the glassystate of water in model and realsystems...

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)


“Purple membrane”bacteriorhodopsin,

(halobacteria halobium)


LYSOZYME


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:


enzymaticactivity

…same threshold !!

protonicconductivity


…threshold phenomena ?

Percolation Theory

•Spatially random events & Topological disorder.

•Critical concentration: long range connectivity.

•At the percolation threshold an extended cluster spansthe system.


σ(p) ∝ (p-pc)t σ(h) ∝ (h-hc)t


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


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 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 ?


A.K. Soper, F. Bruni, M.A. Ricci (1998) J. Chem. Phys., 109 (4), 1486-1494.


Dielectricspectroscopymeasurments

Lysozyme


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).


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


-3-2-101

resi

due

x10

-12

140120100806040200


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


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!


ω(T)=ω0exp[-BT/(T-T0)]

T0(δ→1)=198±1 K

Main relaxation


A proton glass is the electricalanalogous of a spin glass


Are protons really responsible?

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)


“…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)


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]



N. Lemke, I.A. Campbell. (1996), Random walks in a closed space, Physica A, 230, 554 -562.

1.Common value for glasses


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:


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( )


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




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 !

Conclusions

•“migrating protons” as a spin glass

•hydration, and not temperature, is the relevantvariable

•coupling between proton relaxation times and enzymatic activity times

the glassystate of water in model and realsystems...

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