Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 2 | 1 |

Tytuł artykułu

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

Treść / Zawartość

Warianty tytułu

Języki publikacji



Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP) equations that are solved by Finite Element Method (FEM). Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.







Opis fizyczny




  • Center for System Biology, Department of Mathematics, Soochow University, Suzhou 215006, China
  • Center for System Biology, Department of Mathematics, Soochow University, Suzhou 215006, China
  • Department of Bioengineering, Department of Engineering Science and Mechanics Pennsylvania State University, University Park, PA 16802, US
  • Center for System Biology, Department of Mathematics, Soochow University, Suzhou 215006, China
  • Department of Mathematics, Pennsylvania State University, University Park, PA 16802, US


  • [1] T. W. Allena, M. Hoylesa, S. Kuyucakb, and S. H. Chunga. Molecular and brownian dynamics study of ion selectivity and conductivity in the potassium channel. Chem. Phys. Lett., 313:358-365, 1999.
  • [2] O. S. Andersen, R. E. Koeppe, and B. Roux. Gramicidin channels. IEEE T. Nanobiosci., 4:295-306, 2005.
  • [3] H. J. Apell, E. Bamberg, and P. Lauger. E_ects of surface charge on the conductance of the gramicidin channel. Biochem. Biophys. Acta, 552:369-378, 1979.
  • [4] A. Archer. Dynamical density functional theory for dense atomic liquids. J. Phys.: Condens. Matter, 18:5617, 2006.[Crossref]
  • [5] I. Babuska. The _nite element method for elliptic equations with discontinuous coe_cients. Computing, 5:207-218, 1970.[Crossref]
  • [6] R. Capone, S. Blake, M. R. Restrepo, J. Yang, and M. Mayer. Designing nanosensors based on charged derivatives of gramicidin a. J. Am. Chem. Soc., 129:9737-9745, 2007.
  • [7] A. E. Cardenas, R. D. Coalson, and M. G. Kurnikova. Three-dimensional Poisson-Nernst-Planck theory studies: Influence of membrane electrostatics on gramicidin A channel conductance. Biophys. J., 79:80-93, 2000.[Crossref][PubMed]
  • [8] Z. M. Chen and J. Zhou. Finite elemtent methods and their convergence for elliptic and parabolic interface problems. Numer. Math, 79:175-202, 1996.
  • [9] P. G. Ciarlet. The Finite Element Method for Elliptic Problems. Elsevier, 1978.
  • [10] S. Durand-Vidal, J. P. Simonin, and P. Turq. Electrolytes at Interfaces. Kluwer, Boston, 2000.
  • [11] S. Durand-Vidal, P. Turq, O. Bernard, C. Treiner, and L. Blum. perspectives in transport phenomena in electrolytes. Physica A, 231:123-143, 1996.
  • [12] B. Eisenberg, Y. Hyon, and C. Liu. Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids. J. Chem. Phys, 113:104-127, 2010.
  • [13] B. Eisenberg and W. S. Liu. Poisson-Nernst-Planck systems for ion channels with permanent charges. SIAM J. Math. Analysis, 38(6):1932-1966, 2007.
  • [14] J. Forster. Mathematical modeling of complex fluids. master thesis, University of Wurzbur, 2013.
  • [15] H. K. Gummel. A self-consistent iterative scheme for one-dimensional steady state transistor calculations. IEEE T. Electron. Dev., 11, 1964.
  • [16] U. Hollerbach, D. Chen, and R. S. Eisenberg. Two- and three-dimensional Poisson-Nernst-Planck simulations of current flow through gramicidin a. J. Sci. Comput., 16:373-409, 2001.[Crossref]
  • [17] T. Horng, T. Lin, C. Liu, and B. Eisenberg. Pnp equations with steric e_ects: A model of ion flow through channels. J. Phys. Chem. B., 116(37):11422-11441, 2012.
  • [18] H. Hwang, G. C. Schatz, and M. A. Ratner. Incorporation of inhomogeneous ion difiusion coe_cients into kinetic lattice grand canonical monte carlo simulations and application to ion current calculations in a simple model ion channel. J. Phys. Chem., 111(49):12506-12512, 2007.
  • [19] W. Im and B. Roux. Ion permeation and selectivity of OmpF porin: A theoretical study based on molecular dynamics, brownian dynamics and continuum electrodi_usion theory. J. Mol. Biol., 322:851-869, 2002.
  • [20] M. G. Kurnikova, R. D. 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. Biophys. J., 76:642-656, 1999.
  • [21] K. Lee, H. Rui, R. W. Pastor, and W. Im. Brownian dynamics simulations of ion transport through the vdac. Biophys. J., 100:611-619, 2011.
  • [22] L. L. Lee. Molecular Thermodynamics of Electrolyte Solutions. World Scienti_c, Singapore, 2008.
  • [23] B. Lu, M. J. Holst, A. Mccammon, and Y. C. Zhou. Poisson-Nernst-Planck equations for simulating biomolecular di_usionreaction processes I: Finite element solutions. J. Comput. Phys., 229:6979-6994, 2010.
  • [24] B. Lu and Y. C. Zhou. Poisson-Nernst-Planck equations for simulating biomolecular di_usion-reaction processes II: Size e_ects on ionic distributions and di_usion-reaction rates. Biophys. J., 100:2475-2485, 2011.
  • [25] M. X. Macrae, S. Blake, X. Jiang, R. Capone, D. J. Estes, M. Mayer, and J. Yang. A semi-synthetic ion channel platform for detection of phosphatase and protease activity. ACS Nano, 3:3567-3580, 2009.[Crossref][PubMed]
  • [26] M. X. Macrae, S. Blake, M. Mayer, and J. Yang. Nanoscale ionic diodes with tunable and switchable rectifying behavior. J. Am. Chem. Soc., 132:1766-1767, 2010.
  • [27] M. X. Macrae, D. Schlamadinger, J. E. Kim, M. Mayer, and J. Yang. Using charge to control the functional properties of self-assembled nanopores in membranes. Small, 7:2016-2020, 2011.[PubMed][Crossref]
  • [28] S. Majd, C. Yusko, A. D. MacBriar, J. Yang, and M. Mayer. Gramicidin pores report the activity of membrane-active enzymes. J. Am. Chem. Soc., 131:16119-16126, 2009.
  • [29] U. M. B. Marconi and P. Tarazona. Dynamic density functional theory of fluids. J. Chem. Phys., 110:8032, 1999.
  • [30] S. R. Mathur and J. Y. Murthy. A multigrid method for the Poisson-Nernst-Planck equations. SIAM J. Appl. Math., 52:4031-4039, 2009.
  • [31] W. Nonner, D. Gillespie, D. Henderson, and B. Eisenberg. Ion accumulation in a biological calcium channel: E_ects of solvent and con_ning pressure. J. Phys. Chem. B, 105:6427-6436, 2001.[Crossref]
  • [32] S. Y. Noskov, W. Im, and B. Roux. Ion permeation through the _-hemolysin channel: Theoretical studies based on brownian dynamics and Poisson-Nernst-Plank electrodi_usion theory. Biophys. J., 87:2299-2309, 2004.
  • [33] L. Onsager. Reciprocal relations in irreversible processes. I. Phys. Rev., II. Ser. 37:405-426, 1931.[Crossref]
  • [34] L. Onsager. Reciprocal relations in irreversible processes. II. Phys. Rev., 2:2265-2279, 1931.[Crossref]
  • [35] P. O. Persson and G. Strang. A simple mesh generator in matlab. SIAM Rev., 46:329-345, 2004.[Crossref]
  • [36] K. S. Pitzer. Thermodynamics. Mcgraw-Hill College, New York, 1995.
  • [37] K. S. Pitzer and J. J. Kim. Thermodynamics of electrolytes. iv. activity and osmotic coe_cients for mixed electrolytes. J.
  • Am. Chem. Soc., 96:5701-5707, 1974.
  • [38] T. Z. Qian, X. P. Wang, and P. Sheng. A variational approach to the moving contact line hydrodynamics. J. Fluid Mech., 564:333-360, 2006.
  • [39] G. M. Roger, O. Bernard S. Durand-Vidal, and P. Turq. Electrical conductivity of mixed electrolytes: Modeling within the mean spherical approximation. J. Phys. Chem. B, 113:8670-8674, 2009.
  • [40] B. Roux, T. Allen, Simon Berneche, and W. Im. Theoretical and computational models of biological ion channels. Q. Rev. Biophys., 37:15-103, 2 2004.
  • [41] T. Schirmer and P. Phale. Brownian dynamics simulation of ion flow through porin channels. J. Mol. Biol., 294:1159-1167, 1999.
  • [42] G. Stell and C. G. Joslin. The donnan equilibrium a theoretical study of the e_ects of interionic forces. Biophys., 50:855-859, 1986.
  • [43] J. W. Strutt. Some general theorems relating to vibrations. Proc. London Math. Soc., IV:357-368, 1873.
  • [44] V. Thomée. Galerkin _nite element methods for parabolic problems. Springer, 1997.
  • [45] B. Tu, M. X. Chen, Y. Xie, L. B. Zhang, B. Eisenberg, and B. Z. Lu. A parallel _nite element simulator for ion transport through three-dimensional ion channel systems. J. Phys. Chem., 34(24):2065-2078, 2013.
  • [46] L. Vrbka, J. Vondrasek, B. Jagoda-Cwiklik, R. Vacha, and P. Jungwirth. Quanti_cation and rationalization of the higher a_nity of sodium over potassium to protein surfaces. P. Natl. Acad. Sci. USA, 17:15440-15444, 2006.[Crossref]
  • [47] B. A. Wallace. Structure of gramicidin a. Biophys. J., 49:295-306, 1986.[Crossref][PubMed]
  • [48] H. Wu, T. Lin, and C. Liu. On transport of ionic solutions: from kinetic laws to continuum descriptions. arXiv:1306.3053, 2014.
  • [49] J. Xu and L. Zikatanov. A monotone _nite element scheme for convection-di_usion equations. Math. Comp., 68:1429-1446, 1999.
  • [50] S. Xu, P. Sheng, and C. Liu. Energy variational approach for ions transport. Comm. Math. Sci., 12, 1964.
  • [51] S. Yu and G.W. Wei. Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities.
  • J. Comput. Phys., 227(1):602 - 632, 2007.
  • [52] C. Yuan, R. J. O’Connell, P. L. Feinberg-Zadek, L. J. Johnston, and S. N. Treistman. Bilayer thickness modulates the conductance of the bk channel in model membranes. Biophys. J., 86:3620-3633, 2004.
  • [53] Q. Zheng, D. Chen, and G. W. Wei. Second-order Poisson-Nernst-Planck solver for ion transport. J. Comput. Phys., 230:5239-5262, 2011.
  • [54] Y.C. Zhou, S. Zhao, M. Feig, and G.W. Wei. High order matched interface and boundary method for elliptic equations with discontinuous coeficients and singular sources. J. Comput. Phys., 213(1):1 - 30, 2006.

Typ dokumentu



Identyfikator YADDA

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.