The glassy state of water in model and real systems. Is it biologically useful ?
Sara E. Pagnotta
Fabio Bruni, Giorgio Careri, John Rupley, A. Carl Leopold, Jim Clegg, A. K. Soper, Maria Antonietta Ricci, Francesco Pizzitutti, Riccardo Gargana,…
Questions•Biological function: role of water?
•Is the glassy state of interfacial water functional?
The Glassy behavior:A nifty description
or a functional strategy?
•Biological function: role of water?
Tardigradi (Echiniscus spinulosus)
Nematods seeds (es. Zea mays)
•Biological function: role of water?
H/D exchange
enzymaticactivity
•Frequency-dependent sample conductivity, by means of dielectricspectroscopy;•Conductivity is due to proton displacements along hydrogen-bondedwater molecules on the protein surface;
Ionizable groups on the protein surface are sources/sink of migratingprotons
We measured:
•Biological function: role of water?
…threshold phenomena ?
Percolation Theory
•Spatially random events & Topological disorder.
•Critical concentration: long range connectivity.
•At the percolation threshold an extended cluster spansthe system.
•Biological function: role of water?
Critical exponents of percolation conductivity:
Glass and silver-coated discs 1.25
Lysozyme 1.29
Purple membrane 1.23
Maize embryo 1.23
Theory 2D 1.26
Glass and silver-coated spheres 1.75
Artemia cysts 1.65
Theory 3D 1.70
•Biological function: role of water?
Protonic percolation threshold and emergence of biological function
Anhydrous system Hydration triggeredfunction
hc (g/g)
Lysozyme Enzymatic activity 0.16
0.06
0.08
0.35
Purple membrane Photoresponse
Maize embryo Germination
Artemia cysts Pre-metabolism
Questions•Biological function: role of water?
•Is the glassy state of interfacial water functional?
•Biological function: role of water?
Is it glassy?
Interfacial water
Let’s look at the structure…
Water in porous vycor glass(empty pore ≈ globular protein)
• no ordered structures;• supercooling;• distorted network & catalytic activity ?
•Is the glassy state of interfacial water functional?
A.K. Soper, F. Bruni, M.A. Ricci (1998) J. Chem. Phys., 109 (4), 1486-1494.
•Is the glassy state of interfacial water functional?
Sample Cell
a
a
d
b
c
3
4
2
ottone
rexolite
silicone
acciaio
pvc
teflon
crema di silicone
shapal-m
e
m
l
i
h
g
f
1
Ym
Yx
Ycpa
Data analysisThe total measured admittance Ym(ω) is due to the combined admittance of sample Yx(ω) and the admittance of blocking electrodes YCPA(ω).
•Is the glassy state of interfacial water functional?
YCPA ω( )= A jω( )d ,0 ≤ d ≤1
Yx ω( )= jωεoSh
∆ε
1+ jωτ( )α⎛ ⎝ ⎜
⎞ ⎠ ⎟
β
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟
MW
+ εsi+
∆εi
1+ jωτ i( )α i⎛ ⎝ ⎜
⎞ ⎠ ⎟ βi
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟
− j σεoωi
∑
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥⎥⎥⎥⎥
εm* ω( )= h
jωεoSYm ω( )= ′ ε m ω( )− j ′ ′ ε m ω( )
General form for the admittances of circuital elements is:
200
150
100
50
0
Im(Y
m/ω
) x 1
0-12
10 710 610 510 410 310 210 110 010 -110 -2
ω
50
40
30
20
10
0
Re(Y
m / ω) x 10-12
T= 270 K Im(Ym/ω) Re(Ym/ω)
LysozymepH 7 h=0.26 g/g
•Is the glassy state of interfacial water functional?
-3-2-101
resi
due
x10
-12
140120100806040200
•Is the glassy state of interfacial water functional?
Two relaxations
80
60
40
20
0
ε ' (ω
)
10 610 410 210 010 -2
ω
T= 270 K epsx1 MW epsx2
Main relaxation
30
25
20
15
10
5
0
ε '' (ω
)
10 610 410 210 010 -2
ω
T= 270 K epsx1 MW epsx2 sigma
Satellite relaxation
Non - Arrhenius (fragility)
Canonical features of relaxationin glass-forming systems
Non - exponentiality
Non - ergodic below Tg
•Is the glassy state of interfacial water functional?
50
40
30
20
10
0300280260240220
T [K]
10 Hz 40 Hz 160 Hz 400 Hz 1000 Hz 4000 Hz
′ ε ω( )−ε∞ = ∆εg z( )dz
1+ ω ωo( )2 exp 2z( )z1
z2
∫
δ =′ ε ω( )−ε∞
∆ε= I ω,T( )
10 -4
10 -3
10 -2
10 -1
10 0
10 1
10 2
10 3
10 4
10 5
10 6
10 7
320300280260240220200
T [K]
δ = 0.99
δ = 0.80
δ = 0.40
δ = 0.10
δ = 0.01
Frequency-Temperature plots
VFT behavior!
It’s a proton glass!
•Is the glassy state of interfacial water functional?
ω(T)=ω0exp[-BT/(T-T0)]
T0(δ→1)=198±1 K
Main relaxation
•Is the glassy state of interfacial water functional?
A proton glass is the electricalanalogous of a spin glass
10-5
10-4
10-3
10-2
τ (s
)
340320300280260
T(K)
D2O H2O
h=0.23 (g/g)
The temperature dependence of the isotopic ratio reflects a mixed quantum-classical mechanism for the protons exchange between water molecules on protein surface. Thermal fluctuation of the protein’s segments greatly increase the tunnelling rate by shortening the distance the hydrogen must tunnel.
Isotopic effect•Is the glassy state of interfacial water functional?
3.5
3.0
2.5
2.0
1.5
τ D/τ H
360340320300280260
T(K)
h=0.23 (g/g) h=0.28 (g/g)
•Is the glassy state of interfacial water functional?
“…the number of basic sites generally exceeds the average number of protons bound to the proteinso that there exist many possible configurationsof protons, differing little in free energy, amongwhich fluctuations may occur…”
(Kirkwood et al. 1952)
hT
τ h( )= τohexp Bh
h− ho
⎛
⎝ ⎜
⎞
⎠ τ T( )= τoexp BT
T − To
⎛
⎝ ⎜
⎞
⎠
10 -6
10 -5
10 -4
10 -3
τ (s
)
0.320.300.280.260.240.220.20
h (g/g)
T=300 K fit
τ0=5.7 10 -9 sBh=0.65 (g/g)h0=0.16 (g/g)
•Is the glassy state of interfacial water functional?
Percolationthreshold !
h0 = 0.16(g/g) = hC
• t diverges when h ~ hc: protons dynamics frozen due tolack of long range connectivity among hydration water molecules;
• percolative transition indicates the occurrence of long range effects dominated by proton frustration;
Can we look at the glass transition in terms of a percolative transition?
• Random walks among configurations permitted at a giventemperature;
• Random walks on a fractal lead to stretched exponentialrelaxation :
φ(t) = exp [-(t/τKWW)βkww]
•Is the glassy state of interfacial water functional?
•Is the glassy state of interfacial water functional?
N. Lemke, I.A. Campbell. (1996), Random walks in a closed space, Physica A, 230, 554 -562.
1.Common value for glasses
•Is the glassy state of interfacial water functional?
βKWW = 1/3 (near 0.9 TgD)
βKWW = (αβ)1/1.23
βKWW (T) :
βKWW → 1
Two different regimes,above and below:
T = 1.26TgD
2.
Ym
Yx Ycpa
Data analysisThe total measured admittance Ym(ω) is due to the combined admittance of sample Yx(ω) and the admittance of blocking electrodes YCPA(ω).
General form for the admittances of circuital elements is:
•Is the glassy state of interfacial water functional?
YCPA ω( )= A jω( )d ,0 ≤ d ≤1
Yx ω( )= jωεoSh
∆ε
1+ jωτ( )α⎛ ⎝ ⎜
⎞ ⎠ ⎟
β
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟
MW
+ εsi+
∆εi
1+ jωτ i( )α i⎛ ⎝ ⎜
⎞ ⎠ ⎟ βi
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟
− j σεoωi
∑
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥⎥⎥⎥⎥
εm* ω( )= h
jωεoSYm ω( )= ′ ε m ω( )− j ′ ′ ε m ω( )
•Is the glassy state of interfacial water functional?
1.2
1.0
0.8
0.6
0.4
0.2
β KW
W
1.51.41.31.21.11.00.9
T/Tg
pH 5 pH 9
T=268K
1.Common value for glasses
2.
βKWW = 1/3 (near 0.9 TgD)
βKWW = (αβ)1/1.23
βKWW (T) :
βKWW → 1
Two different regimes,above and below:
T = 1.26TgD
Questions
•Is the glassy state of interfacial water functional?
•Biological function: role of water?
•Is the glassy state of interfacial water functional?
Why a glass?
Proton transfer is a fast process: a glassy state will slow it down to match the characteristictime scale of enzymatic activity.
10 -6
10 -5
10 -4
10 -3
τ (s
)
0.320.300.280.260.240.220.20
h (g/g)
T=300 K fit
τ0=5.7 10 -9 sBh=0.65 (g/g)h0=0.16 (g/g)
h0 = 0.16(g/g) = hC
Percolationthreshold !