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