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Kinetics of exclusion-zone formation István N. Huszár and Miklós Kellermayer Department of Biophysics and Radiation Biology, Semmelweis University, Budapest, Hungary 1. The E Z - p has e Hy po t h e s i s

2 . E x p e r i m e n ta l S e t u p

What is EZ?

Flow cell mount

4 . E Z K i n e t ic s I n flu e n c e d by Sa lt s o f t h e H o f me is te r Se r ie s –

Laser beams

F ≈ SO4

Spontaneous exclusion of macroscopic solutes from the vicinity of hydrophilic surfaces leads to the formation of solute-free regions that are referred to as “exclusion zones” (EZs).

electrostatic

Electrostatic repulsion is unlikely to take effect over distances comparable to the size of EZs (50-700 µm) because of the Debye screening.

100

10

Distance (µm)

Could it be repulsion?

Exclusion zone (µm) Debye length (µm)

1

0.01

CF2

0.001

100

1000

104

105

106

KCl (µM)

What could it be?

CF2

The fourth phase of water, G.H. Pollack, 2013.

Restricted auto-diffusivity in the EZ and simultaneous H+-efflux from it are experimental observations that underpin a phase transition. 1. Are there quantifiable kinetic regularities in EZ formation? 2. What kind of mechanisms contribute to the buildup of EZ?

x

CF

CF2

FC

O z

CF2

lm fi a r

CF2

O S

HO

O

x H2O

Data on the right emphasize the role of H-bonds and structure in the process of exclusion.

Nafion

Pa

On the left is a flow cell constructed from two regular microscope slides that are separated by a hollow (pre-cut) sheet of Parafilm, serving as the insulation of the interior channel. A-priori a 6x10mm stripe of Nafion membrane is placed into the channel. Nafion is a sulfonated fluoroethylene based synthetic polymer product that has been used widely to create EZs under experimental conditions.

EZ Development in Time 1min 1.5min 2min 3min EZ around Nafion in a sus-

EZ NAFION

We used 11 different salt contaminants in 5 respective concentrations. In the table below all-average values of the coefficients ‘a’ and ‘b’ are given as their rough estimates: n=46 Mean (±SD)

Values of coefficient b fall in the range 0.5-0.6, which is highly suggestive for a diffusion-related process.

(a ⋅t

Dapparent

a

b

18.50 (±5.90)

0.60 (±0.07)

Ion-specific effects are detailed in the Hofmeister series section.

= x

2

= 2 Dt

2

a −10 m = = 1.71 ⋅10 2 s

2

This theoretical diffusion coefficient corresponds to the cytoplasmic diffusivity of H+:

600

1.4(±0.5)×10

500 400

x(t ) = a ⋅ t

300 200 100 0

)

2 b

Supposing that b were equal to 0.5, one might obtain:

700

pension of 1µm sized carmicrospheres Bulk boxylated and ultrapure MilliQ water. Gradual increments in EZ width always make up for a power law. (shown on the right)

–

–

–

700

10mM NaX CH3COONa

Cosmotropes

600

Na2HPO4 Na2SO4

500

NaBr NaCl

400

NaClO3 300

NaClO4 NaF

200

NaI 100

NaNO3

Chaotropes

0 0

60

120

180

240

300

NaSCN 360

Time [s]

-10

m s

2

Cytoplasmic hydrogen ion diffusion coefficient, Biophys J., 61(6):1470-9., 1992

This result seems to be in concordance with the H+-efflux and limited diffusivity indicated in EZ hypothesis.

b

60

120

180

240

300

The time-dependant growth of aqueous exclusion zones (EZs) follows a power law around Nafion surfaces: x(t) = a·t

b

Structure making anions promote exclusion, whereas structure breaking anions antagonize EZ growth. The closeness of exponent b to 0.5 suggests that the exclusion process is driven by diffusion. Either H2O or H+ is the diffusing entity, the calculated diffusion coefficients indicate restricted diffusivity in comparison with the bulk phase. Values of a2/2 are reasonable approximations of H2O/H+ diffusion coefficients formerly measured by others.

7. Ack n ow le dge me n t The authors would like to express their gratitude to fellow re-

0

6 . Su mma ry

5 . E Z K i n e t i c s Re s e mble D iff u s io n

EZ Size as a Function of Time

EZ width [µm]

30s

–

http://tx.technion.ac.il/~schles/theory.html

3. EZ K i n e t i c s Fo l l ow a Powe r L aw 10s

–

Ion-specific EZ Kinetics

The Hofmeister phenomenon might be related to ion-specific changes in H-bonding. Cosmotropes are thought to stabilize H-bonds, whereas chaotropes are to disrupt/weaken them.

y

CF3

Output

EZ water might be in a physically distinct “fourth” phase with an ordered molecular lattice, whose limited permeability should be responsible for the exclusion of solutes.

–

> CH3COO > Cl > NO3 > Br > ClO3 > I > ClO4 > SCN

Structure making and breaking

CF2

O

Input

Region of interest

0.0001 10

–

Different ions are not equipotent when used to precipitate proteins from a solution. The term "cosmotropic" refers to a group of ions that are more potent in this sense than chloride. Respectively, "chaotropic" refers to less potent ions.

0.1

1

–

The Hofmeister series

Above is an optical tweezer apparatus assembled on a table. Beyond videomicroscopy, it allows direct mechanical manipulation of the microscopic sample via a pair of focused laser beams.

1000

> HPO4

2–

EZ width [µm]

Zheng and Pollack, Phys Rev E 68, 031408, 2003.

2–

360

Time [s] Curve-fitting resulted correlation coefficients over 99% in all cases.

searcher Zsolt Mártonfalvi for his contributions to the present work.

The Project was supported by the European Union and co-financed by the European Social Fund (grant agreement no. TÁMOP-4.2.2.B-