1. Jinn-Liang Liu National Hsinchu University of Education May 31, 2014 1 Poisson-Nernst-Planck-Fermi Theory for Biological Ion Channels 1 2 nd TWSIAM Annual Meeting National Chiao Tung University

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

3. 3 Unified Continuum Theory? Flow: From Meter to Angstrom Life’s Processes: Exocytosis, Contraction, Metabolism, Transcription, Fertilization, etc.

4. 4 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), Dutta-Bagchi (1950), 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)

5. 5 Steric Effects Steric effects arise from the fact that each atom within a molecule occupies a certain amount of space. (Wiki)

6. 6 Steric Effects Boltzmann => Infinity => Unphysical Fermi => Finite => Saturation

7. 7 Correlation Effects Yes, Cor. No Cor. Bazant, Storey, Kornyshev (PRL 2011)

8. 8 different sizes Free Energy of Electrolyte Solutions

9. 9 Fermi Distribution (Classical: Excluded Volume) Steric Potential Liu-Eisenberg (2013 JPhyChem) different valences different sizes Saturation Condition New

10. 10 Poisson-Nernst-Planck-Fermi Model New K Species Ions K+1: Water K+2: Void Correlation

11. 11 Born Ion Model (Ex) Classic Example of Solvation MIBPB: Geng, Yu, Wei (JChP 2007)

12. 12 Charged Wall Models (MC) Overscreening Impossible by PB Solution: NaClSolution: CaCl ₂

13. 13 L-Type Ca Channel Model 1 Boda, Valiskó, Henderson, Eisenberg, Gillespie, Nonner (JGenPhysio 2009)

14. 14 PF vs PB Oxygen Ion Concentration Profile

15. 15 Dielectric Function

16. 16 Ca Binding Curves (MC) # Na + # Ca² ⁺

17. 17 Experiments: Almers, McCleskey, Palade (JPhysio 1984) Single Channel Current Femto Ampere (fA) 10 8 –fold M Variation in [Ca 2+ ] = PNPF vs Ca Channel Experiment

18. 18 PNPF vs NCX Experiment J. Liao,..., Y. Jiang (Science 2012) Crystal Structure of Sodium /Calcium Exchanger (NCX) PNPF = 2.3 Å Exp = 2.4 Å Na Channel Ca Channel

19. 19 Thank You