Water and Proton Conduction Through Carbon Nanotubes Gerhard Hummer by vivi07

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									Water and Proton Conduction Through Carbon Nanotubes Gerhard Hummer
Laboratory of Chemical Physics, NIDDK National Institutes of Health, Bethesda, MD 20892, USA

hummer@helix.nih.gov (Department of Health and Human Services)
Banff, April 2003

Biological “Fuel Cell”: The “Proton Pump” Cytochrome c Oxidase
eO2 + H+ H2O + + H+ H+ + + - ADP ATP O2 + 8H+ + 4e- → 2H2O + 4H+(pumped)

Active-site cavity
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Water Pores: Aquaporin 1

Banff, April 2003

Water in Confinement • Does water fill narrow hydrophobic channels?
– Thermodynamics – Kinetics

• What is the functional role of hydrophobic channels?
– Water conduction – Proton transfer – Proton pumping

Banff, April 2003

Carbon Nanotube as Simplest Molecular Channel • Fullerene-type cylindrical molecules • sp2 carbons in `honeycomb’ lattice • Open or closed ends • Single or multi-wall structure • Diameters of ~1 nm and larger • Chemically functionalizable

Banff, April 2003

Carbon Nanotube in Water
(Hummer, Rasaiah & Noworyta, Nature 414, 188, 2001)

•

Classical molecular dynamics simulation
– Flexible (6,6)-nanotube (8Å diameter, 13.5Å length) – Graphite parameters – ~1000 TIP3P water molecules – AMBER 6.0 – Particle-mesh Ewald – 66 ns

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Water Occupancy

• Nanotube fills within picoseconds and remains filled for 66 ns

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Pair Energy Distribution (rOO < 3.5 Å)

15% unbound pairs

Pair energy (kJ/mol)
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Thermodynamics from Binding Energies: HighEnergy Tail Determines Vapor Pressure
• Channel shields from fluctuations β µ ex = e βu p(u )du • High-energy states weakly populated e

∫

=β(µ-u) βµ

• Excess chemical potentials from histogram analysis
− µexw = -6.05 ± 0.02 kcal/mol (bulk TIP3P water) − µexnt = -6.87 ± 0.07 kcal/mol (nanotube) − -kT ln(<N>/ρ∆V) = -0.87 kcal/mol ~ µnt - µw
Banff, April 2003

water binding energy u (kcal/mol)

Weakly bound states determine chemical potential

Hydrogen Bonds in Narrow Channel

• H-bond angles > 30o
– Water: 37% – Nanotube: <15%

• H-bond Lifetime –Water: 1ps –Nanotube: 5ps

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Dipolar Orientation of Water Chain Flips on Nanosecond Timescale via Defect Propagation
de fe ct
0ps 1ps 2ps

up

down

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Water Transport • >1000 water molecules transported through nanotube

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Single-File Transport as a Continuous-Time Random Walk (Berezhkovskii and Hummer, Phys. Rev. Lett. 89, 064503, 2002) • Ptr = (N+1)-1 ~ L-1

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Water Flow Through Nanotube Membranes under Osmotic Gradient
(Kalra, Garde, and Hummer, Proc. Natl. Acad. Sci. USA, in press, 2003)

H2O NaCl + H2O

NaCl + H2O

• ~5 mol/l NaCl generates net flow of ~5 H2O/ns per tube (~independent of tube length up to at least 5 nm) • Flow rate as in aquaporin-1
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Water Flow and Water Monolayers

• Metastable water monolayer sandwiched for ~60 ns between porous and nonpolar nanotube membranes
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Effects of Interaction Potentials and Solvent Conditions: Modified Carbon-Water Attractions

• Modified carbon parameters
§ εCO = 0.065 (0.114) kcal/mol § σCO = 3.41 (3.28) A

new

kBT

original

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Filling/Emptying Transitions

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Change in potential parameters/solvent conditions results in bimodal occupancy distribution
Average occupancy N~exp(-β∆µex) corresponds to ‘unstable’ fragmented chain → fluctuations between filled and empty states

µex

reduced vdW attraction

µexbulk

µexnt

Bimodal distribution

Average density in tube ~ bulk density

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Two-State Kinetics • Life times
– τfilled= 250 ps – τempty= 2 ns

• Free energies

β∆Fkin = ln(τempty/ τfilled ) = 2.1± 0.5 β∆Feq = ln(pN<4/pN>3) = 2.1± 0.5

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Filling/Emptying Transition Paths
(Waghe, Rasaiah and Hummer, J. Chem. Phys. 117, 10789, 2002)

• Contiguous chains of dipolarly ordered water molecules
– Filling from one side only (not simultaneously)

– Emptying initiated on side with water dipole pointing outward
Banff, April 2003

Proton Transport
(Dellago, Naor and Hummer, Phys. Rev. Lett. 90, 105902, 2003)

• Molecular dynamics simulations of water and excess proton in nanotube
– Car-Parrinello dynamics (DFT/BLYP) – Empirical-valence-bond model (Schmitt and Voth, J.
Phys. Chem. B 102, 5547, 1999)

EVB CPMD

Banff, April 2003

Proton Transport Coupled to Defect Motion
• Proton diffusion approximately 40 times faster than in bulk water: D(H+)≈170x10-5 cm2s-1 • Strong 1/r-coupling to H-bond (D) defect in periodic tube: 10-fold reduction of apparent diffusion constant
D defect
H+ H+/D

L defect

H+

D

H+

D

H+

D

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Implications for Proton Transfer in Proteins • Proton wires ‘on demand’
– Increase in local polarity can trigger water’ influx to establish protonic connectivity

• High ‘delivery speed’
– High mobility of a single proton along ordered water chain inside hydrophobic pore

• Unidirectional wires (‘diode’)
– Hydrogen-bond orientation controlled by electrostatics

• High ‘fidelity’
– Only single proton delivered without reorientation
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Light-driven proton pump: Water Filling/Emptying in Bacteriorhodopsin
(Hummer, Rasaiah, Noworyta, ICCN Proceedings, 2002)

• Reprotonation of Asp-96 from solvent
H+

OH O

O O H+ N

-

O

- O
H+ N

OH O H+ N

N

Banff, April 2003

Proton Shuttle in Cytochrome P450cam: Water Penetration and Side Chain Isomerization
(Taraphder and Hummer, J. Am. Chem. Soc. 125, 3931, 2003)

• Cryo-trapped intermediate with dioxygen bound
– Exposure of amide group to previously empty non-polar cavity induces water filling
(Schlichting et al, Science 287, 1615, 2000)

• Proton shuttle through concerted water penetration and side chain motion

Banff, April 2003

Network Model of Proton Transfer in Proteins • H+ transfer via H bonds and shuttles of ionizable side-chains: H+ + AH…OH…B- → HA…HO…HB

• Recursive network analysis of H+ relay groups
– Sample fluctuations in side-chain orientations and hydration to collect possible H+ paths – Rank paths by using “steric” action
p (i → j ) = exp( − β ∆Eij ) / ∑ exp( − β∆ E ik )
k

p (i1 → i2 → ....in ) = ∏ p (ik → ik +1 ) ≡ exp ( − S )
Banff, April 2003

Energetics of Asp-251 Shuttle in P450cam
• Exhaustive search of sidechain conformers • Sterically optimal path for Asp-251 isomerization

Banff, April 2003

Proton Pumping in Cytochrome C Oxidase
(Wikström, Verkhovsky and Hummer, Biochim. Biophys. Acta-Bioenerget., in press, 2003)

•

Gating of ‘chemistry’ and ‘pumping’
– 2 alternative water-mediated proton pathways through nonpolar cavity for ‘chemistry’ and ‘pumping’ – Water in cavity orientated by electric field between hemes a and a3/CuB – Switching between H+ paths by water orientation (‘diode’)
P

•

Coupling of O2 reduction to pumping
transfer from E286 to heme-a3 propionate provides gate (‘solvent fluctuation’) for electron transfer from heme a to heme-a3/CuB – ‘Pumped’ H+ trapped by electron transfer and reprotonation of E286
Banff, April 2003

–

H+

N

Water-Gated Proton Pump

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Heme-a/Heme-a3/CuB Charge Distribution Switches Water-Chain Orientation
(Wikström, Verkhovsky and Hummer, Biochim. Biophys. Acta-Bioenerget., in press, 2003)

• Reorientation within ~ 1 ps of electron transfer in molecular dynamics simulations
• Heme-a reduced • Heme-a3/CuB oxidized • Heme-a oxidized • Heme-a3/CuB reduced

E

E

Banff, April 2003

Conclusions: Water in Nonpolar Channels • Water can favorably occupy nonpolar channels, despite loss of hydrogen bonds
– Water wetting nanotube interior (Gogotsi et al, Appl.
Phys. Lett., 2001; Maniwa et al., J.Phys.Soc. Jpn., 2002):

• Channels protect from fluctuations
– Narrow distribution of energies – Unbound states rarely populated – Increased life time of hydrogen bonds with rare defects – Long life-time of water-chain orientation
Banff, April 2003

Conclusions: Drying • Water occupancy in nanotube channel extremely sensitive to attractive interactions
– Difficult to predict whether filling of narrow channels occurs under ambient conditions, but small perturbations to near-ambient conditions (T, p, osmolality, etc.) can tune filling

• Sharp two-state transitions between empty and filled states
– Intermediate states are rarely populated because of fragmented hydrogen bonds

Banff, April 2003

Conclusions: Water Transport • Efficient water conduction in greasy channel
– Optimum tradeoff between occupancy and mobility achieved in weakly polar channels such as aquaporin-1

• Rate comparable to biological channels
– ~5 water per ns and pore at 5 mol/l osmotic gradient

• Conduction in bursts
– Tightly hydrogen bonded water molecules move collectively – Quantitatively described by continuous-time random walk
Banff, April 2003

Conclusions: Proton Transport • Proton diffuses ~40 times faster along 1D water chain than through bulk water • Polarity changes can induce water filling and emptying to form and break water wires • Redox-dependent electric fields can gate proton flow by orienting water in weakly polar channel of cytochrome c oxidase • Pumping as solvent-fluctuation required for rapid electron transfer couples redox chemistry to vectorial proton translocation
Banff, April 2003

Acknowledgments
• Nanotube in water
– J. C. Rasaiah (U. Maine) – P. J. Noworyta (U. Maine) – A. Waghe (U. Maine) – S. Vaithee (NIH, U. Maine)

• Proton transport
– C. Dellago (U. Rochester; U. Vienna) – M. Naor (U. Rochester)

• Proton pumping in oxidase
– M. Wikström (U. Helsinki) – M. Verkhovsky (U. Helsinki)

• Water transport
– A. Berezhkovskii (NIH) – A. Kalra (NIH, RPI) – S. Garde (RPI)

• P450cam
– S. Taraphder (NIH, IIT Kharagpur)

Banff, April 2003


								
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