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/

Carbon NanotubesHydrophobic channels - Perfect

Models for Membrane Water Channels

A balance between the size and hydrophobicity

Carbon NanotubesHydrophobic channels - Perfect

Models for Membrane Water Channels

•Much better statistics

•No need for membrane and lipid molecules

Carbon NanotubesHydrophobic channels - Perfect

Models for Membrane Water Channels

•Much better statistics

•No need for membrane and lipid molecules

Water Single-files in Carbon Nanotubes

Water files form polarized chains in nanotubes

Water-Nanotube Interaction can be Easily Modified

Hummer, et. al., Nature, 414: 188-190, 2001

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”

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.

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.

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.

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

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

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

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

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-

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)

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

Semipermeablemembrane

Semipermeablemembrane

(2)

(1)

(1)

NaCl

NaCl

U N

I T

C E

L L

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).

Applying a Pressure Difference Across the Membrane

/P nf A

Applying force on all water molecules.

Not a good idea!

Applying a Pressure Difference Across the Membrane

/P nf A

Applying force on bulk water only.

Very good

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

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

stereoisomers

Stereoselective Transport of Carbohydrates

by GlpF

Some stereoisomers show over tenfold difference in

conductivity.

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

Selectivity filter

Interactive Molecular Dynamics

VMD NAMD

Observed Induced Fit in Filter

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

RibitolOptimal hydrogen

bonding and hydrophobic matching

Arabitol10 times slower

Evidence for Stereoselectivity

-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