molecular dynamics simulation of membrane channels part iii. nanotubes theory, methodology summer...
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Molecular Dynamics Simulation of Membrane
Channels
Part III. NanotubesTheory, Methodology
Summer School on Theoretical and Computational Biophysics
June 2003, University of Illinois at Urbana-Champaign
http://www.ks.uiuc.edu/training/SumSchool03/
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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
A
wd N
Vp
0 can be directly obtained through equilibrium MD simulation by counting “full permeation events”
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carbohydrate
440 nm
scattered light
H2O carbohydrate + H2O
lipid vesicles
channel-containing proteoliposomes
shrinking reswelling
100 mM Ribitol
Liposome Swelling Assay
GlpF is an aquaglyecroporin: both water and carbohydrate can be transported by GlpF.
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Chemical Potential of Water
ln
:
:
:
:
:
:
standard chemical potential of water
molar fraction of water
the gas constant
temperature
pressure
molar volume of water
ow w w
o
w
w
w
wX
R
T
P
V
RT X PV
membrane
(2)(1)
W W
purewater
purewater
0ln1 ww XX
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
wwoww PVXRT ln
)2(ln)1(ln ww XRTXRT
)2()1( ww
Semipermeablemembrane
(2)(1)
W+S W
purewater
dilutesolution
1)2( 1)1( ww XX
Water establishes a net flow from compartment (2) to compartment (1).
Addition of an impermeable solute to one compartment drives the system out of equilibrium.
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Establishment of Osmotic Equilibrium
Semipermeablemembrane
(2)(1)
W+S W
purewater
dilutesolution
1)2( 1)1( ww XX
wwow
wwow
VPXRT
VPXRT
)2()2(ln)2(
)1()1(ln)1(
(2)(1) :um@equilibri ww
At equilibrium, the chemical potential of any species is the same at every point in the system to which it has access.
www VPVPXRT )2()1()1(ln
ln (1) w wPV RT X
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Establishment of an Osmotic Equilibrium
Semipermeablemembrane
(2)(1)
W+S W
purewater
dilutesolution
1)2( 1)1( ww XX
ssw
ssw
XXX
XXX
)1ln(ln
1 ; 1
Solute molar fraction in physiological (dilute) solutions is much smaller than water molar fraction.
sw
RTP X
V
ln (1) w wPV RT X
w sPV RTX
Osmotic pressure
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Establishment of an Osmotic Equilibrium
(2)(1)
W+S W
purewater
dilutesolution
1)2( 1)1( ww XX
Solute concentration (~0.1M) in physiological (dilute) solutions is much smaller than water concentration (55M).
wswtot
s
w
w
w
s
w
s
ws
ss
VCVV
n
V
V
n
n
n
n
nn
nX
ws nn
s w sw
RTP C V RTC
V
sw
RTP X
V
sP RT C
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Osmotic Flow of Water
@equilibrium: 0P
( )v
v p
J P
J L P
Net flow is zero
Volume flux of water
Hydraulic permeability
( )vw f s
w
J PP A C
V RT
Molar flux
of water
Osmotic permeability
(2)(1)
W+S W
purewater
dilutesolution
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Simulation of osmotic pressure induced water transport may be done by adding salt to one side of
the membrane.
Semipermeablemembrane
(1)
(2)
There is a small problem with this setup!
NaClNa++Cl-
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Problem: The solvents on the two sides of a membrane in a conventional periodic system are
connected.(1)
(2)
(1)
(2)
(1)
(2)
(1)
(2)
(1)
(2)
(1)
(2)
(1)
(2)
(1)
(2)
(1)
(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
(2)
(1)
(1)
Semipermeablemembrane
Semipermeablemembrane
NaCl
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Semipermeablemembrane
Semipermeablemembrane
(2)
(1)
(1)
NaCl
NaCl
U N
I T
C E
L L
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The overall translation of the system is prevented by applying constraints or counter forces to the membrane.
membrane
membrane
membrane
water
water
Realizing a Pressure Difference in a Periodic System
f is the force on each water molecule, for n water molecules
1 2 /P P nf P nf A Fangqiang Zhu
F. Zhu, et al., Biophys. J. 83, 154 (2002).
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Applying a Pressure Difference Across the Membrane
/P nf A
Applying force on all water molecules.
Not a good idea!
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Applying a Pressure Difference Across the Membrane
/P nf A
Applying force on bulk water only.
Very good
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Applying a Pressure Difference Across the Membrane
/P nf A
Applying force only on a slab of water in bulk.
Excellent
Pf can be calculated from these simulations
( )w f s
PP A C
RT
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Calculation of osmotic permeability of water
channels
pf: 7.0 ± 0.9 10-14 cm3/sExp: 5.4 – 11.7 10-14 cm3/spf: 1.410-13 cm3/s
GlpF Aquaporin-1
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stereoisomers
Stereoselective Transport of Carbohydrates
by GlpF
Some stereoisomers show over tenfold difference in
conductivity.
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GlpF + glycerolGlpF + water
Channel Constriction
HOLE2: O. Smart et al., 1995
red < 2.3 Å 2.3 Å > green > 3.5 Å blue > 3.5 Å
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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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0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-10 -7. -5 -2. 0 2.5 5 7.5 10 12. 15
Confinement in Filter• Selection occurs in most constrained region.
• Caused by the locking mechanism.
RM
S m
otio
n in
x a
nd
y
z (Å)
Filterregion
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RibitolOptimal hydrogen
bonding and hydrophobic matching
Arabitol10 times slower
Evidence for Stereoselectivity
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-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-10 -7 -4 -1 2 5 8 11 14
Dipole Reversal in Channel• Dipole reversal pattern matches water.
• Selects large molecules with flexible dipole.
cos(
dip
ole
angl
e w
ith
z)
z (Å)
Dipolereversalregion