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A Poisson-Nernst-Planck-Fermi Theory in Bioelectricity and Electrochemistry

Institute of Physics National Chiao Tung University. A Poisson-Nernst-Planck-Fermi Theory in Bioelectricity and Electrochemistry. Jinn-Liang Liu 劉晉良 Department of Applied Mathematics National Hsinchu University of Education, Taiwan Oct. 27, 2016. 1.

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A Poisson-Nernst-Planck-Fermi Theory in Bioelectricity and Electrochemistry

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  1. Institute of Physics National Chiao Tung University A Poisson-Nernst-Planck-Fermi Theory in Bioelectricity and Electrochemistry Jinn-Liang Liu 劉晉良 Department of Applied MathematicsNational Hsinchu University of Education, Taiwan Oct. 27, 2016 1

  2. Bioelectricity, electric potentials and currents produced by or occurring within living organisms. --- Britannica 2

  3. Electrochemistryis a study of chemical processes that produce electricity. Food Energy Medicine Environment 3

  4. Unified Continuum Theory? Flow: From Meter to Angstrom Life’s Processes: Development, Survival, Disease.

  5. Biological Ion Channels(Physiology, Medicine, Pharmaceutical) HypothesizedIon Channel A. L. Hodgkin & A. Huxley Nobel Prize in Physiology or Medicine 1963 (Action Potential) E. Neher & B. Sakmann Nobel Prize in Physiology or Medicine 1991 (Current Measurement) ConfirmedIon Channel P. Agre & R. MacKinnon Nobel Prize in Chemistry 2003 (Crystal Structures) SawIon Channel

  6. Biological Ion Channels (Crystal Structures) • Gramicidin A • Sodium/Calcium Exchanger (NCX) • Transient Receptor Potential Channel (TRPV1) • Voltage-Gated Calcium Channel (CaVAb) • Potassium Channel (KcsA) • We are working on these channel structures from • Protein Data Bank. • 過去57年來，已發表的11萬4千個左右的結構檔案中， • 僅有576個的膜蛋白質 • (1, 1958 to 76495, 2011.10.11 to 114569, 2015.12.23)

  7. From DNA to Protein

  8. Explosion of Protein Structures 114569 2015 Genome Sequencing $3 billion 2000 RCSB PDB 12/21/2015 $1000 1995 3812 2012

  9. US Federal Research Funding, FY1995-2014 2014 NIH ≈ 5.7% Taiwan GDP 2013 科技部預算 ≈ 23.4% NIH

  10. Poisson-Nernst*-Planck*-Fermi*(Steric & Correlation) 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), Bikerman (1942), Grahame (1950), Eigen*-Wicke (1954), Borukhov-Andelman-Orland (1997), Santangelo (2006), Eisenberg-Hyon-Liu (2010), Bazant-Storey-Kornyshev (2011), Wei-Zheng-Chen-Xia (2012) * Nobel Laureates Application: Multiscale Flow in Bio, Chem, Phys, Nano Systems Challenge: Accuracy (vs Monte Carlo, Mol Dynam, Quant) 10

  11. Poisson Boltzmann Nernst* Planck* Fermi* Siméon D. Poisson (1781-1840) Ludwig E. Boltzmann (1844 -1906) Walther H. Nernst (1864 -1941) Max K.Planck (1858 -1947) Enrico Fermi (1901-1954) 11

  12. “Poisson Boltzmann theories are restricted to such low concentrations that the solutions cannot be studied in the laboratory” slight paraphrase of p. 125 of Barthel, Krienke, and Kunz, Springer, 1998 “In regard to concentrated solutions, many workers adopt a counsel of despair, confining their interest to concentrations below about 0.02 M, ... ”p. 302 Electrolyte Solutions (1959) Butterworths , also Dover (2002), emphasis added Physical Chemists areFrustratedby Real Solutions Bob Eisenberg

  13. Steric Effects near Charged Wall Steric effects: Each atom within a molecule occupies a certain amount of space. (Wiki) Boltzmann => Point Charges => Infinity => Unphysical Fermi => Hard Spheres => Finite => Saturation 13

  14. Fermi Distribution (Classical: Volume Exclusion) Different Valences Steric Potential Different Sizes New Saturation Condition Liu-Eisenberg (2014 JChPhy) Liu-Xie-Eisenberg (2016) K Species Ions (Balls) K+1: Water, K+2: Void 14

  15. Steric Potential (Fermi Distribution) K Species Ions, K+1: Water, K+2: Void Liu-Eisenberg (2014 JChPhy) 15

  16. Poisson-Nernst-Planck-Fermi Model Fourth-Order PDE Correlation New Liu-Eisenberg (2014 JChPhy) 16

  17. Correlation Santangelo (2006 PhyRevE) Correlation Length Liu (2013 JCompPhy) Liu-Eisenberg (2013 JPhyChem) 17

  18. Correlation Liu-Xie-Eisenberg (2016) 18

  19. Numerical Methods(3D Simulation Domain) KcsA Gramicidin NCX 19

  20. Molecular Surface & Protein Charges Wei et al. (2011 JCompPhy) 20

  21. Protein Data Bank 114569Structures 21

  22. PDB to PDB2PQR to 3DPNPF++ • Download GA from PDB (1MAG.PDB)PDB: Atomic information of Proteins determined by X-ray crystallography, NMR spectroscopy, and cryo-electron microscopy 1MAG.PDB (1MAG: PDB ID Code of Gramicidin A) 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 ... 22

  23. PDB2PQR • 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 23

  24. PDB2PQR to 3DPNPF++ • 3DPNPF++: 3D C++ Code Developed by Liu Since 2011 for Biological Ion Channel Simulations Using Poisson-Nernst-Planck-Fermi Theory • Main References:J.-L. Liu, Numerical methods for the Poisson-Fermi equation in electrolytes, J. Comp. Phys. 247, 88-99 (2013). J.-L. Liu and B. Eisenberg, Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels, Phys. Rev. E 92, 012711 (2015). 24

  25. Visual Molecular Dynamics(See Proteins) 25

  26. Molecular Surface • Generate Molecular Surface (MS) in 3D uniform grid by van der Waas probe ball to obtain SES(Solvent Excluded Surface) 26

  27. 3D 7-Point Finite Difference Method(SMIB: Simplified Matched Interface & Boundary) 27

  28. Double-Layer Capacitance (vs MC) Solution: NaCl Solution: CaCl₂ Liu (2013 JCompPhy) Bazant et al (2011 PRL) Over-screening by PF (Correlation)Impossible by PB 28

  29. Ion Activity (vs Experiment) • PF: Only 3 adjustable parameters

  30. Activity Coefficients‘normalized’ free energy per mole NaCl Liu-Eisenberg (2015 ChemPhysLett Frontiers Article) CaCl

  31. Debye-Huckel Fails Disastrously Poisson Boltzmann is quite inaccurate Poisson Fermi does Surprisingly Well

  32. Calcium Channel (vs Experiment) Experiments: Almers, McCleskey, Palade (JPhysio 1984) Dielectric Function (Correlation) Liu-Eisenberg (2015 PhyRevE) 108–fold M Variation in [Ca2+] = 32

  33. Gramicidin Channel (vs Experiment) Liu-Eisenberg (2015 PhyRevE) Mass Conservation? PB: No. PF: Yes. (Steric) 33

  34. Inside Gramicidin Water Density Dielectric Function Is OUTPUT

  35. NCX (vs Experiment) Structure: J. Liao, ..., Y. Jiang (Science 2012) Ca Channel Na Channel Stoichiometry: 3Na : 1Ca Liu-Hsieh-Eisenberg (2016 PhyChemB) 35

  36. NCX Pathways Channel Pores by VMD and 3DPNPF++ 36

  37. NCX Binding 4 Binding Ions Chelated by 12 Amino Acids (12 O, -6.36e) 63.4 M in Binding Pocket with 3 Ions 37

  38. PF is Molecular-Continuum Model All Atoms in Pore and Protein. Continuum in Baths. Algebraic Electric + Steric Potentials (N = 4591 Protein Atoms) PDE Electric + Steric Potentials (Continuum) 38

  39. NCX Selectivity Na Moves In from Out, Ca Out from In. Why? 39

  40. Thank You

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