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

1. 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

2. ~nm ~cm ~10 nm ~nm In test tubevs. grafted, between bilayersvs. inside a pore

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

4. Today consider full data sets for two chemically different systems Rand, Rau et al small big Noda et al

5. Transform variables, collapse all data for each polymer type

6. 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

7. 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*

8. Scaled forms Cross at places different from Cp = Cp*

9. Extract ’s; one “universal” curve  = .48 +- .01  = .161 +-.002

10. Width of crossover region

11. 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.

12. ~nm ~cm ~10 nm ~nm Test tubevs. grafted, between bilayersvs. inside a pore

13. Posmotic ~ cm ~nm Schematic of force measurementbetween PEG lipids Equilibrate in high-concentration 9/4-power limit

14. ~nm Multilayer

15. Squeeze with Posmotic ofPEG in bathing solution! + Posmotic

16. PEGylated, close-up of brushes

17. 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

18. 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”)

19. Compressed brushesAlexander – de Gennes

20. 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)

21. ~nm ~cm ~10 nm ~nm Test tubevs. grafted, between bilayersvs. inside a pore

22. ~10 nm ~nm I vs. V I Bezrukov, et al. conductance of channels between polymer solutions

23. ~10 nm ~2nm Little guys easy in Conductance reduced in proportion to bath conductivity

24. ~10 nm ~2nm ~5 nm Big guy tough push,otherwise no go

25. 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

26. Noisy channelpartly filled with medium-sized guys Bezrukov, Vodyanoy, Brutyan, Kasianowicz, Macromolecules 29:8517 (1996) Bezrukov, Vodyanoy, Parsegian, Nature, 370:279-281, 1994

27. 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)

28. 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 %.

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

30. ~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

31. Merci!