Continuum and Atomistic Modeling of Ion Transport Through Biological Channels

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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
GLIC(open) Dutzler R Corringer J 2009
ELIC (closed) Dutzler R 2008
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Ligand Gated Ion Channel
Ligand Binding
Ion Permeation
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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? Whats the nature of the gate? Whats
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 details
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Multi-scale Modeling of Ion Permeation
Atomistic Modeling
Molecular Dynamics
timescale limitation, force filed issues
Continuum Modeling
rigid channel structure, structureless dielectric
solvent and mean-field ion-ion
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MD Simulation of nAChR
120 Å
120 Å
5 subunits, 1835 residues 290 POPC 60600 TIP3P
water molecules 86 Na, and 26 Cl- Ionic
strength 100 mM Total atoms 260,000 NAMD2.6 CH
ARMM27 force field NPNST ensemble r-RESPA method
(4 fs, 2 fs, 1 fs ) SPME electrostatics 20-100
ns production run
180 Å
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Covariance Analysis
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 site
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Dynamical Coupling of F135-I271
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Dynamical Coupling of F135-I271
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Single Channel Experiments
??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 dynamics
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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
H H0 V(Q)
Adaptive Biasing Force
Umbrella Sampling
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The PMF Calculation
Metadynamics
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Barriers to ion translocation
E20 (-2 kcal/mol)
Hydrophobic restriction
9 kcal/mol
5 kcal/mol
E-1 (-2 kcal/mol)
D27 (-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 2. Charge reversal
mutation decreases conductance by up to 80.
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Multi-ion Channels
ion-ion interaction inside the channel
Gramicidin A channel
the bacterial KcsA potassium channel
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PMFs for Ion Permeation
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) 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
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
Poissons 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.
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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. Wang et al. BJ 2008
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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
where,
Electrostatic potential arises from the Poisson
equation
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
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?
Water occupancy in the pore Nw vs time t.
Dzubiella J and Hansen JP J. Chem. Phys. 2005
Probability Popen of a channel as a function of
dcyl. Roth R. et al. BJ 2008
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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)