Liquid-vapour oscillations of water in hydrophobic nanopores

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Alicante 2003 4th European Biophysics Congress Liquid-vapour

1 Alicante th European Biophysics Congress Liquid-vapour oscillations of water in hydrophobic nanopores 7 th July 2003 Oliver Beckstein and Mark S. P. Sansom Department of Biochemistry, Laboratory of Molecular Biophysics, University of Oxford. oliver@biop.ox.ac.uk

2 Outline 1. Introduction: Hydrophobic pores in ion channels 2. Simplified model pore: Molecular dynamics 3. Water in hydrophobic pores: temporal oscillations liquid vapour thermodynamics (equilibrium) dynamics (diffusion, flux, permeability coefficient) 4. Simple thermodynamic model

3 nachr : A hydrophobic gate to ion permeation? N. Unwin, Phil. Trans. Roy. Soc. B 355 (2000) A. Miyazawa, Y. Fujiyoshi and N. Unwin, Nature 423 (2003), drawn from pdb:1oed closed R 3.5Å hydrophobic girdle (Leu, Val, Phe) open R 6.5Å polar pore lining nachr: nicotinic acetylcholine receptor, a cation selective, ligand-gated ion channel

4 Hydrophobic Gates Putative gates are lined by hydrophobic amino acids (Leu, Val, Ile, Phe,... )

Model system R M R z L M L P Molecular Dynamics Hydrophobic atoms :

charges): surface character Harmonically restrained CH 4 : flexibility

1 bar (weak coupling) 52 ns T sim 120 ns Dimensions ( nachr gate) pore

5 Model system R M R z L M L P Molecular Dynamics Hydrophobic atoms : unified methane molecules Hydrophilic: two parallel dipoles (backbone charges): surface character Harmonically restrained CH 4 : flexibility Water model: SPC GROMACS 3, ffgmx Electrostatics: PME; T = 300 K, P = 1 bar (weak coupling) 52 ns T sim 120 ns Dimensions ( nachr gate) pore radius 0.15nm R 1.0nm pore length L P = 0.8nm mouth R M = 1.0nm L M = 0.8nm

6 Average water density z-averaged and radially averaged water density in units of SPC bulk water at 300 K and 1 bar. Grid spacing 0.05 nm.

7 Oscillations in the pore occupancy Strong dependence of the pore state on the radius R. Analysis in terms of 1. density 2. free energy f (T,n;R) 3. state ( openness ω ) 4. kinetics (liquid vapour) 5. dynamical properties O. Beckstein and M. S. P. Sansom, PNAS 100 (2003)

8 Free energy Helmholtz free energy F(T,V, N) from the pore occupancy distribution p(n) (T = 300 K, V = V P = const) Free energy landscape βf = ln p(n) +C Free energy density and chemical potential (n as order parameter) f (T,n) = F V µ(t,n) = f n

9 Characterization of the pore state water-filled ion conducting [ open, ω(t) = 1] if State and Openness n pore n bulk η, empty ions cannot permeate [ closed, ω(t) = 0] state-detection: Schmitt-trigger with η = 0.4 ± 0.25 openness: ω = T open T sim T open : time during which the pore is in the open state

10 Equilibrium liquid vapour openness <ω> R [nm] hydrophobic two dipoles Openess/probability for liquid state: ω = 1 Tsim dt ω(t) = T o T sim 0 T sim Equilibrium constant K: K = T c T o = T sim T o T o = ω 1 1 (open = liquid state, closed = vapour state)

11 Equilibrium liquid vapour openness <ω> hydrophobic two dipoles β Ω = βω c βω ο R [nm] R [nm] -6 Free energy difference (grand potential, µ = const) β Ω(R) = β[ω c (R) Ω o (R)] = lnk(r) = ln ( ω(r) 1 1 )

12 Equilibrium liquid vapour β Ω = βω c βω ο Ω(R) = Ω v (R) Ω l (R) = p v (µ)lπr 2 + 2πRL γ vw + 2πR 2 γ lv ( p l (µ)lπr 2 + 2πRL γ lw ) R [nm] Ω(R) = = [ 2γ lv ( )( µ µ sat nv (T,µ sat ) n l (T,µ sat ) ) ] L πr 2 + 2πL(γ vw γ lw )R [ ] 2γ lv + µ n vl L π R 2 + 2πL γ w R = a 2 R 2 + a 1 R

13 Equilibrium liquid vapour openness <ω> R [nm] hydrophobic two dipoles R [nm] β Ω = βω c βω ο thermodynamic model based on surface energy arguments seems to hold even at atomic dimensions (?!) hydrophobic gating (+ polar pore lining can open a hydrophobic gate) a 2 2πL γ w [k B T /Å 2 ] [k B T /Å] hydrophobic +0.65± ±0.11 two dipoles +0.51± ±0.01 ω(r) = exp[ β Ω(R)] Beckstein, Biggin & Sansom, J. Phys. Chem. B 105 (2001)

14 multi-pass (no single-filing) transition time 30 ps Dynamics τ p mean permeation time τ p,bulk = 29.9 ± 0.1 ps j 0 equilibrium current density j 0,bulk = 320 ± 3 ns 1 nm 2 D z diffusion coefficient in z D bulk = 4.34 ± 0.01 nm 2 ns 1

15 Water transport in experiment and simulation Ref. p f Φ 0 [cm 3 s 1 ] [ns 1 ] Aqp1 (1) Aqp4 (1) AqpZ (2) ga (3) desformyl ga (4) R = 0.20 nm R = 0.30 nm R = 0.35 nm R = 0.40 nm R = 0.45 nm R = 0.50 nm R = 0.55 nm R = 0.60 nm R = 0.70 nm R = 1.0 nm carbon nanotube (5) desformyl ga (DH) (6) non-equilibrium flux Φ = β p f ( P Π) equilibrium flux Φ 0 = ν X /T sim osmotic permeability coefficient 6 p f = 1 2 Φ 0v l Water translocation occurs in bursts 1. Yang, B., van Hoek, A. N., & Verkman, A. S. (1997) Biochemistry 36, Pohl, P., Saparov, S. M., Borgnia, M. J., & Agre, P. (2001) Proc. Natl. Acad. Sci. USA 98, Pohl, P. & Saparov, S. M. (2000) Biophys. J. 78, Saparov, S. M., Antonenko, Y. N.,, & Pohl, P. (2000) Biophys. J. 79, Hummer, G., Rasaiah, J. C., & Noworyta, J. P. (2001) Nature 414, R 0.24 nm 6. de Groot, B. L., Tieleman, D. P., Pohl, P., & Grubmüller, H. (2002) Biophys. J. 82,

Influence of wall flexibility: Squidgy pores Top: k = 0.

031 nm Middle: k = 1.0 kj mol 1 nm 2, RMSD ρ P = 0.

16 Influence of wall flexibility: Squidgy pores Top: k = 0.2 kj mol 1 nm 2, RMSD ρ P = ± nm Middle: k = 1.0 kj mol 1 nm 2, RMSD ρ P = ± nm Bottom: k = 5.0 kj mol 1 nm 2, RMSD ρ P = ± nm greater flexibility shifts equilibrium towards vapour state more than just decreasing effective pore radius R ρ P (k)

hydrophobic gating Summary oscillations liquid vapour explained in a simple thermodynamic model surface tension γ vw γ lw determines hydrophobicity wall-water interaction strength (packing and

17 hydrophobic gating Summary oscillations liquid vapour explained in a simple thermodynamic model surface tension γ vw γ lw determines hydrophobicity wall-water interaction strength (packing and well-depth) is crucial hydrophobic environment induces collective water movements (bursts) accelerates water transport strategically placed hydrophilic groups mimic bulk water environment in Aqps flexible ( jelly ) pores favour vapour

18 Additional slides water structure and radial PMF distribution and lifetimes of open and close times; a mechanism for filling and emptying capillary condensations comparison with Hummer s water in hydrophobic nanotubes and Giaya and Thompson s mean field model

19 Water structure state phase n/n bulk pore saturated, expt. closed vapour open liquid [see also Brovchenko, Geiger & Oleinikova, Phys. Chem. Chem. Phys. 3 (2001)] radial PMF of a water molecule: βf(r) = ln n(r) n bulk +C

Probability p(λ,n n max ) for the formation of a cavity of given radius λ and

20 Lifetimes Average open and closed time τ o = t o and τ c = t c Prob(filling) 1/τ c constant evaporation Prob(emptying) 1/τ o exponential cavitation Probability p(λ,n n max ) for the formation of a cavity of given radius λ and density below n max is an exponential [Hummer et al, Proc. Natl. Acad. Sci. USA 93 (1996)]

Capillary condensation and evaporation Kelvin s equation Young s equation ln p p 0 = βγ lvv l r γ wv = γ wl + γ lv cosθ and geometry p pressure of vapour in equilibrium with liquid p 0 vapour bulk

21 Capillary condensation and evaporation Kelvin s equation Young s equation ln p p 0 = βγ lvv l r γ wv = γ wl + γ lv cosθ and geometry p pressure of vapour in equilibrium with liquid p 0 vapour bulk saturation pressure 1/r curvature v l molecular volume of the liquid γ lv liquid-vapour surface tension γ wv wall-vapour surface tension γ wl wall-liquid surface tension θ contact angle R pore radius R = r cosθ Kelvin s equation for cylindrical pores: ln p(r) p 0 = β(γ wv γ wl )v l R... with hydrophobic walls γ wv < γ wl γ wv γ wl < 0 ln p(r)/p 0 > 0 p(r) > p 0 if actual vapour pressure > p(r) > p 0 condensation

22 Water in a carbon nanotube 1 and a mean field model 2 Ref. ρ w ε f w ε eff R c this work (1) < > 0.24 (2) ρ w density of wall atoms (nm 3 ) ε f w fluid-wall interaction (kj mol 1 ) ε eff effective interaction strength ρ w ε f w (kj mol 1 nm 3 ) R c critical/coexistence pore radius (nm) wall-density influences behaviour strongly 1. Hummer et al., Water conduction through the hydrophobic channel of a carbon nanotube, Nature 414 (2001), Giaya and Thompson, Water confined in cylindrical micropores, J. Chem. Phys. 117 (2002), 3464

Controllable Water Channel Gating of Nanometer Dimensions

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