Simulating Membrane Channels · Simulating Membrane Channels - Nanotubes 12/9/2004 Emad Tajkhorshid 5 Chemical Potential of Water ln::::: =++ standard chemical potential of water

Simulating Membrane Channels - Nanotubes 12/9/2004

Emad Tajkhorshid 1

Simulating Membrane Channels

Part III. NanotubesTheory, Methodology

Theoretical and Computational BiophysicsDec 2004, Boston, MA

http://www.ks.uiuc.edu/Training/

Carbon NanotubesHydrophobic channels - Perfect Models

for Membrane Water Channels

A balance between the size and hydrophobicity


Emad Tajkhorshid 2



• Much betterstatistics

• No need formembrane andlipid molecules



• Much betterstatistics

• No need formembrane andlipid molecules


Emad Tajkhorshid 3

Water Single-files in Carbon Nanotubes

Water files form polarized chains innanotubes

Water-nanotube interaction can beeasily modified

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

Modifying chargesModifying vdW parameters


Emad Tajkhorshid 4

Calculation of Diffusion Permeability from MD

Φ0: number of watermolecules crossing thechannel from the left to theright in unit time

0!=

A

wd

N

Vp

Φ0 can be directly obtained throughequilibrium MD simulation by counting “fullpermeation events”

carbohydrate

440 nm

scattered light

H2O carbohydrate + H2O

lipid vesicles

channel-containingproteoliposomes

shrinking reswelling

100 mM Ribitol

Liposome Swelling Assay

GlpF is an aquaglyecroporin:both water and carbohydratecan be transported by GlpF.


Emad Tajkhorshid 5

Chemical Potential of Waterln

:

:

:

:

:

:

= + +

standard chemical potential of water

molar fraction of water

the gas constant

temperature

pressure

molar volume of water

o

w w w

o

w

w

w

wX

R

T

P

V

RT X PVµ µ

µ

membrane

(2)(1)

W W

purewater

purewater

0ln1 =!=wwXX

Water flow in either direction is thesame, i.e., no net flow of water.

Solutes Decrease the Chemical Potential of Water

ww

o

wwPVXRT ++= lnµµ

)2(ln)1(lnwwXRTXRT <

)2()1(ww

µµ <!

Semipermeablemembrane

(2)(1)

W+S W

purewater

dilutesolution

1)2( 1)1( =<wwXX

Water establishes a net flow fromcompartment (2) to compartment (1).

Addition of an impermeable solute toone compartment drives the systemout of equilibrium.


Emad Tajkhorshid 6

Establishment of Osmotic Equilibrium


(2)(1)

W+S W

purewater

dilutesolution

1)2( 1)1( =<wwXX

ww

o

w

ww

o

w

VPXRT

VPXRT

)2()2(ln)2(

)1()1(ln)1(

++

=++

µ

µ

(2)(1) :um@equilibriww

µµ =

At equilibrium, the chemical potential ofany species is the same at every point inthe system to which it has access.

wwwVPVPXRT )2()1()1(ln =+

ln (1)! = "w w

PV RT X

Establishment of an Osmotic Equilibrium


(2)(1)

W+S W

purewater

dilutesolution

1)2( 1)1( =<wwXX

ssw

ssw

XXX

XXX

!"!=#

<<=+

)1ln(ln

1 ; 1

Solute molar fraction in physiological(dilute) solutions is much smaller thanwater molar fraction.

s

w

RTP X

V!" = # =

ln (1)! = "w w

PV RT X

! =w s

PV RTX

Osmotic pressure


Emad Tajkhorshid 7

Establishment of an Osmotic Equilibrium

(2)(1)

W+S W

purewater

dilutesolution

1)2( 1)1( =<wwXX

Solute concentration (~0.1M) inphysiological (dilute) solutions is muchsmaller than water concentration(55M).

wsw

tot

s

w

w

w

s

w

s

ws

s

s

VCVV

n

V

V

n

n

n

n

nn

nX

==

=!+

=wsnn <<

s w s

w

RTP C V RTC

V! = " = =

! = " =s

w

RTP X

V

sP RT C!" = ! = !

Osmotic Flow of Water@equilibrium: 0P! "!# =

( )

v

v p

J P

J L P

! "!#

= ! "!#

Net flow is zero

Volumeflux ofwater

Hydraulicpermeability

( )vw f s

w

J PP A C

V RT

!" = = #!Molar flux

of water

Osmoticpermeability

(2)(1)

W+S W

purewater

dilutesolution


Emad Tajkhorshid 8

Simulation of osmotic pressure induced water transportmay be done by adding salt to one side of the membrane.


(1)

(2)

There is a small problem with this setup!

NaClNa++Cl-

Problem: The solvents on the two sides of amembrane 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)


Emad Tajkhorshid 9

We can include more layers of membrane and water tocreate two compartment of water that are not in contact

(2)

(1)

(1)



NaCl



(2)

(1)

(1)

NaCl

NaCl

U N

I T

C E

L L


Emad Tajkhorshid 10

The overall translationof the system isprevented by applyingconstraints or counterforces to the membrane.

membrane

membrane

membrane

water

water

Realizing a Pressure Difference in aPeriodic System

f is the forceon each watermolecule,for n watermolecules

1 2/P P nf P nf A= + !" = Fangqiang Zhu

F. Zhu, et al., Biophys. J. 83, 154 (2002).

Applying a Pressure DifferenceAcross the Membrane

/P nf A! =

Applyingforce on allwatermolecules.

Not a goodidea!


Emad Tajkhorshid 11


/P nf A! =

Applyingforce onbulk wateronly.

Very good


/P nf A! =

Applyingforce onlyon a slab ofwater inbulk.Excellent

Pf can be calculated fromthese simulations

( )w f s

PP A C

RT

!" = #!


Emad Tajkhorshid 12

Calculation of osmoticpermeability of water channels

pf: 7.0 ± 0.9 × 10-14 cm3/sExp: 5.4 – 11.7 × 10-14 cm3/spf: 1.4×10-13 cm3/s

GlpF Aquaporin-1

stereoisomers

Stereoselective Transport of Carbohydratesby GlpF

Some stereoisomers showover tenfold difference in

conductivity.


Emad Tajkhorshid 13

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


Emad Tajkhorshid 14

Interactive Molecular Dynamics

VMD NAMD

Observed Induced Fit in Filter


Emad Tajkhorshid 15

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 bondingand hydrophobic matching

Arabitol10 times slower

Evidence for Stereoselectivity


Emad Tajkhorshid 16

-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(

dipo

le a

ngle

with

z)

z (Å)

Dipolereversalregion

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Simulating Membrane Channels · Simulating Membrane Channels - Nanotubes 12/9/2004 Emad Tajkhorshid 5 Chemical Potential of Water ln::::: =++ standard chemical potential of water