C., et al. 2007. Tumor ablation with irreversible electroporation. PLoS One, 2(11), e1135.CrossRefGoogle ScholarPubMed

[10] Alberts, B. 2008. Molecular Biology of the Cell. Garland Science.Google Scholar

[11] Allagui, A., Freeborn, T., Elwakil, A., and Maundy, B. 2016. Reevaluation of performance of electric double layer capacitors from constant-current charge/discharge and cyclic voltammetry. Scientific Reports, 6.Google ScholarPubMed

[12] Allen, T., Andersen, O., and Roux, B. 2006. Molecular dynamics –potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels. Biophysical Chemistry, 124(3), 251–267.CrossRefGoogle ScholarPubMed

[13] Als-Nielsen, J., and Kjaer, K. 1989. X-ray reflectivity and diffraction studies of liquid surfaces and surfactant monolayers. Pages 113–138 in Phase Transitions in Soft Condensed Matter. Springer.Google Scholar

[14] Amestoy, P., Duff, I., L'Excellent, J., and Koster, J. 2001. A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM Journal on Matrix Analysis and Applications, 23(1), 15–41.CrossRefGoogle Scholar

[15] Anderson, N., Richter, L., Stephenson, J., and Briggman, K. 2007. Characterization and control of lipid layer fluidity in hybrid bilayer membranes. Journal of the American Chemical Society, 129(7), 2094–2100.CrossRefGoogle ScholarPubMed

[16] Andronesi, O., Pfeifer, J., Al-Momani, L., et al. 2004. Probing membrane protein orientation and structure using fast magic-angle-spinning solid-state NMR. Journal of Biomolecular NMR, 30(3), 253–265.Google ScholarPubMed

[17] Ansari, A. 2000. Mean first passage time solution of the Smoluchowski equation: Application to relaxation dynamics in myoglobin. Journal of Chemical Physics, 112(5), 2516–2522.CrossRefGoogle Scholar

[18] Appleby, A. 2005. Electron transfer reactions with and without ion transfer. Pages 175–301 in Modern Aspects of Electrochemistry. Springer.Google Scholar

[19] Archer, A., and Evans, R. 2013. Relationship between local molecular field theory and density functional theory for non-uniform liquids. Journal of Chemical Physics, 138(1), 014502.CrossRefGoogle ScholarPubMed

[20] Ashcroft, F. 1999. Ion Channels and Disease. Academic Press.Google ScholarPubMed

[21] Asphahani, F., and Zhang, M. 2007. Cellular impedance biosensors for drug screening and toxin detection. Analyst, 132, 835–841.CrossRefGoogle ScholarPubMed

[22] Asphahani, F., Thein, M., Veiseh, O., et al. 2008. Influence of cell adhesion and spreading on impedance characteristics of cell-based sensors. Biosensors and Bioelectronics, 23(8), 1307–1313.CrossRefGoogle ScholarPubMed

[23] Atkins, A., Wyborn, N., Wallace, A., et al. 2000. Structure-function relationships of a novel bacterial toxin, hemolysin E: The role of αG. Journal of Biological Chemistry, 275(52), 41150–41155.CrossRefGoogle Scholar

[24] Baba, T., Minamikawa, H., Hato, M., and Handa, T. 2001. Hydration and molecular motions in synthetic phytanyl-chained glycolipid vesicle membranes. Biophysical Journal, 81(6), 3377–3386.CrossRefGoogle ScholarPubMed

[25] Baker, M., Maloy, W., Zasloff, M., and Jacob, L. 1993. Anticancer efficacy of Magainin2 and analogue peptides. Cancer Research, 53(13), 3052–3057.Google ScholarPubMed

[26] Barnett, A. 1990. The current-voltage relation of an aqueous pore in a lipid bilayer membrane. Biochimica et Biophysica Acta, Biomembranes, 1025(1), 10–14.CrossRefGoogle Scholar

[27] Barnett, A., and Weaver, J. 1991. Electroporation: A unified, quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes. Bioelectrochemistry and Bioenergetics, 25(2), 163–182.CrossRefGoogle Scholar

[28] Barroso, M., De-Los-Santos-Álvarez, N., Delerue-Matos, C., and Oliveira, M. 2011. Towards a reliable technology for antioxidant capacity and oxidative damage evaluation: Electrochemical (bio) sensors. Biosensors and Bioelectronics, 30(1), 1–12.CrossRefGoogle ScholarPubMed

[29] Bayley, H., and Cremer, P. 2001. Stochastic sensors inspired by biology. Nature, 413(6852), 226.CrossRefGoogle ScholarPubMed

[30] Bazant, M., Kilic, M., Storey, B., and Ajdari, A. 2009. Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions. Advances in Colloid and Interface Science, 152, 48–88.CrossRefGoogle ScholarPubMed

[31] Bazant, M., Storey, B., and Kornyshev, A. 2011. Double layer in ionic liquids: Overscreening versus crowding. Physical Review Letters, 106(4), 046102.CrossRefGoogle ScholarPubMed

[32] Beard, D., and Qian, H. 2008. Chemical Biophysics: Quantitative Analysis of Cellular Systems. Cambridge University Press.CrossRefGoogle Scholar

[33] Beebe, S., Fox, P., Rec, L., Willis, L., and Schoenbach, K. 2003. Nanosecond, high-intensity pulsed electric fields induce apoptosis in human cells. FASEB Journal, 17(11), 1493–1495.Google ScholarPubMed

[34] Belytschko, T., Liu, W., Moran, B., and Elkhodary, K. 2013. Nonlinear Finite Elements for Continua and Structures. John Wiley & Sons.Google Scholar

[35] Bennett, D., and Tieleman, P. 2014. The importance of membrane defects? Lessons from simulations. Accounts of Chemical Research, 47(8), 2244–2251.CrossRefGoogle ScholarPubMed

[36] Bennett, W., and Tieleman, D. 2011. Water defect and pore formation in atomistic and coarse-grained lipid membranes: Pushing the limits of coarse graining. Journal of Chemical Theory and Computation, 7, 2981–2988.CrossRefGoogle ScholarPubMed

[37] Bennett, W., MacCallum, J., and Tieleman, D. 2009. Thermodynamic Analysis of the effect of cholesterol on dipalmitoylphosphatidylcholine lipid membranes. Journal of the American Chemical Society, 131, 1972–1978.CrossRefGoogle ScholarPubMed

[38] Bennett, W., Sapay, N., and Tieleman, D. 2014. Atomistic simulations of pore formation and closure in lipid bilayers. Biophysical Journal, 106, 210–214.CrossRefGoogle ScholarPubMed

[39] Berendsen, H. 2007. Simulating the Physical World: Hierarchical Modeling from Quantum Mechanics to Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar

[40] Berendsen, H., Postma, J., Gunsteren, W., DiNola, A., and Haak, J. 1984. Molecular dynamics with coupling to an external bath. Journal of Chemical Physics, 81(8), 3684–3690.CrossRefGoogle Scholar

[41] Berendsen, H., Spoel, D., and Drunen, R. 1995. GROMACS: A message-passing parallel molecular dynamics implementation. Computer Physics Communications, 91(1–3), 43–56.CrossRefGoogle Scholar

[42] Berkowitz, M. 2009. Detailed molecular dynamics simulations of model biological membranes containing cholesterol. Biochimica et Biophysica Acta, Biomembranes, 1788(1), 86–96.CrossRefGoogle ScholarPubMed

[43] Berneche, S., and Roux, B. 2003. A microscopic view of ion conduction through the K+ channel. Proceedings of the National Academy of Sciences of the United States of America, 100(15), 8644–8648.CrossRefGoogle ScholarPubMed

[44] Bertsekas, D. 1999. Nonlinear Programming. Athena Scientific.Google Scholar

[45] Billingsley, P. 2013. Convergence of Probability Measures. John Wiley & Sons.Google Scholar

[46] Blau, A. 2013. Cell adhesion promotion strategies for signal transduction enhancement in microelectrode array in vitro electrophysiology: An introductory overview and critical discussion. Current Opinion in Colloid & Interface Science, 18(5), 481–492.CrossRefGoogle Scholar

[47] Blum, L., and Stell, G. 1976. Solution of Ornstein–Zernike equation for wall-particle distribution function. Journal of Statistical Physics, 15(6), 439–449.CrossRefGoogle Scholar

[48] Böckmann, R., Groot, B., Kakorin, S., Neumann, E., and Grubmüller, H. 2008. Kinetics, statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations. Biophysical Journal, 95(4), 1837–1850.CrossRefGoogle ScholarPubMed

[49] Bohner, M., and Kästner, J. 2012. An algorithm to find minimum free-energy paths using umbrella integration. Journal of Chemical Physics, 137(3), 034105.CrossRefGoogle ScholarPubMed

[50] Brian, A., and McConnell, H. 1984. Allogeneic stimulation of cytotoxic T cells by supported planar membranes. Proceedings of the National Academy of Sciences of the United States of America, 81(19), 6159–6163.CrossRefGoogle ScholarPubMed

[51] Brody, J., Yager, P., Goldstein, R., and Austin, R. 1996. Biotechnology at low Reynolds numbers. Biophysical Journal, 71(6), 3430–3441.CrossRefGoogle ScholarPubMed

[52] Bronzino, J., and Peterson, D. 2014. Biomedical Signals, Imaging, and Informatics. Boca Raton, FL: CRC Press.Google Scholar

[53] Brown, P., Hindmarsh, A., and Petzold, L. 1994. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM Journal on Scientific Computing, 15(6), 1467–1488.CrossRefGoogle Scholar

[54] Budvytyte, R., Valincius, G., Niaura, G., Voiciuk, V., Mickevicius, M., Chapman, H., Goh, H., Shekhar, P., Heinrich, F., and Shenoy, S. 2013. Structure and properties of tethered bilayer lipid membranes with unsaturated anchor molecules. Langmuir, 29(27), 8645–8656.CrossRefGoogle ScholarPubMed

[55] Bufler, J., Kahlert, S., Tzartos, S., Maelicke, A., and Franke, C. 1996. Activation and blockade of mouse muscle nicotinic channels by antibodies directed against the binding site of the acetylcholine receptor. Journal of Physiology, 492, 107–114.CrossRefGoogle ScholarPubMed

[56] Bunjes, N., Schmidt, E., Jonczyk, A., et al. 1997. Thiopeptide-supported lipid layers on solid substrates. Langmuir, 13(23), 6188–6194.CrossRefGoogle Scholar

[57] Burger, M. 2011. Inverse problems in ion channel modelling. Inverse Problems, 27, 083001.CrossRefGoogle Scholar

[58] Burgess, J., Rhoten, M., and Hawkridge, F. 1998. Cytochrome C oxidase immobilized in stable supported lipid bilayer membranes. Langmuir, 14(9), 2467–2475.Google Scholar

[59] Bussi, G., Donadio, D., and Parrinello, M. 2007. Canonical sampling through velocity rescaling. Journal of Chemical Physics, 126(1), 014101.CrossRefGoogle ScholarPubMed

[60] Cafiso, D. 1994. Alamethicin: A peptide model for voltage gating and protein-membrane interactions. Annual Review of Biophysics and Biomolecular Structure, 23(1), 141–165.CrossRefGoogle ScholarPubMed

[61] Campbell, I. 2012. Biophysical Techniques. Oxford University Press.Google Scholar

[62] Caponetto, R. 2010. Fractional Order Systems: Modeling and Control Applications. Vol. 72. World Scientific.

[63] Cappé, O., Moulines, E., and Rydén, T. 2005. Inference in Hidden Markov Models. Springer-Verlag.Google Scholar

[64] Casciola, M., Bonhenry, D., Liberti, M., Apollonio, F., and Tarek, M. 2014. A molecular dynamic study of cholesterol rich lipid membranes: Comparison of electroporation protocols. Bioelectrochemistry, 100, 11–17.CrossRefGoogle ScholarPubMed

[65] Catterall, W. 2012. Voltage-gated sodium channels at 60: Structure, function and pathophysiology. Journal of Physiology, 590(11), 2577–2589.CrossRefGoogle ScholarPubMed

[66] Cavanagh, J., Fairbrother, W., Palmer, A., and Skelton, N. 1995. Protein NMR Spectroscopy: Principles and Practice. Academic Press.Google Scholar

[67] Chang, D., and Reese, T. 1990. Changes in membrane structure induced by electroporation as revealed by rapid-freezing electron microscopy. Biophysical Journal, 58(1), 1.CrossRefGoogle ScholarPubMed

[68] Charalambous, K., and Wallace, B. 2011. NaChBac: The long lost sodium channel ancestor. Biochemistry, 50(32), 6742–6752.CrossRefGoogle Scholar

[69] Chee, C., Lee, H., and Lu, C. 2008. Using 3D fluid–structure interaction model to analyse the biomechanical properties of erythrocyte. Physics Letters A, 372(9), 1357–1362.CrossRefGoogle Scholar

[70] Chetwynd, A., Wee, C., Hall, B., and Sansom, M. 2010. The energetics of transmembrane helix insertion into a lipid bilayer. Biophysical Journal, 99(8), 2534 –2540.CrossRefGoogle ScholarPubMed

[71] Chinchar, V., Bryan, L., Silphadaung, U., et al. 2004. Inactivation of viruses infecting ectothermic animals by amphibian and piscine antimicrobial peptides. Virology, 323(2), 268–275.CrossRefGoogle ScholarPubMed

[72] Chong, S., Aichele, M., Meyer, H., Fuchs, M., and Baschnagel, J. 2007. Structural and conformational dynamics of supercooled polymer melts: Insights from first-principles theory and simulations. Physical Review E, 76(5), 051806.CrossRefGoogle ScholarPubMed

[73] Chung, S.H., Krishnamurthy, V., and Moore, J.B. 1991. Adaptive processing techniques based on hidden Markov models for characterising very small channel currents buried in noise and deterministic interferences. Philosophical Transactions of the Royal Society B: Biological Sciences, 334, 357–384.CrossRefGoogle Scholar

[74] Chung, S.H., Allen, T.W., and Kuyucak, S. 2002a. Conducting-state properties of the KcsA potassium channel from molecular and Brownian dynamics simulations. Biophysical Journal, 82, 628–645.CrossRefGoogle Scholar

[75] Chung, S.H., Allen, T.W., and Kuyucak, S. 2002b. Modeling diverse range of potassium channels with Brownian dynamics. Biophysical Journal, 83, 263–277.CrossRefGoogle Scholar

[76] Chung, S.H., Andersen, O., and Krishnamurthy, V. (eds). 2007. Biological Membrane Ion Channels: Dynamics, Structure and Applications. Springer-Verlag.CrossRefGoogle Scholar

[77] Cicero, G., Calzolari, A., Corni, S., and Catellani, A. 2011. Anomalous wetting layer at the Au (111) surface. Journal of Physical Chemistry Letters, 2(20), 2582–2586.CrossRefGoogle Scholar

[78] Cirac, A., Moiset, G., Mika, J., et al. 2011. The molecular basis for antimicrobial activity of pore forming cyclic peptides. Biophysical Journal, 100(10), 2422 –2431.CrossRefGoogle ScholarPubMed

[79] Cisneros, G., Wikfeldt, K., Ojamaäe, L., et al. 2016. Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions. Chemical Reviews, 116(13), 7501–7528.Google ScholarPubMed

[80] Coalson, R., and Kurnikova, M. 2007. Poisson–Nernst–Planck theory of ion permeation through biological channels. Pages 449–484 in Chung, S. H., Andersen, O., and Krishnamurthy, V. (eds.), Biological Membrane Ion Channels. Springer-Verlag.Google Scholar

[81] Cole, K. 1968. A Quantitiative Description of Membrane Current and Its Application to Conductance and Excitation in Nerve. Berkeley: University of California Press.Google Scholar

[82] Conlon, J., Mechkarska, M., et al. 2012. Host-defense peptides in skin secretions of the tetraploid frog Silurana epitropicalis with potent activity against methicillin-resistant Staphylococcus aureus (MRSA). Peptides, 37(1), 113–119.CrossRefGoogle Scholar

[83] Cornell, B. 2002. Membrane-based biosensors. Page 457 in Ligler, F.S., and Taitt, C.A.R. (eds), Optical Biosensors: Present and Future. Elsevier.Google Scholar

[84] Cornell, B., Braach-Maksvytis, V., King, L., et al. 1997. A biosensor that uses ion-channel switches. Nature, 387, 580–583.CrossRefGoogle ScholarPubMed

[85] Cornell, B., Krishna, G., Osman, P., Pace, R., and Wieczorek, L. 2001. Tethered bilayer lipid membranes as a support for membrane-active peptides. Biochemical Society Transactions, 29(4), 613–617.CrossRefGoogle ScholarPubMed

[86] Cornell, B., Scolan, G., Powl, A., Carnie, S., and Wallace, B. 2012. Comparative study of the bacterial sodium channel NaChBac function using patch clamp and AC impedance spectroscopy in a tethered membrane. Biophysical Journal, 102(3), 338a.CrossRefGoogle Scholar

[87] Coster, H., Chilcott, T., and Coster, A. 1996. Impedance spectroscopy of interfaces, membranes and ultrastructures. Bioelectrochemistry and Bioenergetics, 40(2), 79–98.CrossRefGoogle Scholar

[88] Cranfield, C., Cornell, B., Grage, S., et al. 2014. Transient potential gradients and impedance measures of tethered bilayer lipid membranes: Pore-forming peptide insertion and the effect of electroporation. Biophysical Journal, 106(1), 182–189.CrossRefGoogle ScholarPubMed

[89] Cruickshank, C., Minchin, R., Dain, A., and Martinac, B. 1997. Estimation of the pore size of the large-conductance mechanosensitive ion channel of Escherichia coli . Biophysical Journal, 73(4), 1925–1931.CrossRefGoogle ScholarPubMed

[90] Daillant, J., and Gibaud, A. 2008. X-Ray and Neutron Reflectivity: Principles and Applications. Vol. 770. Springer.Google Scholar

[91] Daily, M., Olsen, B., Schlesinger, P., Ory, D., and Baker, N. 2014. Improved coarse-grained modeling of cholesterol-containing lipid bilayers. Journal of Chemical Theory and Computation, 10(5), 2137–2150.CrossRefGoogle ScholarPubMed

[92] Das, S. 2011. Functional Fractional Calculus. Springer Science & Business Media.CrossRefGoogle Scholar

[93] De Rosa, M., Gamacorta, M.A., Nicolaus, B., Chappe, B., and Albrecht, P. 1983. Isoprenoid ethers; backbone of complex lipids of the archaebacterium Sulfolobus solfataricus . Biochimica et Biophysica Acta, 753, 249–256.Google Scholar

[94] de With, G. 2013. Liquid-State Physical Chemistry: Fundamentals, Modeling, and Applications. Vol. 1. Wiley.CrossRefGoogle Scholar

[95] DeBruin, K., and Krassowska, W. 1999a. Modeling electroporation in a single cell. I. Effects of field strength and rest potential. Biophysical Journal, 77(3), 1213–1224.Google Scholar

[96] DeBruin, K., and Krassowska, W. 1999b. Modeling electroporation in a single cell. II. Effects of ionic concentrations. Biophysical Journal, 77(3), 1225–1233.Google Scholar

[97] Dehghan, M. 2004. Numerical solution of the three-dimensional advection-diffusion equation. Applied Mathematics and Computation, 150, 5–19.CrossRefGoogle Scholar

[98] Delemotte, L., and Tarek, M. 2012. Molecular dynamics simulations of lipid membrane electroporation. Journal of Membrane Biology, 245(9), 531–543.CrossRefGoogle ScholarPubMed

[99] Deminsky, M., Eletskii, A., Kniznik, A., et al. 2013. Molecular dynamic simulation of transmembrane pore growth. Journal of Membrane Biology, 246(11), 821–831.CrossRefGoogle ScholarPubMed

[100] Deng, P., Lee, Y., Lin, R., and Zhang, T. 2012. Nonlinear electro-mechanobiological behavior of cell membrane during electroporation. Applied Physics Letters, 101(5), 053702.CrossRefGoogle Scholar

[101] Deniaud, A., Rossi, C., Berquand, A., et al. 2007. Voltage-dependent anion channel transports calcium ions through biomimetic membranes. Langmuir, 23(7), 3898–3905.CrossRefGoogle ScholarPubMed

[102] Devasahayam, S. 2012. Signals and Systems in Biomedical Engineering: Signal Processing and Physiological Systems Modeling. Springer Science & Business Media.Google Scholar

[103] Diaz, A., Albertorio, F., Daniel, S., and Cremer, P. 2008. Double cushions preserve transmembrane protein mobility in supported bilayer systems. Langmuir, 24(13), 6820–6826.CrossRefGoogle ScholarPubMed

[104] Diethelm, K., and Freed, A. 1998. The FracPECE subroutine for the numerical solution of differential equations of fractional order. Forschung und wissenschaftliches Rechnen, 1999, 57–71.Google Scholar

[105] Dorairaj, S., and Allen, T. 2007. On the thermodynamic stability of a charged arginine side chain in a transmembrane helix. Proceedings of the National Academy of Sciences of the United States of America, 104, 4943–4948.CrossRefGoogle Scholar

[106] DuMont, A., and Torres, V. 2014. Cell targeting by the Staphylococcus aureus pore-forming toxins: It's not just about lipids. Trends in Microbiology, 22(1), 21–27.CrossRefGoogle Scholar

[107] Dunlop, J., Bowlby, M., Peri, R., Vasilyev, D., and Arias, R. 2008. High-throughput electrophysiology: An emerging paradigm for ion-channel screening and physiology. Nature Reviews Drug Discovery, 7(4), 358–368.CrossRefGoogle ScholarPubMed

[108] Dura, J., Pierce, D., Majkrzak, C., et al. 2006. AND/R: Advanced neutron diffractometer/ reflectometer for investigation of thin films and multilayers for the life sciences. Review of Scientific Instruments, 77(7), 074301.CrossRefGoogle Scholar

[109] Edwards, David A. 1999. Estimating rate constants in a convection-diffusion system with a boundary reaction. IMA Journal of Applied Mathematics, 63, 89–112.CrossRefGoogle Scholar

[110] Eifler, N., Vetsch, M., Gregorini, M., et al. 2006. Cytotoxin ClyA from Escherichia coli assembles to a 13-meric pore independent of its redox-state. EMBO Journal, 25(11), 2652–2661.CrossRefGoogle ScholarPubMed

[111] El-Andaloussi, S., Lee, Y., Lakhal-Littleton, S. 2012. Exosome-mediated delivery of siRNA in vitro and in vivo. Nature Protocols, 7(12), 2112–2126.CrossRefGoogle ScholarPubMed

[112] Elliott, J., Needham, D., Dilger, J., and Haydon, D. 1983. The effects of bilayer thickness and tension on gramicidin single-channel lifetime. Biochimica et Biophysica Acta, Biomembranes, 735(1), 95–103.CrossRefGoogle ScholarPubMed

[113] Ernst, R., Bodenhausen, G., and Wokaun, A. 1987. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Clarendon Press Oxford.Google Scholar

[114] Esfandyarpour, R., Javanmard, M., Koochak, Z., et al. 2013. Label-free electronic probing of nucleic acids and proteins at the nanoscale using the nanoneedle biosensor. Biomicrofluidics, 7(4), 044114.Google ScholarPubMed

[115] Evans, L. 2010. Partial Differential Equations. American Mathematical Society.Google Scholar

[116] Fang, Y., Persson, B., Löfås, S., and Knoll, W. 2004. Protein Microarray Technology.Wiley InterScience. Chapter 6: Surface Plasmon Fluorescence Spectroscopy for Protein Binding Studies, pp. 131–151.

[117] Ferguson, T., and Bazant, M. 2012. Nonequilibrium thermodynamics of porous electrodes. Journal of the Electrochemical Society, 159(12), A1967–A1985.CrossRefGoogle Scholar

[118] Fernández, L., and Reigada, R. 2014. Effects of dimethyl sulfoxide on lipid membrane electroporation. Journal of Physical Chemistry B, 118(31), 9306–9312.CrossRefGoogle ScholarPubMed

[119] Fernández, L., Marshall, G., Sagués, F., and Reigada, R. 2010. Structural and kinetic molecular dynamics study of electroporation in cholesterol-containing bilayer. Journal of Physical Chemistry B, 114(20), 6855–6865.CrossRefGoogle Scholar

[120] Fertig, N., Blick, R.H., and Behrends, J.C. 2002. The cell patch clamp recording performed on a planar glass chip. Biophysical Journal, 82(June), 3056–3062.CrossRefGoogle ScholarPubMed

[121] Filippov, A., Orädd, G., and Lindblom, G. 2007. Domain formation in model membranes studied by pulsed-field gradient-NMR: The role of lipid polyunsaturation. Biophysical Journal, 93(9), 3182–3190.CrossRefGoogle ScholarPubMed

[122] Fischer, H., Polikarpov, I., and Craievich, A. 2004. Average protein density is a molecularweight- dependent function. Protein Science, 13(10), 2825–2828.Google Scholar

[123] Fitter, J., Gutberlet, T., and Katsaras, J. 2006. Neutron Scattering in Biology: Techniques and Applications. Springer Science & Business Media.Google Scholar

[124] Flenner, E., Das, J., Rheinstädter, M., and Kosztin, I. 2009. Subdiffusion and lateral diffusion coefficient of lipid atoms and molecules in phospholipid bilayers. Physical Review E, 79(1), 011907.CrossRefGoogle ScholarPubMed

[125] Franceschetti, D., Macdonald, R., and Buck, R. 1991. Interpretation of finite-length- Warburg-type impedances in supported and unsupported electrochemical cells with kinetically reversible electrodes. Journal of the Electrochemical Society, 138(5), 1368–1371.CrossRefGoogle Scholar

[126] Freeman, S., Wang, M., and Weaver, J. 1994. Theory of electroporation of planar bilayer membranes: Predictions of the aqueous area, change in capacitance, and pore-pore separation. Biophysical Journal, 67(1), 42–56.CrossRefGoogle ScholarPubMed

[127] Frenkel, D., and Smit, B. 2001. Understanding Molecular Simulation: From Algorithms to Applications. Vol. 1. Academic Press.Google Scholar

[128] Fromherz, P. 2003. Neuroelectronics interfacing: Semiconductor chips with ion channels, nerve cells and brain. Pages 781–810 in Weise, R. (ed), Nanoelectronics and Information Technology. Wiley-VCH.Google Scholar

[129] Garett, R., and Grisham, C. 2016. Biochemistry. Brooks Cole.Google Scholar

[130] Ge, L., Bernasconi, L., and Hunt, P. 2013. Linking electronic and molecular structure: Insight into aqueous chloride solvation. Physical Chemistry Chemical Physics, 15(31), 13169–13183.CrossRefGoogle ScholarPubMed

[131] Georganopoulou, D. 2009 (April). Reagentless electrochemical biosensors for clinical diagnostics. In: 41st Annual Oak Ridge Conference. Frontiers in Clinical Diagnostics, Baltimore, MD.Google Scholar

[132] Giera, B., Henson, N., Kober, E., Shell, S., and Squires, T. 2015. Electric double-layer structure in primitive model electrolytes: Comparing molecular dynamics with local-density approximations. Langmuir, 31(11), 3553–3562.CrossRefGoogle ScholarPubMed

[133] Giess, F., Friedrich, M., Heberle, J., Naumann, R., and Knoll, W. 2004. The protein-tethered lipid bilayer: A novel mimic of the biological membrane. Biophysical Journal, 87(5), 3213–3220.CrossRefGoogle ScholarPubMed

[134] Gillespie, D. 2010. Analytic theory for dilute colloids in a charged slit. Journal of Physical Chemistry B, 114(12), 4302–4309.CrossRefGoogle Scholar

[135] Gillespie, D. 2015. A review of steric interactions of ions: Why some theories succeed and others fail to account for ion size. Microfluidics and Nanofluidics, 18(5–6), 717–738.CrossRefGoogle Scholar

[136] Glaser, R., Leikin, S., Chernomordik, L., Pastushenko, V., and Sokirko, A. 1988. Reversible electrical breakdown of lipid bilayers: Formation and evolution of pores. Biochimica et Biophysica Acta, Biomembranes, 940(2), 275–287.CrossRefGoogle ScholarPubMed

[137] Glaser, R., Sachse, C., Dürr, U., et al. 2005. Concentration-dependent realignment of the antimicrobial peptide PGLa in lipid membranes observed by solid-state 19F-NMR. Biophysical Journal, 88(5), 3392–3397.CrossRefGoogle ScholarPubMed

[138] Glaser, R.W. 1993. Antigen-antibody binding and mass transport by convection and diffusion to a surface: A two-dimensional computer model of binding and dissociation kinetics. Analytical Biochemistry, 213, 152–161.CrossRefGoogle ScholarPubMed

[139] Gliozzi, A., Rolandi, R., De Rosa, M., and Gamacorta, A. 1983. Monolayer black membranes from bipolar lipids of archaebacteria and their temperature-induced structural changes. Journal of Membrane Biology, 75(1), 45–56.CrossRefGoogle ScholarPubMed

[140] Goldstein, B., Coombs, D., He, X., Pineda, A.R., and Wofsy, C. 1999. The influence of trasnport on the kinetics of binding to surface receptors: Application to cell and BIAcore. Journal of Molecular Recognition, 12, 293–299.3.0.CO;2-M>CrossRefGoogle Scholar

[141] Gordon, D., Krishnamurthy, V., and Chung, S. 2009. Generalized Langevin models of molecular dynamics simulations, with applications to ion channels. Journal of Chemical Physics, 131, 111.CrossRefGoogle ScholarPubMed

[142] Graf, P., Kurnikova, M., Coalson, R., and Nitzan, A. 2004. Comparison of dynamic lattice Monte Carlo simulations and the dielectric self-energy Poisson–Nernst–Planck continuum theory for model ion channels. Journal of Physical Chemistry B, 108(6), 2006–2015.CrossRefGoogle Scholar

[143] Grenier, E., Louvet, V., and Vigneaux, P. 2014. Parameter estimation in non-linear mixed effects models with SAEM algorithm: Extension from ODE to PDE. ESAIM:Mathematical Modelling and Numerical Analysis, 48(5), 1303–1329.CrossRefGoogle Scholar

[144] Griebel, M., Knapek, S., and Zumbusch, G. 2007. Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications. Vol. 5. Springer Science & Business Media.Google Scholar

[145] Gurtovenko, A., and Lyulina, A. 2014. Electroporation of asymmetric phospholipid membranes. Journal of Physical Chemistry B, 118(33), 9909–9918.CrossRefGoogle ScholarPubMed

[146] Hänggi, P., Talkner, P., and Borkovec, M. 1990. Reaction-rate theory: Fifty years after Kramers. Reviews of Modern Physics, 62(2), 251.CrossRefGoogle Scholar

[147] Hansen, J., and McDonald, I. 1990. Theory of Simple Liquids. Elsevier.Google Scholar

[148] Harms, G., Orr, G., Montal, M., et al. 2003. Probing conformational changes of gramicidin ion channels by single-molecule patch-clamp fluorescence microscopy. Biophysical Journal, 85(3), 1826–1838.CrossRefGoogle ScholarPubMed

[149] Haskins, J., and Lawson, J. 2016. Evaluation of molecular dynamics simulation methods for ionic liquid electric double layers. Journal of Chemical Physics, 144(18), 184707.Google ScholarPubMed

[150] Hatlo, M., Van Roij, R., and Lue, L. 2012. The electric double layer at high surface potentials: The influence of excess ion polarizability. EPL, 97(2), 28010.CrossRefGoogle Scholar

[151] Heinrich, F. 2016. Deuteration in biological neutron reflectometry. Methods in Enzymology, 566, 211–230.Google ScholarPubMed

[152] Heinrich, F., Ng, T., Vanderah, D., et al. 2009. A new lipid anchor for sparsely tethered bilayer lipid membranes. Langmuir, 25(7), 4219–4229.CrossRefGoogle ScholarPubMed

[153] Henderson, D., Abraham, F., and Barker, J. 1976. The Ornstein–Zernike equation for a fluid in contact with a surface. Molecular Physics, 31(4), 1291–1295.CrossRefGoogle Scholar

[154] Hess, B., Kutzner, C., Spoel, D., and Lindahl, E. 2008. GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation. Journal of Chemical Theory Computation, 4(3), 435–447.CrossRefGoogle ScholarPubMed

[155] Heysel, S., Vogel, H., Sanger, M., and Sigrist, H. 1995. Covalent attachment of functionalized lipid bilayers to planar waveguides for measuring protein binding to biomimetic membranes. Protein Science, 4(12), 2532–2544.Google Scholar

[156] Hille, B. 2001. Ionic Channels of Excitable Membranes. 3rd edition. Sinauer Associates, Inc.Google Scholar

[157] Hobbie, R., and Roth, B. 2007. Intermediate Physics for Medicine and Biology. Springer.Google Scholar

[158] Hoffmann, J., and Gillespie, D. 2013. Ion correlations in nanofluidic channels: Effects of ion size, valence, and concentration on voltage- and pressure-driven currents. Langmuir, 29(4), 1303–1317.CrossRefGoogle ScholarPubMed

[159] Hofsäß, C., Lindahl, E., and Edholm, O. 2003. Molecular dynamics simulations of phospholipid bilayers with cholesterol. Biophysical Journal, 84(4), 2192–2206.CrossRefGoogle ScholarPubMed

[160] Hoiles, W., and Krishnamurthy, V. 2015. Dynamic modeling of antimicrobial pore formation in engineered tethered membranes. IEEE Transactions on Molecular, Biological and Multi-Scale Communications, 1(3), 265–276.Google Scholar

[161] Hoiles, W., Krishnamurthy, V., and Cornell, B. 2012. Mathematical models for sensing devices constructed out of artificial cell membranes. Nanoscale Systems: Mathematical Modeling, Theory and Applications, 1, 143–171.Google Scholar

[162] Hoiles, W., Krishnamurthy, V., Cranfield, C., and Cornell, B. 2014. An engineered membrane to measure electroporation: Effect of tethers and bioelectronic interface. Biophysical Journal, 107(6), 1339–1351.CrossRefGoogle ScholarPubMed

[163] Hoiles, W., Krishnamurthy, V., and Cornell, B. 2014. Modelling the bioelectronic interface in engineered tethered membranes: From biosensing to electroporation. IEEE Transactions on Biomedical Circuits and Systems, PP(99), 1–13.

[164] Hoiles, W., Krishnamurthy, V., and Cornell, B. 2015. Membrane bound molecular machines for sensing. Journal of Analytical & Bioanalytical Techniques, 1.Google Scholar

[165] Hoiles, W., Gupta, R., Cornell, B., Cranfield, C., and Krishnamurthy, V. 2016. The effect of tethers on artificial cell membranes: A coarse-grained molecular dynamics study. PLoS One, 11(10), e0162790.Google ScholarPubMed

[166] Hoover, W. 1985. Canonical dynamics: Equilibrium phase-space distributions. Physical Review A, 31(3), 1695.CrossRefGoogle ScholarPubMed

[167] Horng, T., Lin, T., Liu, C., and Eisenberg, B. 2012. PNP Equations with steric effects: A model of ion flow through channels. Journal of Physical Chemistry B, 116(37), 11422–11441.CrossRefGoogle ScholarPubMed

[168] Howorka, S., Nam, J., Bayley, H., and Kahne, D. 2004. Stochastic detection of monovalent and bivalent protein-ligand interactions. Angewandte Chemie, International Edition, 43, 842–846.CrossRefGoogle ScholarPubMed

[169] Hoyles, M., Krishnamurthy, V., Siksik, M., and Chung, S.H. 2008. Brownian Dynamics theory for predicting internal and external blockages of tetraethylammonium in the KcsA potassium channel. Biophysical Journal, 94(January), 366–378.CrossRefGoogle ScholarPubMed

[170] Hu, Q., and Joshi, R. 2009. Transmembrane voltage analyses in spheroidal cells in response to an intense ultrashort electrical pulse. Physical Review E, 79, 011901.CrossRefGoogle Scholar

[171] Hughes, T. 2012. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Courier Corporation.Google Scholar

[172] Humphrey, W., Dalke, A., and Schulten, K. 1996. VMD: Visual Molecular Dynamics. Journal of Molecular Graphics, 14(1), 33–38.CrossRefGoogle ScholarPubMed

[173] Hung, W., Lee, M., Chen, F., and Huang, H. 2007. The condensing effect of cholesterol in lipid bilayers. Biophysical Journal, 92(11), 3960–3967.CrossRefGoogle ScholarPubMed

[174] Husslein, T., Newns, D., Pattnaik, P., et al. 1998. Constant pressure and temperature molecular-dynamics simulation of the hydrated diphytanolphosphatidylcholine lipid bilayer. Journal of Chemical Physics, 109(7), 2826–2832.CrossRefGoogle Scholar

[175] Ikonen, E. 2008. Cellular cholesterol trafficking and compartmentalization. Nature Reviews Molecular Cell Biology, 9(2), 125–138.CrossRefGoogle ScholarPubMed

[176] Im, W., and Roux, B. 2002. 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(4), 851–869.CrossRefGoogle ScholarPubMed

[177] Ingólfsson, H., and Andersen, O. 2010. Screening for small molecules' bilayer-modifying potential using a gramicidin-based fluorescence assay. Assay and Drug Development Technologies, 8(4), 427–436.CrossRefGoogle ScholarPubMed

[178] Israelachvili, J. 2011. Intermolecular and Surface Forces: Revised Third Edition. Academic Press.Google Scholar

[179] Jafari, H., and Daftardar-Gejji, V. 2006. Solving a system of nonlinear fractional differential equations using Adomian decomposition. Journal of Computational and Applied Mathematics, 196(2), 644–651.CrossRefGoogle Scholar

[180] Jeon, J., Monne, H., Javanainen, M., and Metzler, R. 2012. Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins. Physical Review Letters, 109(18), 188103.CrossRefGoogle Scholar

[181] Jesus, I., and Machado, T. 2009. Development of fractional order capacitors based on electrolyte processes. Nonlinear Dynamics, 56(1-2), 45–55.CrossRefGoogle Scholar

[182] Jeuken, L. 2009. Electrodes for integral membrane enzymes. Natural Product Reports, 26(10), 1234–1240.CrossRefGoogle ScholarPubMed

[183] Jiang, F., Bouret, Y., and Kindt, J. 2004. Molecular dynamics simulations of the lipid bilayer edge. Biophysical Journal, 87, 182–192.CrossRefGoogle ScholarPubMed

[184] Jiang, Y., and Kindt, J. 2007. Simulations of edge behaviour in a mixed bilayer: Fluctuation analysis. Journal of Chemical Physics, 126, 045105–9.CrossRefGoogle Scholar

[185] Jo, S., Lim, J., Klauda, J., and Im, W. 2009. CHARMM-GUI membrane builder for mixed bilayers and its application to yeast membranes. Biophysical Journal, 97(1), 50–58.CrossRefGoogle ScholarPubMed

[186] Joannis, J., Jiang, F., and Kindt, J. 2006. Coarse-grained model simulations of mixed-lipid systems: Composition and line tension of a stabilized bilayer edge. Langmuir, 22, 998–1005.CrossRefGoogle ScholarPubMed

[187] Johnson, C. 2012. Numerical Solution of Partial Differential Equations by the Finite Element Method. Courier Corporation.Google Scholar

[188] Joshi, R., and Schoenbach, K. 2000. Electroporation dynamics in biological cells subjected to ultrafast electrical pulses: A numerical simulation study. Physical Review E, 62, 1025–1033.CrossRefGoogle ScholarPubMed

[189] Joshi, R., Hu, Q., Schoenbach, K., and Hjalmarson, H. 2002. Improved energy model for membrane electroporation in biological cells subjected to electrical pulses. Physical Review E, 65, 041920.Google ScholarPubMed

[190] Junghans, A., and Koöper, I. 2010. Structural analysis of tethered bilayer lipid membranes. Langmuir, 26(13), 11035–11040.CrossRefGoogle ScholarPubMed

[191] Junghans, A., Watkins, E., Barker, R., et al. 2015. Analysis of biosurfaces by neutron reflectometry: From simple to complex interfaces. Biointerphases, 10(1), 019014.CrossRefGoogle ScholarPubMed

[192] Kakorin, S., Brinkmann, U., and Neumann, E. 2005. Cholesterol reduces membrane electroporation and electric deformation of small bilayer vesicles. Biophysical Chemistry, 117(2), 155–171.CrossRefGoogle ScholarPubMed

[193] Kalinowski, S., Ibron, G., Bryl, K., and Figaszewski, Z. 1998. Chronopotentiometric studies of electroporation of bilayer lipid membranes. Biochimica et Biophysica Acta, Biomembranes, 1369(2), 204–212.CrossRefGoogle ScholarPubMed

[194] Kanthou, C., Kranjc, S., Sersa, et al. 2006. The endothelial cytoskeleton as a target of electroporation-based therapies. Molecular Cancer Therapeutics, 5(12), 3145–3152.CrossRefGoogle ScholarPubMed

[195] Karatzas, I., and Shreve, S. 1991. Brownian Motion and Stochastic Calculus. Second edition. Springer.Google Scholar

[196] Karjiban, R., Shaari, N., Gunasakaran, U., and Basri, M. 2013. A coarse-grained molecular dynamics study of DLPC, DMPC, DPPC, and DSPC mixtures in aqueous solution. Journal of Chemistry, 2013, 931051.Google Scholar

[197] Kästner, J. 2011. Umbrella sampling. Wiley Interdisciplinary Reviews: Computational Molecular Science, 1(6), 932–942.Google Scholar

[198] Kayser, R., and Raveché, H. 1982. Derivation of the Ornstein–Zernike differential equation from the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy. Physical Review A, 26(4), 2123.CrossRefGoogle Scholar

[199] Kendall, J., Johnson, B., Symonds, P., et al. 2010. Effect of the structure of cholesterolbased tethered bilayer lipid membranes on ionophore activity. ChemPhysChem, 11(10), 2191–2198.CrossRefGoogle Scholar

[200] Ketchem, R., Hu, W., and Cross, T. 1993. High-resolution conformation of gramicidin A in a lipid bilayer by solid-state NMR. Science, 261, 1457–1457.CrossRefGoogle Scholar

[201] Khalil, H. 2002. Nonlinear Systems. Prentice Hall.Google Scholar

[202] Kim, S., Cho, H., et al. 2009. Nanogap biosensors for electrical and label-free detection of biomolecular interactions. Nanotechnology, 20(45), 455502.Google Scholar

[203] Kirchner, B., Dio, P., and Hutter, J. 2012. Real-world predictions from ab initio molecular dynamics simulations. Pages 109–153 in Multiscale Molecular Methods in Applied Chemistry. Springer.CrossRefGoogle Scholar

[204] Knight, J., Lerner, M., Marcano-Velázquez, J., Pastor, R., and Falke, J. 2010. Single molecule diffusion of membrane-bound proteins: Window into lipid contacts and bilayer dynamics. Biophysical Journal, 99(9), 2879–2887.CrossRefGoogle ScholarPubMed

[205] Knoll, W., Bender, K., Förch, R., et al. 2010. Polymer-tethered bimolecular lipid membranes. Pages 197–233 in Polymer Membranes/Biomembranes. Springer.Google Scholar

[206] Kok, T., Mickan, L., and Burrell, C. 1994. Routine diagnosis of seven respiratory viruses and Mycoplasma pneumoniae by enzyme immunoassay. Journal of Virological Methods, 50(1–3), 87–100.CrossRefGoogle ScholarPubMed

[207] Kokotovic, P., Khalil, H., and O'Reilly, J. 1999. Singular Perturbation Methods in Control: Analysis and Design. SIAM.CrossRefGoogle Scholar

[208] Kong, X., Lu, D., Liu, Z., and Wu, J. 2015. Molecular dynamics for the charging behavior of nanostructured electric double layer capacitors containing room temperature ionic liquids. Nano Research, 8(3), 931–940.CrossRefGoogle Scholar

[209] Kornyshev, A. 2013. The simplest model of charge storage in single file metallic nanopores. Faraday Discussions, 164, 117–133.CrossRefGoogle ScholarPubMed

[210] Koronkiewicz, S., and Kalinowski, S. 2004. Influence of cholesterol on electroporation of bilayer lipid membranes: Chronopotentiometric studies. Biochimica et Biophysica Acta, Biomembranes, 1661(2), 196–203.CrossRefGoogle ScholarPubMed

[211] Kotulska, M., Basalyga, J., Derylo, M., and Sadowski, P. 2010. Metastable pores at the onset of constant-current electroporation. Journal of Membrane Biology, 236(1), 37–41.CrossRefGoogle ScholarPubMed

[212] Kozuch, J., Weichbrodt, C., Millo, D., et al. 2014. Voltage-dependent structural changes of the membrane-bound anion channel hVDAC1 probed by SEIRA and electrochemical impedance spectroscopy. Physical Chemistry Chemical Physics, 16(20), 9546–9555.CrossRefGoogle ScholarPubMed

[213] Kramar, P., Delemotte, L., Lebar, A., et al. 2012. Molecular-level characterization of lipid membrane electroporation using linearly rising current. Journal of Membrane Biology, 245(10), 651–659.CrossRefGoogle ScholarPubMed

[214] Krassowska, W., and Filev, P. 2007. Modeling electroporation in a single cell. Biophysical Journal, 92(2), 404–417.CrossRefGoogle Scholar

[215] Kresák, S., Hianik, T., and Naumann, R. 2009. Giga-seal solvent-free bilayer lipid membranes: From single nanopores to nanopore arrays. Soft Matter, 5(20), 4021–4032.CrossRefGoogle Scholar

[216] Krishnamurthy, V. 2016. Partially Observed Markov Decision Processes: From Filtering to Controlled Sensing. Cambridge University Press.Google Scholar

[217] Krishnamurthy, V., and Chung, S.H. 2007. Large-Scale Dynamical Models and Estimation for Permeation in Biological Membrane Ion Channels. Proceedings of the IEEE, 95(5), 853–880.CrossRefGoogle Scholar

[218] Krishnamurthy, V., and Cornell, B. 2012. Engineering aspects of biological ion channels: from biosensors to computational models for permeation. Protoplasma, 249, 3–9.CrossRefGoogle ScholarPubMed

[219] Krishnamurthy, V., Luk, K., Cornell, B., and Martin, D. 2007. Gramicidin ion channel based nano-biosensors: Construction, stochastic dynamical models and statistical detection algorithms. IEEE Sensors Journal, 7(9), 1281–1288.CrossRefGoogle Scholar

[220] Krishnamurthy, V., Monfared, S., and Cornell, B. 2010. Ion-channel biosensors –part I: Construction, operation and clinical studies. IEEE Transactions on Nanotechnology (Special Issue on Nanoelectronic Interface to Biomolecules and Cells), 9(3), 303–312.Google Scholar

[221] Krishnamurthy, V., Monfared, S., and Cornell, B. 2010. Ion-channel biosensors –part II: Dynamic modeling, analysis and statistical signal processing. IEEE Transactions on Nanotechnology (Special Issue on Nanoelectronic Interface to Biomolecules and Cells), 9(3), 313–321.Google Scholar

[222] Kruskal, P., Jiang, Z., Gao, T., and Lieber, C. 2015. Beyond the patch clamp: Nanotechnologies for intracellular recording. Neuron, 86(1), 21–24.CrossRefGoogle ScholarPubMed

[223] Kučerka, N., Nagle, J., Sachs, J., et al. 2008. Lipid bilayer structure determined by the simultaneous analysis of neutron and X-ray scattering data. Biophysical Journal, 95(5), 2356–2367.CrossRefGoogle ScholarPubMed

[224] Kurnikova, M., Coalson, R., Graf, P., and Nitzan, A. 1999. A lattice relaxation algorithm for three-dimensional Poisson–Nernst–Planck theory with application to ion transport through the gramicidin A channel. Biophysical Journal, 76(2), 642–656.CrossRefGoogle ScholarPubMed

[225] Kushner, H.J. 1990. Weak Convergence and Singularly Perturbed Stochastic Control and Filtering Problems. Birkhauser.CrossRefGoogle Scholar

[226] Kushwaha, S.C., Kates, M., Sprott, G.D., and Smith, I.C. 1981. Novel complex polar lipids from the methanogenic archaebacterium Methanospirillum hungatei . Science, 211, 1163–1164.CrossRefGoogle ScholarPubMed

[227] Kuzmenkin, A., Bezanilla, F., and Correa, A. 2004. Gating of the bacterial sodium channel, NaChBac: Voltage-dependent charge movement and gating currents. Journal of General Physiology, 124(4), 349–356.CrossRefGoogle ScholarPubMed

[228] Latz, A., and Zausch, J. 2013. Thermodynamic derivation of a Butler–Volmer model for intercalation in Li-ion batteries. Electrochimica Acta, 110, 358–362.CrossRefGoogle Scholar

[229] Lauffenburger, D., and Linderman, J. 1993. Receptors: Models for Binding, Tracking, and Signaling. Oxford University Press.Google Scholar

[230] Leake, M. 2016. Biophysics: Tools and Techniques. CRC Press.Google Scholar

[231] Lee, S., Cascão-Pereira, L., Sala, R., Holmes, S., Ryan, K., and Becker, T. 2005. Ion channel switch array: A biosensor for detecting multiple pathogens. Industrial Biotechnology, 1(1), 26–31.CrossRefGoogle Scholar

[232] Lee, H., Vries, A., Marrink, S., and Pastor, R. 2009. A coarse-grained model for polyethylene oxide and polyethylene glycol: Conformation and hydrodynamics. Journal of Physical Chemistry B, 113(40), 13186–13194.CrossRefGoogle ScholarPubMed

[233] Lee, YiKuen, and Deng, PeiGang. 2012. Review of micro/nano technologies and theories for electroporation of biological cells. Science China Physics, Mechanics & Astronomy, 55(6), 996–1003.CrossRefGoogle Scholar

[234] Lenzi, E., Zola, R., Rossato, R., et al. 2017. Asymptotic behaviors of the Poisson–Nernst–Planck model, generalizations and best adjust of experimental data. Electrochimica Acta, 226, 40–45.Google Scholar

[235] Lenzi, K., de Paula, L., Silva, R., and Evangelista, R. 2013. A connection between anomalous Poisson–Nernst–Planck model and equivalent circuits with constant phase elements. The Journal of Physical Chemistry C, 117(45), 23685–23690.CrossRefGoogle Scholar

[236] Leontiadou, H., Mark, A., and Marrink, S. 2004. Molecular dynamics simulations of hydrophilic pores in lipid bilayers. Biophysical Journal, 86(4), 2156–2164.CrossRefGoogle ScholarPubMed

[237] Levine, R. 2005. Molecular Reaction Dynamics. Cambridge University Press.CrossRefGoogle Scholar

[238] Li, J., and Lin, H. 2010. The current-voltage relation for electropores with conductivity gradients. Biomicrofluidics, 4(1), 013206.CrossRefGoogle ScholarPubMed

[239] Li, S., Cutrera, J., Heller, R., and Teissie, J. 2014. Electroporation Protocols: Preclinical and Clinical Gene Medicine. Humana.CrossRefGoogle Scholar

[240] Li-Fries, J. 2007. Ion Channels in Mixed Tethered Bilayer Lipid Membranes. Ph.D. thesis, Max Planck Institut für Polymerforschung.

[241] Ligler, F., Fare, T., Seib, E., et al. 1988. Fabrication of key components of a receptor-based biosensor. Medical Instrumentation, 22(5), 247–256.Google ScholarPubMed

[242] Lim, J., and Klauda, J. 2011. Lipid chain branching at the iso- and anteiso-positions in complex chlamydia membranes: A molecular dynamics study. Biochimica et Biophysica Acta, Biomembranes, 1808(1), 323–331.CrossRefGoogle ScholarPubMed

[243] Lin, Y., Minner, D., Herring, V.L., and Naumann, C. 2012. Physisorbed polymer-tethered lipid bilayer with lipopolymer gradient. Materials, 5(11), 2243–2257.CrossRefGoogle Scholar

[244] Lipinski, C. 2004. Lead- and drug-like compounds: The rule-of-five revolution. Drug Discovery Today: Technologies, 1(4), 337–341.Google ScholarPubMed

[245] Liu, C., and Faller, R. 2012. Conformational, dynamical, and tensional study of tethered bilayer lipid membranes in coarse-grained molecular simulations. Langmuir, 28, 15907–15915.CrossRefGoogle ScholarPubMed

[246] Liu, J., and Eisenberg, B. 2013. Correlated ions in a calcium channel model: A Poisson–Fermi theory. Journal of Physical Chemistry B, 117(40), 12051–12058.CrossRefGoogle Scholar

[247] Liu, J., and Eisenberg, B. 2014. Poisson–Nernst–Planck–Fermi theory for modeling biological ion channels. Journal of Chemical Physics, 141(22), 12B640_1.CrossRefGoogle ScholarPubMed

[248] Liu, J., and Eisenberg, B. 2015. Numerical methods for a Poisson–Nernst–Planck–Fermi model of biological ion channels. Physical Review E, 92(1), 012711.CrossRefGoogle ScholarPubMed

[249] Liu, P., Harder, E., and Berne, B. 2004. On the calculation of diffusion coefficients in confined fluids and interfaces with an application to the liquid–vapor interface of water. Journal of Physical Chemistry B, 108(21), 6595–6602.Google Scholar

[250] Ljung, L. 1999. System Identification: Theory for the User. Wiley Online Library.Google Scholar

[251] Lomize, A., Orekhov, V., and Arsen'ev, A. 1992. Refinement of the spatial structure of the gramicidin A ion channel. Bioorganicheskaya Khimiya, 18(2), 182–200.Google ScholarPubMed

[252] Lopatin, A.N., Makhina, E.N., and Nichols, C.G. 1995. The mechanism of inward rectification of potassium channels: Long-pore plugging by cytoplasmic polyamines. Journal of General Physiology, 106(November), 923–955.CrossRefGoogle ScholarPubMed

[253] Lopreore, C., Bartol, T., Coggan, J., et al. 2008. Computational modeling of threedimensional electrodiusion in biological systems: Application to the node of Ranvier. Biophysical Journal, 95(6), 2624–2635.CrossRefGoogle Scholar

[254] Lu, B., Zhou, Y., Huber, G., et al. 2007. Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution. Journal of Chemical Physics, 127, 135102.CrossRefGoogle ScholarPubMed

[255] Lu, B., Holst, M., McCammon, J., and Zhou, Y. 2010. Poisson–Nernst–Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions. Journal of Computational Physics, 229(19), 6979–6994.CrossRefGoogle ScholarPubMed

[256] Lu, H. 2005. Probing single-molecule protein conformational dynamics. Accounts of Chemical Research, 38(7), 557–565.CrossRefGoogle ScholarPubMed

[257] Lu, X.D., Ottova, A.L., and Tien, H.T. 1996. Biophysical aspects of agar-gel supported bilayer lipid nembranes: A new method for forming and studying planar bilayer lipid membranes. Bioelectrochemistry and Bioenergetics, 39(2), 285–289.CrossRefGoogle Scholar

[258] Lück, J., and Latz, A. 2016. Theory of reactions at electrified interfaces. Physical Chemistry Chemical Physics, 18, 17799–17804.Google ScholarPubMed

[259] Ludwig, A., Völkerink, G., and Rhein, C., et al. 2010. Mutations affecting export and activity of cytolysin A from Escherichia coli . Journal of Bacteriology, 192(15), 4001–4011.CrossRefGoogle ScholarPubMed

[260] Léobon, B., Garcin, I., Menasché, P., et al. 2003. Myoblasts transplanted into rat infarcted myocardium are functionally isolated from their host. Proceedings of the National Academy of Sciences of the United States of America, 100(13), 7808–7811.CrossRefGoogle ScholarPubMed

[261] Maffeo, C., Bhattacharya, S., Yoo, J., Wells, D., and Aksimentiev, A. 2012. Modeling and simulation of ion channels. Chemical Reviews, 112(12), 6250–6284.CrossRefGoogle ScholarPubMed

[262] Majhi, A., Kanchi, S., Venkataraman, V., Ayappa, K., and Maiti, P. 2015. Estimation of activation energy for electroporation and pore growth rate in liquid crystalline and gel phases of lipid bilayers using molecular dynamics simulations. Soft Matter, 11(44), 8632–8640.CrossRefGoogle ScholarPubMed

[263] Majkrzak, C., Carpenter, E., Heinrich, F., and Berk, N. 2011. When beauty is only skin deep: Optimizing the sensitivity of specular neutron reflectivity for probing structure beneath the surface of thin films. Journal of Applied Physics, 110(10), 102212.CrossRefGoogle Scholar

[264] Mamonov, A., Coalson, R., Nitzan, A., and Kurnikova, M. 2003. The role of the dielectric barrier in narrow biological channels: A novel composite approach to modeling singlechannel currents. Biophysical Journal, 84(6), 3646–3661.CrossRefGoogle Scholar

[265] Mamonov, A., Kurnikova, M., and Coalson, R. 2006. Diffusion constant of K+ inside gramicidin A: A comparative study of four computational methods. Biophysical Chemistry, 124(3), 268–278.CrossRefGoogle ScholarPubMed

[266] Markel, V. 2016. Introduction to the Maxwell Garnett approximation: Tutorial. Journal of the Optical Society of America A, 33(7), 1244–1256.Google ScholarPubMed

[267] Marrink, S., and Tieleman, P. 2013. Perspective on the MARTINI model. Chemical Society Reviews, 42, 6801–6822.CrossRefGoogle ScholarPubMed

[268] Marrink, S., Risselada, H., Yefimov, S., Tieleman, D., and Vries, A. 2007. The MARTINI force field: A coarse grained model for biomolecular simulations. Journal of Physical Chemistry B, 111(27), 7812–7824.CrossRefGoogle ScholarPubMed

[269] Martinac, B., Nomura, T., Chi, G., et al. 2014. Bacterial mechanosensitive channels: Models for studying mechanosensory transduction. Antioxidants & Redox Signaling, 20(6), 952–969.Google ScholarPubMed

[270] Masel, R. 1996. Principles of Adsorption and Reaction on Solid Surfaces. Vol. 3. John Wiley & Sons.Google Scholar

[271] Mason, T., Pineda, A.R., Wofsy, C., and Goldstein, B. 1999. Effective rate models for the analysis of transport-dependent biosensor data. Mathematical Bioscience, 159, 123–144.CrossRefGoogle ScholarPubMed

[272] Maynard, J., Lindquist, N., Sutherland, J., et al. 2009. Surface plasmon resonance for highthroughput ligand screening of membrane-bound proteins. Biotechnology Journal, 4(11), 1542–1558.CrossRefGoogle Scholar

[273] McGillivray, D., Valincius, G., Vanderah, D., et al. 2007. Molecular-scale structural and functional characterization of sparsely tethered bilayer lipid membranes. Biointerphases, 2(1), 21–33.CrossRefGoogle ScholarPubMed

[274] McGillivray, D., Valincius, G., Heinrich, F., et al. 2009. Structure of functional Staphylococcus aureus α-hemolysin channels in tethered bilayer lipid membranes. Biophysical Journal, 96(4), 1547–1553.CrossRefGoogle ScholarPubMed

[275] Melikov, K., Frolov, V., Shcherbakov, A., et al. 2001. Voltage-induced nonconductive prepores and metastable single pores in unmodified planar lipid bilayer. Biophysical Journal, 80(4), 1829–1836.CrossRefGoogle Scholar

[276] Meyn, S., and Tweedie, R. 2012. Markov Chains and Stochastic Stability. Springer Science & Business Media.Google Scholar

[277] Miguel, V., Perillo, M., and Villarreal, M. 2016. Improved prediction of bilayer and monolayer properties using a refined BMW-MARTINI force field. Biochimica et Biophysica Acta, Biomembranes, 1858(11), 2903–2910.Google ScholarPubMed

[278] Miloshevsky, G., and Jordan, P. 2006. The open state gating mechanism of gramicidin A requires relative opposed monomer rotation and simultaneous lateral displacement. Structure, 14(8), 1241–1249.CrossRefGoogle ScholarPubMed

[279] Mocenni, C., Madeo, D., and Sparacino, E. 2011. Linear least squares parameter estimation of nonlinear reaction diffusion equations. Mathematics and Computers in Simulation, 81(10), 2244–2257.CrossRefGoogle Scholar

[280] Modi, N., Winterhalter, M., and Kleinekathofer, U. 2012. Computational modeling of ion transport through nanopores. Nanoscale, 4, 6166–6180.CrossRefGoogle ScholarPubMed

[281] Molleman, A. 2003. Patch Clamping: An Introductory Guide to Patch Clamp Electrophysiology. John Wiley & Sons.Google Scholar

[282] Momani, S., and Odibat, Z. 2007. Numerical approach to differential equations of fractional order. Journal of Computational and Applied Mathematics, 207(1), 96–110.CrossRefGoogle Scholar

[283] Monfared, S., Krishnamurthy, V., and Cornell, B. 2012. A molecular machine biosensor: Construction, predictive models, and experimental studies. Biosensors and Bioelectronics, 34, 261–266.Google Scholar

[284] Monticelli, L., Kandasamy, S., Periole, X., Larson, R., Tieleman, P., and Marrink, S. 2008. The MARTINI coarse-grained force field: Extension to proteins. Journal of Chemical Theory and Computation, 4(5), 819–834.CrossRefGoogle ScholarPubMed

[285] Motesharei, K., and Ghadiri, M.R. 1997. Diffusion-limited size-selective ion sensing based on SAM-supported peptide nanotubes. Journal of the American Chemical Society, 119, 11306–11312.CrossRefGoogle Scholar

[286] Movahed, S., and Li, D. 2013. A theoretical study of single-cell electroporation in a microchannel. Journal of Membrane Biology, 246, 151–160.CrossRefGoogle Scholar

[287] Mueller, P., Rudin, D., Tien, T., and Wescott, W. 1962. Reconstitution of cell membrane structure in vitro and its transformation into an excitable system. Nature, 194(4832), 979–980.CrossRefGoogle ScholarPubMed

[288] Myszka, D.G., Morton, T.A., Doyle, M.L., and Chaiken, I.M. 1997. Kinetic analysis of a protein antigen–antibody interaction limited by mass transport on an optical biosensor. Biophysical Chemistry, 64, 127–137.CrossRefGoogle ScholarPubMed

[289] Naumann, C., Prucker, O., Lehmann, T., et al. 2001a. The polymer-supported phospholipid bilayer: Tethering as a new approach to substrate-membrane stabilization. Biomacromolecules, 3, 27–35.Google Scholar

[290] Naumann, C.A., Knoll, W., and Frank, C.W. 2001b. Hindered diffusion in polymer-tethered membranes: A monolayer study at the air–water interface. Biomacromolecules, 2(4), 1097–1103.CrossRefGoogle Scholar

[291] Naumann, R., Schmidt, E.K., Jonczyk, A., et al. 1996. Self-assembly in natural and unnatural systems. Angewandte Chemie, International Edition, 35(11), 1154–1196.Google Scholar

[292] Naumann, R., Schmidt, E., Jonczyk, A., et al. 1999. The peptide-tethered lipid membrane as a biomimetic system to incorporate cytochrome C oxidase in a functionally active form. Biosensors and Bioelectronics, 14(7), 651–662.CrossRefGoogle Scholar

[293] Naumann, R., Baumgart, T., Gräber, P., et al. 2002. Proton transport through a peptidetethered bilayer lipid membrane by the H+-ATP synthase from chloroplasts measured by impedance spectroscopy. Biosensors and Bioelectronics, 17(1), 25–34.CrossRefGoogle ScholarPubMed

[294] Naumann, R., Schiller, S., Giess, F., et al. 2003. Tethered lipid bilayers on ultraflat gold surfaces. Langmuir, 19(13), 5435–5443.CrossRefGoogle Scholar

[295] Neher, E. 2001. Molecular biology meets microelectronics. Nature Biotechnology, 19(2), 114.CrossRefGoogle ScholarPubMed

[296] Nelson, D., Lehninger, A., and Cox, M. 2008. Principles of Biochemistry. Macmillan.Google Scholar

[297] Neu, J., and Krassowska, W. 1999. Asymptotic model of electroporation. Physical Review E, 59, 3471–3482.Google Scholar

[298] Neu, J., and Krassowska, W. 2003. Modeling postshock evolution of large electropores. Physical Review E, 67, 021915.CrossRefGoogle ScholarPubMed

[299] Neu, J., and Krassowska, W. 2006. Singular perturbation analysis of the pore creation transient. Physical Review E, 74, 031917.CrossRefGoogle ScholarPubMed

[300] Neu, J., Smith, K., and Krassowska, W. 2003. Electrical energy required to form large conducting pores. Bioelectrochemistry, 60(1), 107–114.CrossRefGoogle ScholarPubMed

[301] Newman, J. 1966. Resistance for flow of current to a disk. Journal of the Electrochemical Society, 113(5), 501–502.CrossRefGoogle Scholar

[302] Nölting, B. 2009. Methods in Modern Biophysics. Springer Science & Business Media.Google Scholar

[303] Nosé, S. 1984. A molecular dynamics method for simulations in the canonical ensemble. Molecular Physics, 52(2), 255–268.CrossRefGoogle Scholar

[304] Nosé, S., and Klein, M. 1983. Constant pressure molecular dynamics for molecular systems. Molecular Physics, 50(5), 1055–1076.CrossRefGoogle Scholar

[305] Obergrussberger, A., Stölzle-Feix, S., Becker, N., Brüggemann, A., Fertig, N., and Möller, C. 2015. Novel screening techniques for ion channel targeting drugs. Channels, 9(6), 367–375.CrossRefGoogle ScholarPubMed

[306] Ogier, S., Bushby, R., Cheng, Y., et al. 2000. Suspended planar phospholipid bilayers on micromachined supports. Langmuir, 16(13), 5696–5701.CrossRefGoogle Scholar

[307] Oh, S., Cornell, B., Smith, D., et al. 2008. Rapid detection of influenza A virus in clinical samples using an ion channel switch biosensor. Biosensors and Bioelectronics, 23(7), 1161–1165.CrossRefGoogle ScholarPubMed

[308] Ohvo-Rekilä, H., Ramstedt, B., Leppimäki, P., and Slotte, P. 2002. Cholesterol interactions with phospholipids in membranes. Progress in Lipid Research, 41(1), 66–97.CrossRefGoogle ScholarPubMed

[309] Oscarsson, J., Mizunoe, Y., Li, L., et al. 1999. Molecular analysis of the cytolytic protein ClyA (SheA) from Escherichia coli . Molecular Microbiology, 32(6), 1226–1238.CrossRefGoogle ScholarPubMed

[310] Otter, W. 2013. Revisiting the exact relation between potential of mean force and freeenergy profile. Journal of Chemical Theory and Computation, 9(9), 3861–3865.Google Scholar

[311] Ovchinnikov, V., Nam, K., and Karplus, M. 2016. A simple and accurate method to calculate free energy profiles and reaction rates from restrained molecular simulations of diffusive processes. Journal of Physical Chemistry B, 120(33), 8457–8472.Google ScholarPubMed

[312] Pabst, M., Wrobel, G., Ingebrandt, S., Sommerhage, F., and Offenhäusser, A. 2007. Solution of the Poisson–Nernst–Planck equations in the cell–substrate interface. European Physical Journal E: Soft Matter and Biological Physics, 24, 1–8.CrossRefGoogle ScholarPubMed

[313] Paesani, F. 2016. Getting the right answers for the right reasons: Toward predictive molecular simulations of water with many-body potential energy functions. Accounts of Chemical Research, 49(9), 1844–1851.Google ScholarPubMed

[314] Pakhomov, A., Miklavcic, D., and Markov, M. 2010. Advanced Electroporation Techniques in Biology and Medicine. CRC Press.Google Scholar

[315] Parrinello, M., and Rahman, A. 1981. Polymorphic transitions in single crystals: A new molecular dynamics method. Journal of Applied Physics, 52(12), 7182–7190.CrossRefGoogle Scholar

[316] Pastor, R., and Karplus, M. 1988. Parametrization of the friction constant for stochastic simulations of polymers. Journal of Physical Chemistry, 92(9), 2636–2641.CrossRefGoogle Scholar

[317] Pastushenko, V., and Chizmadzhev, Y. 1982. Stabilization of conducting pores in BLM by electric current. General Physiology and Biophysics, 1, 43–52.Google Scholar

[318] Pastushenko, V., Chizmadzhev, Yu., and Arakelyan, V. 1979. Electric breakdown of bilayer lipid membranes: II. Calculation of the membrane lifetime in the steady-state diffusion approximation. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 104, 53–62.CrossRefGoogle Scholar

[319] Pedrotty, D., Koh, J., Davis, B., et al. 2005. Engineering skeletal myoblasts: Roles of threedimensional culture and electrical stimulation. American Journal of Physiology: Heart and Circulatory Physiology, 288(4), H1620–H1626.Google Scholar

[320] Peng, Z., Tang, J., Han, X., Wang, E., and Dong, S. 2002. Formation of a supported hybrid bilayer membrane on gold: A sterically enhanced hydrophobic effect. Langmuir, 18(12), 4834–4839.CrossRefGoogle Scholar

[321] Periole, X., and Marrink, S. 2012. The Martini coarse-grained force field. Pp. 533–565 in Biomolecular Simulations. Methods in Molecular Biology, vol. 924. Springer.Google Scholar

[322] Peterman, M.C., Ziebarth, J.M., Braha, O., et al. 2002. Ion channels and lipid bilayer membranes under high potentials using microfabricated apertures. Biomedical Microdevices, 4, 236–236.CrossRefGoogle Scholar

[323] Petrov, E., Rohde, P., Cornell, B., and Martinac, B. 2012. The protective effect of osmoprotectant TMAO on bacterial mechanosensitive channels of small conductance MscS/MscK under high hydrostatic pressure. Channels, 6(4), 262–271.CrossRefGoogle ScholarPubMed

[324] Piggot, T., Holdbrook, D., and Khalid, S. 2011. Electroporation of the E. coli and S. aureus membranes: Molecular dynamics simulations of complex bacterial membranes. Journal of Physical Chemistry B, 115(45), 13381–13388.CrossRefGoogle Scholar

[325] Pintelon, R., and Schoukens, J. 2012. System Identification: A Frequency Domain Approach. John Wiley & Sons.CrossRefGoogle Scholar

[326] Plant, A. 1993. Self-assembled phospholipid/alkanethiol biomimetic bilayers on gold. Langmuir, 9(11), 2764–2767.CrossRefGoogle Scholar

[327] Plant, A.L. 1999. Supported hybrid bilayer membranes as rugged cell membrane mimics. Langmuir, 15, 5128–5135.CrossRefGoogle Scholar

[328] Podlubny, I. 1998. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Vol. 198. Academic Press.Google Scholar

[329] Polak, A., Bonhenry, D., Dehez, F., Kramar, P., Miklavčič, D., and Tarek, M. 2013. On the electroporation thresholds of lipid bilayers: Molecular dynamics simulation investigations. Journal of Membrane Biology, 246(11), 843–850.CrossRefGoogle ScholarPubMed

[330] Polak, A., Tarek, M., Tomšič, M., et al. 2014. Electroporation of archaeal lipid membranes using MD simulations. Bioelectrochemistry, 100, 18–26.CrossRefGoogle ScholarPubMed

[331] Prashar, J., Sharp, P., Scarffe, M., and Cornell, B. 2007. Making lipid membranes even tougher. Journal of Materials Research, 22(08), 2189–2194.CrossRefGoogle Scholar

[332] Qian, S., and Bau, H.H. 2003. A mathematical model of lateral flow bioreactions applied to sandwich assays. Analytical Biochemistry, 322, 89–98.CrossRefGoogle ScholarPubMed

[333] Qiao, Y., Liu, X., Chen, M., and Lu, B. 2016. A local approximation of fundamental measure theory incorporated into three dimensional Poisson–Nernst–Planck equations to account for hard sphere repulsion among ions. Journal of Statistical Physics, 163(1), 156–174.Google Scholar

[334] Rabiner, L. 1989. A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 77(2), 257–286.CrossRefGoogle Scholar

[335] Ragaliauskas, T., Mickevicius, M., Rakovska, B., et al. 2017. Fast formation of low-defectdensity tethered bilayers by fusion of multilamellar vesicles. Biochimica et Biophysica Acta, Biomembranes, 1859(5), 669–678.Google ScholarPubMed

[336] Raguse, B., Braach-Maksvytis, V., Cornell, B., et al. 1998. Tethered lipid bilayer membranes: Formation and ionic reservoir characterization. Langmuir, 14(3), 648–659.CrossRefGoogle Scholar

[337] Raicu, V., and Popescu, A. 2008. Integrated Molecular and Cellular Biophysics. Springer.CrossRefGoogle Scholar

[338] Redick, S., Settles, D., Briscoe, G., and Erickson, H. 2000. Defining Fibronectin9s Cell Adhesion Synergy Site by Site-Directed Mutagenesis. The Journal of cell biology, 149(2), 521–527.CrossRefGoogle ScholarPubMed

[339] Rapaport, D. 2002. The Art of Molecular Dynamics Simulation. Vol. 2. Cambridge University Press.Google Scholar

[340] Reigada, R. 2014. Electroporation of heterogeneous lipid membranes. Biochimica et Biophysica Acta, Biomembranes, 1838(3), 814–821.CrossRefGoogle ScholarPubMed

[341] Ren, D., Navarro, B., Xu, H., Yue, L., Shi, Q., and Clapham, D. 2001. A prokaryotic voltage-gated sodium channel. Science, 294(5550), 2372–2375.CrossRefGoogle ScholarPubMed

[342] Richter, R., Bérat, R., and Brisson, A. 2006. Formation of solid-supported lipid bilayers: An integrated view. Langmuir, 22(8), 3497–3505.CrossRefGoogle Scholar

[343] Ring, A. 1992. Influence of ion occupancy and membrane deformation on gramicidin A channel stability in lipid membranes. Biophysical Journal, 61(5), 1306–1315.CrossRefGoogle ScholarPubMed

[344] Risken, H. 1984. Fokker–Planck equation. Pages 63–95 in The Fokker-Planck Equation. Springer.CrossRefGoogle Scholar

[345] Robelek, R., Lemker, E., Wiltschi, B., et al. 2007. Incorporation of in vitro synthesized GPCR into a tethered artificial lipid membrane system. Angewandte Chemie, International Edition, 46(4), 605–608.CrossRefGoogle ScholarPubMed

[346] Robinson, J. 2001. Infinite-Dimensional Dynamical Systems. Cambridge University Press.Google Scholar

[347] Rollins-Smith, L., Doersam, J., Longcore, J., et al. 2002. Antimicrobial peptide defenses against pathogens associated with global amphibian declines. Developmental & Comparative Immunology, 26(1), 63–72.Google ScholarPubMed

[348] Rols, M., and Teissié, J. 1992. Experimental evidence for the involvement of the cytoskeleton in mammalian cell electropermeabilization. Biochimica et Biophysica Acta, Biomembranes, 1111(1), 45–50.CrossRefGoogle ScholarPubMed

[349] Römer, W., and Steinem, C. 2004. Impedance analysis and single-channel recordings on nano-black lipid membranes based on porous alumina. Biophysical Journal, 86(2), 955–965.CrossRefGoogle ScholarPubMed

[350] Römer, W., Lam, Y., Fischer, D., et al. 2004. Channel activity of a viral transmembrane peptide in micro-BLMs: Vpu1-32 from HIV-1. Journal of the American Chemical Society, 126(49), 16267–16274.CrossRefGoogle Scholar

[351] Rosazza, C., Escoffre, J., Zumbusch, A., and Rols, M. 2011. The actin cytoskeleton has an active role in the electrotransfer of plasmid DNA in mammalian cells. Molecular Therapy, 19(5), 913–921.CrossRefGoogle ScholarPubMed

[352] Roux, B., Allen, T., Bemeche, S., and Im, W. 2004. Theoretical and computational models of biological ion channels. Quarterly Reviews of Biophysics, 37(1), 15–103.CrossRefGoogle ScholarPubMed

[353] Rubinstein, I. 1990. Electrodiffusion of Ions. SIAM Studies in Applied Mathematics.CrossRefGoogle Scholar

[354] Sackmann, E. 1996. Supported membranes: Scientific and practical applications. Science, 271(5245), 43–48.CrossRefGoogle ScholarPubMed

[355] Sackmann, E., and Tanaka, M. 2000. Supported membranes on soft polymer cushions: Fabrication, characterization and applications. Trends in Biotechnology, 18(2), 58–64.CrossRefGoogle ScholarPubMed

[356] Sakmann, B. 2013. Single-Channel Recording. Springer Science & Business Media.Google Scholar