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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/SumSchool03/.

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Molecular dynamics simulation of membrane channels

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/SumSchool03/


Carbon nanotubes hydrophobic channels perfect models for membrane water channels
Carbon NanotubesHydrophobic channels - Perfect Models for Membrane Water Channels

A balance between the size and hydrophobicity


Carbon nanotubes hydrophobic channels perfect models for membrane water channels1
Carbon NanotubesHydrophobic channels - Perfect Models for Membrane Water Channels

  • Much better statistics

  • No need for membrane and lipid molecules


Carbon nanotubes hydrophobic channels perfect models for membrane water channels2
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 Single-files in Carbon Nanotubes

Water files form polarized chains in nanotubes


Water nanotube interaction can be easily modified
Water-Nanotube Interaction can be Easily Modified

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


Calculation of diffusion permeability from md
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”


Liposome swelling assay
Liposome Swelling Assay

carbohydrate

440 nm

H2O

carbohydrate +

H2O

shrinking

reswelling

scattered light

lipid vesicles

100 mM Ribitol

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

channel-containing proteoliposomes


Chemical potential of water
Chemical Potential of Water

pure

water

pure

water

W

W

(1)

(2)

membrane

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


Solutes decrease the chemical potential of water
Solutes Decrease the Chemical Potential of Water

Addition of an impermeable solute to one compartment drives the system out of equilibrium.

dilute

solution

pure

water

W+S

W

(1)

(2)

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

Semipermeable

membrane


Establishment of osmotic equilibrium
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.

dilute

solution

pure

water

W+S

W

(1)

(2)

Semipermeable

membrane


Establishment of an osmotic equilibrium
Establishment of an Osmotic Equilibrium

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

dilute

solution

pure

water

W+S

W

(1)

(2)

Semipermeable

membrane

Osmotic pressure


Establishment of an osmotic equilibrium1
Establishment of an Osmotic Equilibrium

dilute

solution

pure

water

Solute concentration (~0.1M) in physiological (dilute) solutions is much smaller than water concentration (55M).

W+S

W

(1)

(2)


Osmotic flow of water
Osmotic Flow of Water

dilute

solution

pure

water

Net flow is zero

W+S

W

(1)

(2)

Volume flux of water

Hydraulic permeability

Osmotic permeability

Molar flux of water


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

NaClNa++Cl-

(1)

Semipermeable

membrane

(2)

There is a small problem with this setup!


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)


NaCl conventional periodic system are connected.

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)


U N I T C E L L conventional periodic system are connected.

NaCl

(1)

Semipermeable

membrane

(2)

Semipermeable

membrane

NaCl

(1)


Realizing a Pressure Difference in a Periodic System conventional periodic system are connected.

membrane

water

membrane

water

membrane

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).


Applying a Pressure Difference Across the Membrane conventional periodic system are connected.

Applying force on all water molecules.

Not a good idea!


Applying a Pressure Difference Across the Membrane conventional periodic system are connected.

Applying force on bulk water only.

Very good


Applying a Pressure Difference Across the Membrane conventional periodic system are connected.

Applying force only on a slab of water in bulk.

Excellent

Pf can be calculated from these simulations


Calculation of osmotic permeability of water channels conventional periodic system are connected.

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


Stereoselective transport of carbohydrates by glpf
Stereoselective Transport of Carbohydrates conventional periodic system are connected.by GlpF

Some stereoisomers show over tenfold difference in conductivity.

stereoisomers


Channel constriction
Channel Constriction conventional periodic system are connected.

GlpF + glycerol

GlpF + water

red < 2.3 Å

2.3 Å > green > 3.5 Å

blue > 3.5 Å

HOLE2: O. Smart et al., 1995


Selectivity filter conventional periodic system are connected.


Interactive molecular dynamics
Interactive Molecular Dynamics conventional periodic system are connected.

VMD

NAMD


Observed induced fit in filter
Observed Induced Fit in Filter conventional periodic system are connected.


Confinement in filter
Confinement in Filter conventional periodic system are connected.

  • Selection occurs in most constrained region.

  • Caused by the locking mechanism.

RMS motion in x and y

z (Å)

Filter

region


Evidence for conventional periodic system are connected.Stereoselectivity

Ribitol

Optimal hydrogen bonding and hydrophobic matching

Arabitol

10 times slower


Dipole reversal in channel
Dipole Reversal in Channel conventional periodic system are connected.

  • Dipole reversal pattern matches water.

  • Selects large molecules with flexible dipole.

z (Å)

cos(dipole angle with z)

Dipole

reversal

region


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