Part III. Nanotubes Theory, Methodology

Transcription

1 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

2 Carbon Nanotubes Hydrophobic channels - Perfect Models for Membrane Water Channels A balance beteen the size and hydrophobicity

3 Carbon Nanotubes Hydrophobic channels - Perfect Models for Membrane Water Channels Much better statistics No need for membrane and lipid molecules

4 Carbon Nanotubes Hydrophobic channels - Perfect Models for Membrane Water Channels Much better statistics No need for membrane and lipid molecules

5 Water Single-files in Carbon Nanotubes Water files form polarized chains in nanotubes

6 Water-Nanotube Interaction can be Easily Modified Hummer, et. al., Nature, 414: , 2001

7 Calculation of Diffusion Permeability from MD Φ 0 : number of ater molecules crossing the channel from the left to the right in unit time p d = V N A Φ 0 Φ 0 can be directly obtained through equilibrium MD simulation by counting full permeation events

8 Liposome Selling Assay carbohydrate 440 nm H 2 O carbohydrate + H 2 O shrinking reselling scattered light 100 mm Ribitol lipid vesicles GlpF is an aquaglyecroporin: both ater and carbohydrate can be transported by GlpF. channel-containing proteoliposomes

9 Chemical Potential of Water o µ = µ + RT ln X + PV µ R : T : P : o X V : : : standard chemical potential of ater molar fraction of ater the gas constant temperature pressure molar volume of ater X 1 ln X = = pure ater W pure ater W 0 Water flo in either direction is the same, i.e., no net flo of ater. membrane

10 Solutes Decrease the Chemical Potential of Water µ = µ ln o RT ln X < + RT X + RT ln X µ ( 1) < µ PV Addition of an impermeable solute to one compartment drives the system out of equilibrium. X ( 1) 1 X = 1 dilute solution W+S < pure ater W Water establishes a net flo from compartment to compartment. Semipermeable membrane

11 Establishment of Osmotic : µ = µ At equilibrium, the chemical potential of any species is the same at every point in the system to hich it has access. X ( 1) 1 X = 1 dilute solution < pure ater µ + RT ln X o o + µ + RT ln X P V + = P V W+S W RT ln X + P V = P V PV = RT ln X Semipermeable membrane

12 Establishment of an Osmotic Equilibrium PV = RT ln X Solute molar fraction in physiological (dilute) solutions is much smaller than ater molar fraction. X ( 1) 1 X = 1 dilute solution < pure ater X + X s ln X = 1 ; X PV = s << 1 = ln(1 X RTX s s ) X s W+S W = P = RT V X s Osmotic pressure Semipermeable membrane

13 Establishment of an Osmotic Equilibrium Solute concentration (~0.1M) in physiological (dilute) solutions is much smaller than ater concentration (55M). X RT = P= Xs V s = = n s n V s tot n + s V n = n n s s C V = n n s V V RT Π= P = CV = RTC V s s n s << n X ( 1) 1 X = 1 dilute solution W+S < pure ater W Π = P = RT C s

14 Osmotic Flo of P Π= 0 J v J = L ( P Π) v Net flo is zero P p Π dilute solution W+S pure ater W Volume flux of ater Molar flux of ater Hydraulic permeability Jv P Φ = = Pf A( Cs) V RT Osmotic permeability

15 Simulation of osmotic pressure induced ater transport may be done by adding salt to one side of the membrane. NaCl Na + +Cl - Semipermeable membrane There is a small problem ith this setup!

16 Problem: The solvents on the to sides of a membrane in a conventional periodic system are connected.

17 We can include more layers of membrane and ater to create to compartment of ater that are not in contact NaCl Semipermeable membrane Semipermeable membrane

18 NaCl U N I T C E L L NaCl Semipermeable membrane Semipermeable membrane

19 Realizing a Pressure Difference in a Periodic System P1 = P2 + nf P = nf / A f is the force on each ater molecule, for n ater molecules Fangqiang Zhu membrane ater membrane The overall translation of the system is prevented by applying constraints or counter forces to the membrane. ater membrane F. Zhu, et al., Biophys. J. 83, 154 (2002).

20 Applying a Pressure Difference Across the Membrane P = nf / A Applying force on all ater molecules. Not a good idea!

21 Applying a Pressure Difference Across the Membrane P = nf / A Applying force on bulk ater only. Very good

22 Applying a Pressure Difference Across the Membrane P = nf / A Applying force only on a slab of ater in bulk. Excellent P f can be calculated from these simulations P Φ = Pf A( Cs ) RT

23 Calculation of osmotic permeability of ater channels GlpF Aquaporin-1 p f : cm 3 /s p f : 7.0 ± cm 3 /s Exp: cm 3 /s

24 Stereoselective Transport of Carbohydrates by GlpF Some stereoisomers sho over tenfold difference in conductivity. stereoisomers

25 Channel Constriction GlpF + glycerol GlpF + ater HOLE2: O. Smart et al., 1995 red < 2.3 Å 2.3 Å > green > 3.5 Å blue > 3.5 Å

26 Selectivity filter

27 Interactive Molecular Dynamics VMD NAMD

28 Observed Induced Fit in Filter

29 0.4 Confinement in Filter Selection occurs in most constrained region. Caused by the locking mechanism. RMS motion in x and y Filter region z (Å)

30 Evidence for Stereoselectivity Ribitol Optimal hydrogen bonding and hydrophobic matching Arabitol 10 times sloer

31 Dipole Reversal in Channel Dipole reversal pattern matches ater. Selects large molecules ith flexible dipole. 0.6 cos(dipole angle ith z) Dipole reversal region z (Å)