jinn-liang liu national hsinchu university of education jan. 5, 2013
DESCRIPTION
Jinn-Liang Liu National Hsinchu University of Education Jan. 5, 2013. 台灣大學數學系. 3D Poisson-Fermi-Nernst-Planck Modeling of Biological Ion Channels. 1. Outline. Ion Channel PNP w. Steric and Correlations VMD (Visual Molecular Dynamics) From Protein Data Bank to PNP Numerical Methods - PowerPoint PPT PresentationTRANSCRIPT
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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.
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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 ".
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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