Jinn-Liang LiuNational Hsinchu University of Education

May 31, 2014

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Poisson-Nernst-Planck-Fermi Theory

for

Biological Ion Channels

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2nd TWSIAM Annual MeetingNational Chiao Tung University

P. Agre & R. MacKinnonNobel Prize in Chemistry 2003(Crystal Structures)

E. Neher & B. SakmannNobel Prize in Physiology or Medicine 1991(Current Measurement)

A. L. Hodgkin & A. Huxley Nobel Prize in Physiology or Medicine 1963(Action Potential)

HypothesizedIon Channel

ConfirmedIon Channel

SawIon Channel

Ion Channel(Physiology, Medicine, Pharmaceutical)

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Unified Continuum Theory?Flow: From Meter to Angstrom

Life’s Processes: Exocytosis, Contraction, Metabolism,Transcription, Fertilization, etc.

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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 SystemsChallenge: Accuracy (vs Monte Carlo, Mol Dynam, Quant)

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

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Steric Effects

Boltzmann => Infinity => UnphysicalFermi => Finite => Saturation

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Correlation Effects

Yes, Cor.

No Cor.

Bazant, Storey, Kornyshev (PRL 2011)

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different sizes

Free Energy of Electrolyte Solutions

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Fermi Distribution(Classical: Excluded Volume)

Steric Potential

Liu-Eisenberg (2013 JPhyChem)

different valences

different sizesSaturation Condition

New

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Poisson-Nernst-Planck-Fermi Model

New

K Species Ions K+1: WaterK+2: Void

Correlation

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Born Ion Model (Ex) Classic Example of

Solvation

MIBPB: Geng, Yu, Wei (JChP 2007)

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Charged Wall Models (MC)

OverscreeningImpossible by

PB

Solution: NaCl Solution: CaCl₂

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L-Type Ca Channel Model 1

Boda, Valiskó, Henderson, Eisenberg, Gillespie, Nonner (JGenPhysio 2009)

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PF vs PB

Oxygen Ion Concentration

Profile

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Dielectric Function

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Ca Binding Curves (MC)

# Na+

# Ca²⁺

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Experiments: Almers, McCleskey, Palade (JPhysio 1984)SingleChannelCurrentFemto Ampere (fA)

108–fold M Variation in [Ca2+] =

PNPF vs Ca Channel Experiment

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PNPF vs NCX ExperimentJ. Liao, ..., Y. Jiang (Science 2012) Crystal Structure of Sodium /Calcium

Exchanger (NCX)

PNPF = 2.3 ÅExp = 2.4 Å Na Channel

Ca Channel

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Thank

You