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Jinn-Liang Liu National Hsinchu University of Education Oct. 31, Nov. 13, 2011

Jinn-Liang Liu National Hsinchu University of Education Oct. 31, Nov. 13, 2011. 靜宜大學財務與計算數學系. 3D Poisson-Nernst-Planck Modeling of Biological Ion Channels. 1. Outline. Ion Channel Steric PNP Model VMD (Visual Molecular Dynamics) From Protein Data Bank to PNP Numerical Methods

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Jinn-Liang Liu National Hsinchu University of Education Oct. 31, Nov. 13, 2011

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  1. Jinn-Liang Liu National Hsinchu University of Education Oct. 31, Nov. 13, 2011 靜宜大學財務與計算數學系 3D Poisson-Nernst-Planck Modelingof Biological Ion Channels 1

  2. Outline • Ion Channel • Steric PNP Model • 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% Ion Channel

  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 PNP Model sPNP 6

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

  8. Simulation Domain KcsA Channel Gramicidin A (GA) Channel sPNP 8

  9. Simulation Domain sPNP 9

  10. Visual Molecular Dynamics VMD 10

  11. Protein Data Bank 76495Structures PDB 11

  12. Visual Molecular Dynamics Build Structure  Place Membrane  Add Water  Add Ions  Melt Lipid  Run MD Simulation VMD 12

  13. 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 ... PDB 13

  14. PDB to PNP • Call PDB2PQR to get 1MAG.PQR(Q = Atomic Charges, R = Radii, 554 Atoms) 1MAG.PQR ATOM 4 N VAL 1 -3.043 -2.601 -3.416 -0.4700 1.8500 ATOM 5 CA VAL 1 -2.415 -3.640 -2.601 0.0700 2.2750 .... ATOM 544 OT2 TRP 15 2.857 1.096 -15.510 -0.6700 1.7000 PDB 14

  15. Molecular Surface • Generate Molecular Surface (MS) in 3D uniform grid by van der Waas probe ball PDB 15

  16. Molecular Surface Rolling Ball Algorithm Shrake-Rupley (1973) Ball (Water) Radius: 1.4ŠError: 1-3 Ų PDB 16

  17. Numerical Methods • 7-Point Finite Difference Method • Rolling Ball Method for MS • MIB (Matched Interface and Boundary Method) and IIM (Immersed Interface Method) to treat jump conditions • Solvers: CG, SOR • Use Chern-Liu-Wang method to treat singular charges • Gummel’s Nonlinear Iterations • Continuity Method on Steric Function Numerical Methods 17

  18. IIM & MIB IIM Jump Position MIB Jump Jump Value Numerical Methods 18

  19. 3D Results (IIM vs MIB) Goal: 2nd Order Convergence Results 19

  20. 3D Results (IIM vs MIB) Results 20

  21. 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 21

  22. 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 22

  23. Order and Time of MIB Results 23

  24. L-type Calcium Channel Results 24

  25. L-type Calcium Channel Results 25

  26. 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 26

  27. L-type Calcium Channel Model Results 27

  28. Ca Binding Results by 3D sPNP Results 28

  29. Outlook • Correlation Effects in PNP Models • Charged Wall Models • PNP vs Monte Carlo Simulations • Ca, GA, K Channel Models • Fast Linear & Nonlinear Solvers Results 29

  30. Coworkers • Bob Eisenberg, Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago • Dezső Boda, Department of Physical Chemistry, University of Pannonia, Hungary • Tzyy-Leng Horng, Department of Applied Mathematics, Feng Chia University, Taiwan • Tai-Chia Lin, Department of Mathematics, National Taiwan University, Taiwan Results 30

  31. ~ Thank You ~

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