Jinn-Liang LiuNational Hsinchu University of Education

Jan. 5, 2013

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3D Poisson-Fermi-Nernst-

Planck Modelingof Biological Ion

Channels

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台灣大學數學系

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Outline

Ion Channel PNP w. Steric and Correlations VMD (Visual Molecular Dynamics) From Protein Data Bank to PNP Numerical Methods Preliminary Results Outlook

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Ion Channel

Nervous system (0:50)

Action Potentials (3:24)

Potassium Channel (1:42)

K+ radius: 0.133 nm, Na+ radius: 0.095 nm(0.133-0.095)/0.133 = 28.6%

Biological ion channels seem to be a precondition for all living matter.

P. Agre & R. MacKinnon(Nobel Prize in Chemistry 2003)for their discoveries concerning "channels in cell membranes".

Hodgkin–Huxley Model on Ion Channel

E. Neher & B. Sakmann(Nobel Prize in Physiology or Medicine 1991)for their discoveries concerning "the function of single ion channels in cells".

A. L. Hodgkin & A. Huxley (Nobel Prize in Physiology or Medicine 1963)for their discoveries concerning " the ionic mechanisms in the nerve cell membrane ".

Ion ChannelIon channels regulate the flow of ions across the membrane in all cells.

(Ions in water are the liquid of Life.)

Figures from Bob Eisenberg

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Steric & Correlation PNPPoisson-Fermi*-Nernst*-

Planck*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), Bazant-Storey-Kornyshev (2011)* Nobel Laureates

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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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Steric Effects

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

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Correlation Effects

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Simulation Domain

KcsA Channel Gramicidin A (GA) Channel

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Simulation Domain

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Visual Molecular Dynamics

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Protein Data Bank

76495Structures

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Visual Molecular DynamicsBuild Structure Place Membrane

Add Water Add Ions Melt Lipid Run MD

Simulation

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PDB to PNP Download GA from PDB (1MAG.PDB)PDB: Atomic information of Proteins determined by X-ray crystallography, NMR spectroscopy, and cryo-electron microscopy1MAG.PDB

ATOM 1 C FOR A 1A -3.690 -1.575 -2.801 1.00 0.00 C

ATOM 2 O FOR A 1A -3.774 -1.363 -1.586 1.00 0.00 O

...

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PDB to PNP Call PDB2PQR to get 1MAG.PQR(Q = Atomic Charges, R = Radii, 554 Atoms)

1MAG.PQRATOM 1 C -3.690 -1.575 -2.801 0.000

2.000....ATOM 554 OT2 2.857 1.096 -15.510 -0.6700

1.7000

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Molecular Surface Generate Molecular Surface (MS) in 3D uniform grid by van der Waas probe ball

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Rolling Ball Algorithm Shrake-Rupley (1973)Ball (Water) Radius: 1.4Å

Error: 1-3 Ų

Molecular Surface

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Numerical Methods

Numerical Methods

Rolling Ball Method for MS 7-Point Finite Difference Method MIB (Matched Interface and Boundary Method)

Solvers: CG, SOR Use Chern-Liu-Wang method to treat singular charges

Newton’s Method Continuity Method on Steric Functionaland Correlation length

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Simplified MIB

Numerical Methods

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3D Results (Wei’s MIB)

Results

Zheng, Chen, Wei, Second-order Poisson Nernst-Planck solver for ion channel transport , JCP 2011. (Examples Taken)

Wei’s > 27-pt FDMOurs 7-pt FDM

h= 0.25ÅMatrix Size = 4,096,000

MS Error: 1-3 Ų

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Our MIB vs Wei’s

Results

Ours is simpler, efficient, accurate but mid-point interface.Channel pore radius is only 4Å. May not have sufficient pts for high order MIB.

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Order and Time of MIB

Results

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Born Ion ModelClassic Example of

Solvation

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Charged Wall Models

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Charged Wall Models

OverscreeningImpossible by

PB

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L-type Calcium Channel

Results

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L-type Calcium Channel

Results

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L-type Calcium Channel

Results

Calcium Channel BlockersDiltiazem 為一種「鈣離子阻斷劑」的降血壓及預防心絞痛藥物

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L-type Calcium Channel Model

Results

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Ca Binding Results by 3D sPNP

Results

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Outlook Equilibrium and Nonequilibrium Systems

Dielectric Response, Viscosity Ion-Surface Interactions, Density Fluctuations

Electro-Osmotic Mobility, Surface Conductivity & Capacitance

PFNP vs Monte Carlo Simulations GA, Ca, KcsA Channel Simulations Mathematical and Numerical Analysis

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Thank You