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Jinn-Liang Liu National Hsinchu University of Education Jan. 5, 2013

Jinn-Liang Liu National Hsinchu University of Education Jan. 5, 2013. 台灣大學數學系. 3D Poisson-Fermi-Nernst-Planck Modeling of Biological Ion Channels. 1. Outline. Ion Channel PNP w. Steric and Correlations VMD (Visual Molecular Dynamics) From Protein Data Bank to PNP Numerical Methods

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Jinn-Liang Liu National Hsinchu University of Education Jan. 5, 2013

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  1. Jinn-Liang Liu National Hsinchu University of Education Jan. 5, 2013 台灣大學數學系 3D Poisson-Fermi-Nernst-Planck Modelingof Biological Ion Channels 1

  2. Outline • Ion Channel • PNP w. Steric and Correlations • VMD (Visual Molecular Dynamics) • From Protein Data Bank to PNP • Numerical Methods • Preliminary Results • Outlook

  3. Ion Channel Biological ion channels seem to be a precondition for all living matter. Nervous system (0:50) Action Potentials (3:24) Potassium Channel (1:42) K+ radius: 0.133 nm, Na+ radius: 0.095 nm (0.133-0.095)/0.133 = 28.6%

  4. A. L. Hodgkin & A. Huxley (Nobel Prize in Physiology or Medicine 1963) for their discoveries concerning " the ionic mechanisms in the nerve cell membrane ". E. Neher & B. Sakmann (Nobel Prize in Physiology or Medicine 1991) for their discoveries concerning "the function of single ion channels in cells". Hodgkin–Huxley Model on Ion Channel P. Agre & R. MacKinnon (Nobel Prize in Chemistry 2003) for their discoveries concerning "channels in cell membranes".

  5. Ion Channel Ion channels regulate the flow of ions across the membrane in all cells. (Ionsin water are the liquid of Life.) Figures from Bob Eisenberg

  6. Steric & Correlation PNPPoisson-Fermi*-Nernst*-Planck* Steric & Correlation in Poisson-Boltzmann: 100-Year Old Problems since Gouy (1910) & Chapman (1913) Historical Developments: Bjerrum (1918), Debye*-Huckel (1923), Stern* (1924), Onsager * (1936), Kirkwood (1939), Dutta-Bagchi (1950), Grahame (1950), Eigen*-Wicke (1954), Borukhov-Andelman-Orland (1997), Bazant-Storey-Kornyshev (2011) * Nobel Laureates 6

  7. Steric Effects Steric effects arise from the fact that each atom within a molecule occupies a certain amount of space. (Wiki) 7

  8. Steric Effects Boltzmann => Infinity => Unphysical Fermi => Finite => Saturation 8

  9. Steric Effects Boltzmann => Infinity => Unphysical Fermi => Finite => Saturation 9

  10. Correlation Effects 10

  11. 11

  12. Simulation Domain KcsA Channel Gramicidin A (GA) Channel 12

  13. Simulation Domain 13

  14. Visual Molecular Dynamics 14

  15. Protein Data Bank 76495Structures 15

  16. Visual Molecular Dynamics Build Structure  Place Membrane  Add Water  Add Ions  Melt Lipid  Run MD Simulation 16

  17. PDB to PNP • Download GA from PDB (1MAG.PDB)PDB: Atomic information of Proteins determined by X-ray crystallography, NMR spectroscopy, and cryo-electron microscopy 1MAG.PDB ATOM 1 C FOR A 1A -3.690 -1.575 -2.801 1.00 0.00 C ATOM 2 O FOR A 1A -3.774 -1.363 -1.586 1.00 0.00 O ... 17

  18. PDB to PNP • Call PDB2PQR to get 1MAG.PQR(Q = Atomic Charges, R = Radii, 554 Atoms) 1MAG.PQR ATOM 1 C -3.690 -1.575 -2.801 0.000 2.000 .... ATOM 554 OT2 2.857 1.096 -15.510 -0.6700 1.7000 18

  19. Molecular Surface • Generate Molecular Surface (MS) in 3D uniform grid by van der Waas probe ball 19

  20. Molecular Surface Rolling Ball Algorithm Shrake-Rupley (1973) Ball (Water) Radius: 1.4ŠError: 1-3 Ų 20

  21. Numerical Methods • Rolling Ball Method for MS • 7-Point Finite Difference Method • MIB (Matched Interface and Boundary Method) • Solvers: CG, SOR • Use Chern-Liu-Wang method to treat singular charges • Newton’s Method • Continuity Method on Steric Functionaland Correlation length Numerical Methods 21

  22. Simplified MIB Numerical Methods 22

  23. 3D Results (Wei’s MIB) Zheng, Chen, Wei, Second-order Poisson Nernst-Planck solver for ion channel transport , JCP 2011. (Examples Taken) Wei’s > 27-pt FDM Ours 7-pt FDM h= 0.25Å Matrix Size = 4,096,000 MS Error: 1-3 Ų Results 23

  24. Our MIB vs Wei’s Ours is simpler, efficient, accurate but mid-point interface. Channel pore radius is only 4Å. May not have sufficient pts for high order MIB. Results 24

  25. Order and Time of MIB Results 25

  26. Born Ion ModelClassic Example of Solvation 26

  27. Charged Wall Models 27

  28. Charged Wall Models OverscreeningImpossible by PB 28

  29. L-type Calcium Channel Results 29

  30. L-type Calcium Channel Results 30

  31. L-type Calcium Channel Calcium Channel Blockers Diltiazem為一種「鈣離子阻斷劑」的降血壓及預防心絞痛藥物 Results 31

  32. L-type Calcium Channel Model Results 32

  33. Ca Binding Results by 3D sPNP Results 33

  34. Outlook • Equilibrium and Nonequilibrium Systems • Dielectric Response, Viscosity • Ion-Surface Interactions, Density Fluctuations • Electro-Osmotic Mobility, Surface Conductivity & Capacitance • PFNP vs Monte Carlo Simulations • GA, Ca, KcsA Channel Simulations • Mathematical and Numerical Analysis 34

  35. Thank You

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