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Jinn-Liang Liu National Hsinchu University of Education, Taiwan May 30, 2016

Jinn-Liang Liu National Hsinchu University of Education, Taiwan May 30, 2016. 2016 Banff Workshop. Poisson-Nernst-Planck-Fermi Theory for Biological Ion Channels. 1. Unified Continuum Theory? Flow: From Meter to Angstrom. Life’s Processes: Development, Survival, Disease.

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Jinn-Liang Liu National Hsinchu University of Education, Taiwan May 30, 2016

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  1. Jinn-Liang Liu National Hsinchu University of Education, Taiwan May 30, 2016 2016 Banff Workshop Poisson-Nernst-Planck-Fermi Theory for Biological Ion Channels 1

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

  3. 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

  4. 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.

  5. Explosion of Protein Structures 2016 118928 Only 2809 Transmembrane Proteins in PBD by 5/20/2016 1995 3812

  6. US Federal Research Funding, FY1995-2014

  7. 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) 7

  8. 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) 8

  9. “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

  10. Werner Kunz “It is still a fact that over the last decades, it was easier to fly to the moonthan to describe the free energy of even the simplest salt solutions beyond a concentration of 0.1M or so.” W. Kunz, "Specific Ion Effects" World Scientific, Singapore, 2009; p 11.

  11. Crowded Active Sitesin 573 Enzymes (Density in M)

  12. 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 12

  13. Fermi Distribution (Classical: Volume Exclusion) Different Valences Steric Potential New Different Sizes Saturation Condition K Species Ions K+1: Water, K+2: Void Liu-Eisenberg (2014 JChemPhy) 13

  14. Poisson-Nernst-Planck-Fermi Model Correlation New K Species Ions K+1: WaterK+2: Void Liu-Eisenberg (2014 JChemPhy) 14

  15. Correlation Santangelo (2006 PhyRevE) Correlation Length Liu (2013 JCompPhy) Liu-Eisenberg (2013 JPhyChem) 15

  16. Steric (Fermi Distribution) Liu-Eisenberg (2014 JChemPhy) 16

  17. Numerical Methods(3D Simulation Domain) KcsA Gramicidin NCX 17

  18. Molecular Surface & Protein Charges Wei et al. (2011 JCompPhy) 18

  19. 3D 7-Point Finite Difference Method(SMIB: Simplified Matched Interface & Boundary) 19

  20. SMIB vs Wei’s MIB SMIB is second order. SMIB is simpler, efficient, accurate but mid-point interface. Channel pore radius is only 4Å. May not have sufficient pts for high order MIB. Liu (2013 JCompPhy) 20

  21. Charged Wall Models (vs MC) Solution: NaCl Solution: CaCl₂ Liu (2013 JCompPhy) Bazant et al (2011 PRL) Over-screening by PF (Correlation)Impossible by PB 21

  22. Ion Activity (vs Experiment) • PF: Only one adjustable parameter

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

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

  25. Calcium Channel (vs Experiment) Experiments: Almers, McCleskey, Palade (JPhysio 1984) Dielectric Function (Correlation) Liu-Eisenberg (2015 PhyRevE) 108–fold M Variation in [Ca2+] = 25

  26. Gramicidin Channel (vs Experiment) Liu-Eisenberg (2015 PhyRevE) Mass Conservation? PB: No. PF: Yes. (Steric) 26

  27. Inside Gramicidin Water Density Dielectric Function Is OUTPUT

  28. NCX (vs Experiment) Structure: J. Liao, ..., Y. Jiang (Science 2012) Ca Channel Na Channel Stoichiometry: 3Na : 1Ca Liu-Hsieh-Eisenberg (2016 PhyChemB) 28

  29. NCX Pathways Channel Pores by VMD and 3DPNPF++ 29

  30. NCX Binding 4 Binding Ions Chelated by 12 Amino Acids (12 O, -6.36e) 63.4 M in Binding Pocket with 3 Ions 30

  31. 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) 31

  32. NCX Selectivity Na Moves In from Out, Ca Out from In. Why? 32

  33. Thank You

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