Molecular Dynamics Simulation of Membrane Channels

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Molecular Dynamics Simulation of Membrane Channels

• Part III. Nanotubes
• Theory, Methodology

Summer School on Theoretical and Computational
Biophysics June 2003, University of Illinois at
Urbana-Champaign http//www.ks.uiuc.edu/training/S
umSchool03/
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Carbon NanotubesHydrophobic channels - Perfect
Models for Membrane Water Channels
A balance between the size and hydrophobicity
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Carbon NanotubesHydrophobic channels - Perfect
Models for Membrane Water Channels

• Much better statistics
• No need for membrane and lipid molecules

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Carbon NanotubesHydrophobic channels - Perfect
Models for Membrane Water Channels

• Much better statistics
• No need for membrane and lipid molecules

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Water Single-files in Carbon Nanotubes
Water files form polarized chains in nanotubes
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Water-Nanotube Interaction can be Easily Modified
Hummer, et. al., Nature, 414 188-190, 2001
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Calculation of Diffusion Permeability from MD
?0 number of water molecules crossing the
channel from the left to the right in unit time
?0 can be directly obtained through equilibrium
MD simulation by counting full permeation events
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Liposome Swelling Assay
carbohydrate
440 nm
H2O
carbohydrate H2O
shrinking
reswelling
scattered light
lipid vesicles
100 mM Ribitol
channel-containing proteoliposomes
GlpF is an aquaglyecroporin both water and
carbohydrate can be transported by GlpF.
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Chemical Potential of Water
pure water
pure water
W
W
(2)
(1)
membrane
Water flow in either direction is the same, i.e.,
no net flow of water.
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Solutes Decrease the Chemical Potential of Water
Addition of an impermeable solute to one
compartment drives the system out of equilibrium.
pure water
dilute solution
WS
W
(2)
(1)
Water establishes a net flow from compartment (2)
to compartment (1).
Semipermeable membrane
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Establishment of Osmotic Equilibrium
At equilibrium, the chemical potential of any
species is the same at every point in the system
to which it has access.
pure water
dilute solution
WS
W
(2)
(1)
Semipermeable membrane
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Establishment of an Osmotic Equilibrium
Solute molar fraction in physiological (dilute)
solutions is much smaller than water molar
fraction.
pure water
dilute solution
WS
W
(2)
(1)
Semipermeable membrane
Osmotic pressure
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Establishment of an Osmotic Equilibrium
pure water
dilute solution
Solute concentration (0.1M) in physiological
(dilute) solutions is much smaller than water
concentration (55M).
WS
W
(2)
(1)
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Osmotic Flow of Water
pure water
dilute solution
Net flow is zero
WS
W
(2)
(1)
Volume flux of water
Hydraulic permeability
Osmotic permeability
Molar flux of water
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Simulation of osmotic pressure induced water
transport may be done by adding salt to one side
of the membrane.
NaCl?NaCl-
(1)
Semipermeable membrane
(2)
There is a small problem with this setup!
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Problem The solvents on the two sides of a
membrane in a conventional periodic system are
connected.
(1)
(1)
(1)
(2)
(2)
(2)
(1)
(1)
(1)
(2)
(2)
(2)
(1)
(1)
(1)
(2)
(2)
(2)
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We can include more layers of membrane and water
to create two compartment of water that are not
in contact
(1)
Semipermeable membrane
(2)
Semipermeable membrane
(1)
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NaCl
(1)
Semipermeable membrane
(2)
Semipermeable membrane
NaCl
(1)
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Realizing a Pressure Difference in a Periodic
System
Fangqiang Zhu
f is the force on each water molecule, for n
water molecules
The overall translation of the system is
prevented by applying constraints or counter
forces to the membrane.
F. Zhu, et al., Biophys. J. 83, 154 (2002).
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Applying a Pressure Difference Across the Membrane
Applying force on all water molecules.
Not a good idea!
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Applying a Pressure Difference Across the Membrane
Applying force on bulk water only.
Very good
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Applying a Pressure Difference Across the Membrane
Applying force only on a slab of water in bulk.
Excellent
Pf can be calculated from these simulations
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Calculation of osmotic permeability of water
channels
Aquaporin-1
GlpF
pf 7.0 0.9 ? 10-14 cm3/s Exp 5.4 11.7 ?
10-14 cm3/s
pf 1.4?10-13 cm3/s
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Stereoselective Transport of Carbohydratesby GlpF
Some stereoisomers show over tenfold difference
in conductivity.
stereoisomers
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Channel Constriction
GlpF glycerol GlpF water
red lt 2.3 Å 2.3 Å gt green gt 3.5
Å blue gt 3.5 Å
HOLE2 O. Smart et al., 1995
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Selectivity filter
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Interactive Molecular Dynamics
VMD
NAMD
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Observed Induced Fit in Filter
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Confinement in Filter

• Selection occurs in most constrained region.
• Caused by the locking mechanism.

RMS motion in x and y
z (Å)
Filter region
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Evidence for Stereoselectivity
Ribitol Optimal hydrogen bonding and hydrophobic
matching
Arabitol 10 times slower
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Dipole Reversal in Channel

• Dipole reversal pattern matches water.
• Selects large molecules with flexible dipole.

cos(dipole angle with z)
z (Å)
Dipole reversal region