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Confined Polymers: unity of thought * in the test tube * in polymer brushes * in mesoscopic channels. Adrian Parsegian and many friends: Sergey Bezrukov, Joel Cohen, Per Lyngs Hansen, Rudi Podgornik, et al., et al. Laboratory of Physical and Structural Biology,

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confined polymers unity of thought in the test tube in polymer brushes in mesoscopic channels

Confined Polymers: unity of thought * in the test tube * in polymer brushes * in mesoscopic channels

Adrian Parsegian and many friends:

Sergey Bezrukov, Joel Cohen, Per Lyngs Hansen, Rudi Podgornik, et al., et al.

Laboratory of Physical and Structural Biology,

National Institute of Child Health and Human Development,

National Institutes of Health

http://lpsb.nichd.nih.gov

slide3

Peter Rand, Don Rau & VAP (1973 - ?)measure osmotic pressures of neutral polymer solutionsused then to measure forces between molecules under osmotic stress

Posmotic

today consider full data sets for two chemically different systems
Today consider full data sets for two chemically different systems

Rand, Rau et al

small

big

Noda et al

how do the data collapse

cp = molar concentration

Cp = weight concentration

Mm = monomer weight

N = degree of polymerization

How do the data collapse?

Low concentration, van’t Hoff law

High conc, des Cloiseaux 9/4ths law

Cp* ~ polymer concentration at which there is one polymer occupying each "pervaded" volume of a random coil polymer whose size is that at infinite dilution.

~ 1, crudely speaking

Ansatz: Add these two limits

a happy consequence of adding
A happy consequence of adding

and

Neat trick (Joel Cohen): Take Cp/N = (Cp/Cp*) Cp*/N

Recall Cp*~ N-4/5 /V-bar from the constraint that dC shows no N dependence).

Plot N9/5 vs. Cp/Cp*

extract s one universal curve
Extract ’s; one “universal” curve

 = .48 +- .01

 = .161 +-.002

what have we done cohen podgornik parsegian 2007
What have we done? [Cohen, Podgornik, Parsegian 2007]

Added van’t Hoff and des Cloiseaux forms.

Extracted N9 from each term, vH and dC.

Defined C# = -4/5 C*

All the  and N dependence factored out to give a new “universal” form.

(Maybe think of C# as what C* would have been if we had our lives to live over.)

Weird thought: If/when this procedure is reliable, we need only one osmotic pressure measurement - well into the des Cloiseaux regime - for the entire set of sizes and concentrations.

schematic of force measurement between peg lipids

Posmotic

~ cm

~nm

Schematic of force measurementbetween PEG lipids

Equilibrate in high-concentration 9/4-power limit

grafted 5000 mw peg polymers p osmotic vs separation
grafted 5000 MW PEG polymersPosmoticvs. separation

% PEG-grafted lipids

Fit by Hansen et al. BJ (2003)

Des Cloizeaux

9/4 limit

Data from Kenworthy et al. BJ (1995)

Normal

exp(-df/3A) hydration forces

slide18

De Gennes, Adv. Coll. & Interf. Sci. 27:189 (1987)Two types of grafted surfaces: a) low grafting – the distance between heads D is larger than the coil size RF, (“mushroom”)b)high grafting density D < RF, (“brush”)

grafted peg polymers p osmotic vs separation
grafted PEG polymers Posmoticvs. separation

Fit by Hansen et al. BJ (2003)

9/4 des Cloizeaux 

plus 3/4 elastic grafting constraints

Normal

exp(-df/3A) hydration forces

Data from Kenworthy et al. BJ (1995)

i vs v

~10 nm

~nm

I vs. V

I

Bezrukov, et al.

conductance of channels between polymer solutions

little guys easy in

~10 nm

~2nm

Little guys easy in

Conductance reduced

in proportion to bath conductivity

hemolysin channel conductance vs peg bezrukov krasilnikov kasianowicz

Zero Partitioning big guys

1000

800

600

Conductance, pS

400

Equipartitioning small guys

200

0

5

10

15

20

25

30

PEG, weight %

PEG3400

PEG200

PEG1500

PEG2000

-Hemolysin Channel conductance vs. [PEG]Bezrukov, Krasilnikov, Kasianowicz
noisy channel partly filled with medium sized guys
Noisy channelpartly filled with medium-sized guys

Bezrukov, Vodyanoy, Brutyan, Kasianowicz, Macromolecules 29:8517 (1996)

Bezrukov, Vodyanoy, Parsegian, Nature, 370:279-281, 1994

peg 3400 pushed into hemolysin channel

1.0

0.8

Partition Coefficient

(from conductance ratio)

0.6

0.4

c*

0.2

0.0

0

5

10

15

20

25

30

PEG 3400, weight %

PEG 3400 pushed into -Hemolysin channel

~ 2/3 of a molecule inside

at 30 wt %

Krasilnikov & Bezrukov, Macromolecules 37 (2004)

MW 3400 ~ 77 monomers of length 3.4 Angstroms

Stretches to ~ 28 nm (vs. ~10 nm length of pore)

Rg ~ 2.5 nm in dilute solution ( vs. ~ 1 nm radius of pore)

slide28
How big (small) to fill a channel without any leftover?(S. Bezrukov, personal communication, last Thursday)

Consider 30 wt % PEG solu, just at the concentration to fill the pore:

300 (gm/liter) /44 (gm/mole) = 6.8 molar monomer PEG

x 6x1023 x 103 litre/m3 ==> 4.1 monomers/nanometer3

2) Channel volume: radius = 1 nm, length = 5 nm; v = 5  = 16 nm3

3) 4.1 monomers/nm3 x 16 nm3 = 66 monomers/channel volume

4) 66 monomers x 44 gm/mole monomer =

2,948 -- the MW of a PEG that fills pore at 30 wt %.

MW 3400 PEG slightly more than fills channel at 30 wt %.

slide29

High-concentration regime as “ideal” limit (des Cloizeaux) Pressure of bath ==>* small correlation length, * drive into channel of similar dimensionMovement of molecules in cells

slide30

~nm

~cm

~10 nm

~nm

Test-tubes, brushes, pores new unity in thinking about * large molecules at high concentration *the interior of cells and pores