Transcript Document

Continuum and Atomistic Modeling of Ion
Transport Through Biological Channels
Xiaolin Cheng
UT/ORNL Center for Molecular Biophysics
September 16th, 2009
Beijing, China
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Overview and Background
From Molecular Biology of the Cell. 4th ed. New York: Garland Publishing; 2002.
Synaptic Transmission
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Cryo-EM structure of nAChR from Torpedo marmorata, Unwin N 2005
ELIC (closed)
GLIC(open)
Dutzler R 2008
Dutzler R & Corringer J 2009
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Ligand Gated Ion Channel
Channel Gating
Ligand Binding
Ion Permeation4
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, currentconcentration relationship (saturation), conductancecharge/valence relationship…?
multiple approaches at various levels of details
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Multi-scale Modeling of Ion Permeation
Atomistic Modeling
Molecular Dynamics
timescale limitation, force filed issues
Continuum Modeling
Brownian Dynamics
Poisson-Boltzmann
Poisson-Nernst-Planck
rigid channel structure, structureless dielectric solvent and mean-field ion-ion
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MD Simulation of nAChR
120 Å
5 subunits, 1835 residues
~290 POPC
~60600 TIP3P water molecules
~86 Na+, and 26 ClIonic strength: 100 mM
Total atoms
~260,000
120 Å
180 Å
NAMD2.6
CHARMM27 force field
NPNST ensemble
r-RESPA method
(4 fs, 2 fs, 1 fs )
SPME electrostatics
20-100 ns production run
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Covariance Analysis
cij  (ri (t )  ri (t ) )  (rj (t )  rj (t ) ) ,
cij 
cij
cii1/ 2c1jj/ 2
residues that form a physically connected network of van der Waals interactions
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within the protein core that may connect the binding site with the distant gating
Dynamical Coupling of F135-I271
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Dynamical Coupling of F135-I271
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Single Channel Experiments
F135
L273
Gint = (Gwm + Gmw) – Gmm = 1.06 kcal/mol
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Channel Hydration Profile
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Water Dynamics inside the Channel
composition, size and membrane potential
on-off transitions of single channel currents Eisenberg RE BJ 2008
fast (burst) phase on-off transition may be related to water dynamics13
Barriers to Ion Translocation
A( z )  kBT ln Pz  A0
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 x> x
x
FABF   Fx
H = H0 + V(Q)
A 
A e
u( x )
 ln | J |
 k BT
x
x
x
A(x )   FABF  dx
V( Q )
e V( Q )
x

bias
bias
Umbrella Sampling
Adaptive Biasing Force
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The PMF Calculation
 | s  s( ti ) |2 

G( s ,t )   h exp 
2
2
w
ti
1


A. Laio and M. Parrinello, PNAS, 2002
 dq ( x' ( q )  x )e
P( x ) 
 dqe
V ( q ) / k BT
V ( q ) / k BT
In complex systems:
non-ergodic effect, not converge properly
increase local roughness  slow diffusion
Metadynamics
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Barriers to ion translocation
Hydrophobic restriction
5 kcal/mol
9 kcal/mol
E20’ (-2 kcal/mol)
D27’ (-2 kcal/mol)
E-1’ (-2 kcal/mol)
PMF for translocation of Na+ and Cl- within the nAChR pore
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Snapshots from individual windows
D27’
E20’
V13’
L9’
Translocation of Na+ ion in the pore of nAChR. Snapshots
from window 2, 4 and 6 of the ABF simulations.
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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
Hydrophobic restriction
Electrostatic effect
PMF for translocation of Na+ and Cl- within the GLIC channel
with improved metadynamics in LAMMPS
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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;
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2. Charge reversal mutation decreases conductance by up to 80%.
Multi-ion Channels
ion-ion interaction inside the channel
Gramicidin A channel
the bacterial KcsA potassium channel
PMFs for Ion Permeation
intracellular
Harmonic Fourier beads method
Khavrutskii IV JCP, 2006
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)
extracellular
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.
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PMFs for K+ and Na+ Permeation
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Continuum Modeling of Ion Permeation
What is missing from the atomistic simulation?
insufficient sampling – direct observation of ion conduction
inadequacy in force fields - polarization
Brownian Dynamics
Poisson-Boltzmann
Poisson-Nernst-Planck
long duration of time – kinetics, flux
simulation scale can be much greater
simple – gain fundamental insights
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Electrostatics Potentials across the
Channels
Poisson-Boltzmann electrostatics for the TM domains of nAChR and GlyR.
Electrostatic potentials along the z coordinate are shown below.
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Protein Flexibility Affects Ion Conduction
Wang HL et al. PLoS Comput. Biol. 2007
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Pore Size Fluctuations and Ion Conduction
Average pore sizes in different simulation windows (unpublished results)
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Protein Flexibility Affects PB Calculations
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.
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BioMOCA Simulation
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 LennardJones potential.
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BioMOCA Simulation
Time-averaged ion distributions in pre-TMD (left) and post-TMD (right) models
Note: cation density increases in the narrow region of the channel.
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Wang et al. BJ 2008
BioMOCA 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.
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Poisson Nernst Planck Equation
Average ion fluxes in terms of density and potential gradients

 
 (r ,t )






j (r ,t)   D(r )[ (r ,t ) 
Weff (r ,t )] where,Weff (r ,t )  Ucore (r )  q (r ,t )
k BT
Electrostatic potential arises from the Poisson equation




  [ (r ) (r )]  -4 ( c (r )   q  (r ))

3D PNP solver: Kurnikova MG, BJ 1999; Zhou Y et al. JPCB 2008
“Good agreement with experimental measurements is obtained (currentvoltage 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
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Continuum 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 Channels
How is water dynamics related to channel gating?
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
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Acknowledgements
Prof. J. Andrew McCammon (UCSD)
Dr. Benzhuo Lu
Dr. Ivaylo Ivanov
Dr. 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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