Continuum and Atomistic Modeling of Ion Transport Through Biological Channels

Xiaolin ChengUT/ORNL Center for Molecular Biophysics

September 16th, 2009Beijing, China

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Overview and BackgroundOverview and Background

Synaptic Transmission

From Molecular Biology of the Cell. 4th ed. New York: Garland Publishing; 2002.

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Cryo-EM structure of nAChR from Torpedo marmorata, Unwin N 2005

GLIC(open)Dutzler R & Corringer J 2009

ELIC (closed)Dutzler R 2008

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Ligand Gated Ion ChannelLigand Gated Ion Channel

Ligand Binding Ion Permeation

Channel Gating

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Outstanding Ion Permeation Questions

What is the conduction mechanism at the atomic level?Where is the gate (ion binding site) located?What’s the nature of the gate? What’s the origin of the charge selectivity?

Can we predict and provide microscopic explanations for macroscopic observations, such as channel conductance, current-voltage relationship, current-concentration relationship (saturation), conductance-charge/valence relationship…?

multiple approaches at various levels of detailsmultiple approaches at various levels of details

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Multi-scale Modeling of Ion Permeation

Molecular Dynamics

Atomistic Modeling Atomistic Modeling

Continuum Modeling Continuum Modeling

Poisson-Boltzmann

Brownian Dynamics

Poisson-Nernst-Planck

timescale limitation, force filed issues

rigid channel structure, structureless dielectric solvent and mean-field ion-ion6

5 subunits, 1835 residues~290 POPC~60600 TIP3P water molecules~86 Na+, and 26 Cl- Ionic strength: 100 mM

Total atoms~260,000

NAMD2.6CHARMM27 force fieldNPNST ensembler-RESPA method (4 fs, 2 fs, 1 fs )SPME electrostatics

20-100 ns production run

120 Å120 Å

180 Å

MD Simulation of nAChR

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Covariance Analysis

2/12/1,))()(())()((

jjii

ijijjjiiij cc

cctrtrtrtrc

residues that form a physically connected network of van der Waals interactions within the protein core that may connect the binding site with the distant gating site8

Dynamical Coupling of F135-I271

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Dynamical Coupling of F135-I271

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F135 L273

Single Channel Experiments

Gint = (Gwm + Gmw) – Gmm = 1.06 kcal/mol11

Channel Hydration Profile

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Water Dynamics inside the Channel

composition, size and membrane potentialon-off transitions of single channel currents Eisenberg RE BJ 2008

fast (burst) phase on-off transition may be related to water dynamics13

0APlnTk)z(A zB

Barriers to Ion Translocation

Potential of Mean Force (PMF) the relative thermodynamic stability of states along channel axis z

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The PMF Calculation

A

FABF= - <F

dFA

JTk

xuFF

ABF

BABF

)(

||ln)(

Adaptive Biasing Force

H = H0 + V(Q)

bias

QVbias

QV

e

eAA

)(

)(

Umbrella Sampling 15

it

i

w

|)t(ss|exph)t,s(G

21

2

2

A. Laio and M. Parrinello, PNAS, 2002

non-ergodic effect, not converge properly increase local roughness slow diffusion

Tk/)(V

Tk/)(V

B

B

ed

e))('(d)(P

q

q

q

qq

In complex systems:

The PMF Calculation

Metadynamics 16

PMF for translocation of Na+ and Cl- within the nAChR pore

E20’ (-2 kcal/mol)

D27’ (-2 kcal/mol)

Hydrophobic restriction

E-1’ (-2 kcal/mol)

5 k

cal/

mol

9 k

cal/

mol

Barriers to ion translocation

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Translocation of Na+ ion in the pore of nAChR. Snapshots from window 2, 4 and 6 of the ABF simulations.

V13’L9’

E20’

D27’

Snapshots from individual windows

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Water around a sodium ion

partial desolvation within the narrowest (hydrophobic) region of the pore

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Barriers to Ion Translocation

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PMF for translocation of Na+ and Cl- within the GLIC channel

with improved metadynamics in LAMMPS

Electrostatic effect

Hydrophobic restriction

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Ion Translocation under Membrane Potentials

cation pausing periods in the extracellular domain - these charged rings along the ion translocation pathway concentrate ions, giving rise to charge selectivity.

1. co-crystallization of acetylcholine binding protein with sulfate ions; 2. Charge reversal mutation decreases conductance by up to 80%.

Gramicidin A channel the bacterial KcsA potassium channel

Multi-ion ChannelsMulti-ion Channels

ion-ion interaction inside the channel

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The reactant state:E(C1); S0(W1); S1(C2); S2(W2); S3(C3); S4(W3)

The product state: S1(C1); S2(W1); S3(C2); S4(W2); I(C3); I(W3)

Reaction coordinate space includes all three cations, the oxygen atoms of the three water molecules in the single file and some protein degrees of freedom except the backbone of residues 67 to 74 and 80 to 82 during transition path optimization.

Harmonic Fourier beads method Khavrutskii IV JCP, 2006

extracellular

intracellular

PMFs for Ion PermeationPMFs for Ion Permeation

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PMFs for KPMFs for K++ and Na and Na+ + PermeationPermeation

Continuum Modeling of Ion Permeation

What is missing from the atomistic simulation? insufficient sampling – direct observation of ion conduction inadequacy in force fields - polarization

Poisson-Boltzmann

Brownian Dynamics

Poisson-Nernst-Planck

long duration of time – kinetics, fluxsimulation scale can be much greatersimple – gain fundamental insights

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Poisson-Boltzmann electrostatics for the TM domains of nAChR and GlyR. Electrostatic potentials along the z coordinate are shown below.

Electrostatics Potentials across the Electrostatics Potentials across the ChannelsChannels

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Protein Flexibility Affects Ion ConductionProtein Flexibility Affects Ion Conduction

Wang HL et al. PLoS Comput. Biol. 2007

Average pore sizes in different simulation windows (unpublished results)

Pore Size Fluctuations and Ion Conduction Pore Size Fluctuations and Ion Conduction

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Protein Flexibility Affects PB CalculationsProtein Flexibility Affects PB Calculations

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Left: 10 representative snapshots taken from an unbiased simulation with only water in the channel; Right: 10 representative snapshots are taken from each umbrella window. (unpublished results)

Note: GLIC channel is narrower than the nAChR channel.

BioMOCA SimulationBioMOCA Simulation

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BioMOCA - A Transport Monte Carlo approach to Ion Channel Simulation that simulates ion transport in electrolytes by computing trajectories of ions moving in a continuum dielectric background that represents water.

Brownian dynamics

Ion-water interactions are accounted for by randomly interrupting the trajectories using a scattering rate.

The local electric field is obtained by solving Poisson’s equation over the entire domain, which provides a simple way to include an applied bias and the effects of image charges induced at dielectric boundaries.

The finite ion size is addressed here by including a pairwise Lennard-Jones potential.

BioMOCA SimulationBioMOCA Simulation

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Time-averaged ion distributions in pre-TMD (left) and post-TMD (right) modelsNote: cation density increases in the narrow region of the channel.

Wang et al. BJ 2008

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BioMOCA SimulationBioMOCA Simulation

Current-voltage relationships. Wang et al. BJ 2008

Inward current rectification - the reduced conductance at positive potentials the conductance is 69 pS at negative potentials, while the conductance is 32 pS at positive potentials.

Poisson Nernst Planck EquationPoisson Nernst Planck Equation

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3D PNP solver: Kurnikova MG, BJ 1999; Zhou Y et al. JPCB 2008

“Good agreement with experimental measurements is obtained (current-voltage characteristics)” in the study of ion transport through gramicidin A dimer. Kurnikova MG, BJ 1999

“Good agreement with experimental measurements is obtained (current-voltage characteristics)” in the study of ion transport through gramicidin A dimer. Kurnikova MG, BJ 1999

“In simple cylindrical channels, considerable differences are found between the two theories (PNP vs. BD) with regard to the concentration profiles in the channel and its conductance properties. These tests unequivocally demonstrate that the mean-field approximation in the Poisson-Nernst-Planck theory breaks down in narrow ion channels that have radii smaller than the Debye length.” Corry B BJ 2009

“In simple cylindrical channels, considerable differences are found between the two theories (PNP vs. BD) with regard to the concentration profiles in the channel and its conductance properties. These tests unequivocally demonstrate that the mean-field approximation in the Poisson-Nernst-Planck theory breaks down in narrow ion channels that have radii smaller than the Debye length.” Corry B BJ 2009

)]()(

)()[()( t,rWTk

t,rt,rrD,trj eff

B

)()()( t,rqrUt,rW coreeff

))()((-4)]()([ rqrrr c

where,

Average ion fluxes in terms of density and potential gradients

Electrostatic potential arises from the Poisson equation

Continuum Modeling of Ion ChannelsContinuum Modeling of Ion Channels

Continuum model: size - local heterogeneity

PB: 1. effective dielectric constant inside the channel; 2. protein flexibility; 3. microscopic structure: solvation structure, van der Waals interactions, hydrogen bonding, …

PNP: rigid channel structure, continuum electrostatics, and mean-field ion-ion interactions, diffusion coefficient inside the channel, …

how to include these effects in the continuum models?

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Continuum Modeling of Ion ChannelsContinuum Modeling of Ion Channels

How is water dynamics related to channel gating?

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Probability Popen of a channel as a function of dcyl. Roth R. et al. BJ 2008

Water occupancy in the pore Nw vs time t. Dzubiella J and Hansen JP J. Chem. Phys. 2005

AcknowledgementsAcknowledgements

Prof. J. Andrew McCammon (UCSD)Dr. Benzhuo LuDr. Ivaylo IvanovDr. Ilja V. Khavrutskii

Prof. Steven M Sine (Mayo Clinic)Dr. Hailong Wang (Mayo Clinic)

Sebastian Fritsch (Heidelberg University/ORNL)Corinne Wacker (Heidelberg University/ORNL)

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