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National Chiao Tung University

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1 National Chiao Tung University
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

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

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

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

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

7 From DNA to Protein

8 Explosion of Protein Structures
114569 2015 Genome Sequencing $3 billion 2000 RCSB PDB 12/21/2015 1995 $1000 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 ( ) Ludwig E. Boltzmann ( ) Walther H. Nernst ( ) Max K. Planck ( ) Enrico Fermi ( ) 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 are Frustrated by 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 (Classical: Volume Exclusion)
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 Structures 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 C FOR A 1A C ATOM O FOR A 1A O ... 22

23 PDB2PQR Call PDB2PQR to get 1MAG.PQR (Q = Atomic Charges, R = Radii, 554 Atoms) 1MAG.PQR ATOM C .... ATOM OT 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, (2013). J.-L. Liu and B. Eisenberg, Numerical methods for a Poisson-Nernst- Planck-Fermi model of biological ion channels, Phys. Rev. E 92, (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 PF: Only 3 adjustable parameters
Ion Activity (vs Experiment) PF: Only 3 adjustable parameters

30 Activity Coefficients ‘normalized’
NaCl Activity Coefficients ‘normalized’ free energy per mole 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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