TMV Diffusion in Complex Solutions: When Science Goes WrongRandy Cush* & Paul RussoLouisiana State University

Indiana University Purdue University Indianapolis October 30, 2002

Generic Talk Outline

• Thank hosts for wonderful day

• Tell joke or story

• Explain what we’re trying to do

• Explain what we did• Explain why that is so cool • Destroy evil-doers • Thank friends

• Explain why that is totally wrong • Fix it • Move on

Entanglement in solution?Entanglement in solution?

To isolate spaghetti in "solution" with a fork is To isolate spaghetti in "solution" with a fork is difficult: hydrodynamic interactions interfere difficult: hydrodynamic interactions interfere with entanglement. After solvent is drained to with entanglement. After solvent is drained to obtain a "melt" the entire blob is easily handled. obtain a "melt" the entire blob is easily handled.

Collander

See, e.g., Lodge & Muthukumar, J. Phys. Chem. 1996, 100, 13275-13292

DLS for Molecular Rheology of Complex Fluids:Prospects & Problems

+ + + Wide-ranging autocorrelators> 10 decades of time in one measurement!

– – – Contrast stinks: everything scatters, esp.in aqueous systems or most supercritical fluids, where refractive index matching cannot hide the matrix.

Studied a lot

Barely studied

Our Hypothesis

Solutions containing rodlike diffusers may provide evidence for entanglement-like phenomena in solution…or at least prove interesting, fun and challenging while helping us develop micro-rheology tools.

Evidence would be: * sudden drop-offs in mobility with concentration * failure to follow continuum mechanics

Yeah, challenging…. Early de Gennes paper on

rod/coil diffusion: 19 citations

Same era de Gennes paper on coil/coil reptation: 479 citations

We may expect some problems!

Why it’s worth it: composite precursorfluids, dissolution rate, phase separation rate, relation to GPC, CGE of rods, intracellulartransport.

Desirable rod properties

Stiff—no bendingMonodisperse (all the same size)Non-aggregatingWater-solubleWe don’t have to make ‘em!

Let mother nature do the work: plants make viruses (unwillingly) with most of these qualities.

Seedlings

Sick Plants And close-up of mosaic pattern.

DIY farming--keeping the “A” in LSU A&M

TMV CharacterizationTMV Characterization

Sedimentation, Electron Microscopy and DLS

•Most TMV is intact.•Some TMV is fragmented

–(weaker, faster mode in CONTIN)

•Intact TMV is easy to identify –(stronger, slower mode in CONTIN)

Better Views

http://www.uct.ac.za/depts/mmi/stannard/linda.html

An ear of corn has about as many kernels as TMVhas protein subunits (ca. 2130). The protein

subunits enfold a spiral-wound strand of RNA whichwill encode the next generation. TMV is more

extended than an ear of corn.

A Minnesota Farmboy’s Corny View of TMV

Tobacco from the Carolinas to Connecticut

If tobacco goes away…“Traditionally in Kentucky great mounds of brush are piled and burned in February to prepare a bed for tobacco seedlings. I remember spending most of the day hauling and piling brush. My dad would start the fire in late afternoon and we would sit up most of a cold February or March night stoking the fire, watching the stars, and roasting hot dogs or marshmallows over the bonfire. Many times neighbors would stop by and sit with us for a spell around the fire, talking into the night.”

From: http://www.webcom.com/duane/farm2.html

Rotation & Diffusion of TMV in Polymer Solutions

++ + + Fabulous new autocorrelators for scattering10 decades of time in one measurement!

– – – Contrast for scattering stinks: everything scatters, esp. in aqueous systems where refractive index matching cannot hide matrix.

Matrix Polymer

Solvent

TMV Probe

Solution: Use Polarizers to Hide Matrix

Dynamic Light ScatteringDynamic Light Scattering

Hv = q2Dtrans + 6Drot

LASERVV

HH

PMT

Hv Geometry Hv Geometry (Depolarized)(Depolarized)

Uv Geometry Uv Geometry (Polarized)(Polarized)

VV

Uv = q2Dtrans

o

nq

2/sin4

PMT

LASER

q2

6Drot

q2

Dtrans

StrategyStrategy

•Find polymer that should not “entangle”

•Find a rodlike probe that is visible in DDLS

•Measure its diffusion in solutions of each polymer separately

•Random coil

•Polysaccharide

•Invisible in HvDLS

•Highly-branched

•Polysaccharide

•Invisible in HvDLS

•Rigid rod

•Virus

•Visible in HvDLS

Dextran

Ficoll

TMV

•Find polymer that should (???) “entangle”

BARELYBARELY

0 5 10 15 20 25 30 35 400

1

2

3

4

5

6

7

8

9

10

11

BothViscosity

sp/c

/dL

-g-1

c/g-dL-1

Dextran 670,000 Ficoll 420,000

As expected…

0.0 0.5 1.0 1.5 2.0 2.5 3.0

200

300

400

500D

t /10-8cm

2s-1

Dr /

s-110 L3

c/mg-mL-1

0

1

2

3

4

5

6

Rotation

Translation

Experiments are in dilute regime. TMV overlap (1/L3)

All measurements made at low TMV concentrations—no self-entanglement

Hv correlation Hv correlation functions for 14.5% functions for 14.5% dextran and 28% dextran and 28% ficoll with and ficoll with and without added without added 0.5 mg/mL TMV0.5 mg/mL TMV

The dilute TMV The dilute TMV easily “outscatters” easily “outscatters” either matrixeither matrix

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10 100

1.0

1.2

1.4

Ficoll >6000 s acquisition

TMV + Ficoll 600s aquisition

g(2

)

t/s

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10 1000.9

1.0

1.1

1.2

1.3

Dextran >6000 s acquisition

TMV + Dextran 215 s acquisition

g(2

)

t/s

Matrix is invisible

0 1 2 3 4 5

0

500

1000

1500

2000

2500

3000

3500

4000

Hv TMV / Dextran / Buffer

Uv TMV / Buffer

Hv TMV / Buffer

/s-1

q2/1010 cm-2

Hey, it works!

I didn’t think—I experimented.

---Wilhelm Conrad Roentgen

0 2 4 6 8 10 12 14 160

1

2

3

4

5

6

Dtr

ans/1

0-8 c

m2

s-1

wt% dextran0 2 4 6 8 10 12 14 16

0

50

100

150

200

250

300

350

Dro

t/ s-

1

wt% dextran

Early results—very slight errors

rotation translationMacromolecules 1997,30, 4920-6.

Stokes-Einstein Plots: if SE works, thesewould be flat. Instead, apparent deviations in

different directions for Drot and Dtrans

0 2 4 6 8 10 12 14 16

0.0

0.5

1.0

1.5

Dt /10

-9g-cm

-s-2

Dr /

g-cm

-1-s

-1

wt% Dextran

0

2

4

0 2 4 6 8 10 12 14 16

0 5 10 15 20

0

2

4

6

8 /cP

Dr/D

t /1

09 cm-2

wt % dextran

0 5 10 15 20

0

20

40

60

80

Dextran overlap

Macromolecules 1997,30, 4920-6.

At the sudden transition: L/c.m. ~ 13 and L/ ~ 120

L

cm

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 300

1

2

3

4

5

6

Dtr

an

s/10-

8 cm

2 s-

1

wt% ficoll

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

0

50

100

150

200

250

300

350

Dro

t/ s-

1

wt% ficoll

rotation

translation

END OF PUBLISHED DATA

We believed that the transition represented topological constraints.

It was suggested that more systems be studied.

BEGIN FICOLL

When we did Ficoll, many more points were added!

0 5 10 15 20 25 300.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Dtra

ns /10

-9g-cm-1-s

-1

Dro

t /g-

cm-1-s

-1

wt% ficoll

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Huh? Drot still diving in Ficoll?

rotationtranslation

Maybe we should think now.

The chiral dextran and ficoll alter polarization slightly before and after the scattering center.

With a strongly depolarizing probe, this would not matter, but…

TMV = IHv/IUv ~ 0.003

While matrix scattering is minimal, polarized scattering from TMV itself leaks through a “twisted” Hv setup.

Most damaging at low angles

Mixing in Polarized TMV Light

Uv light from misalign True Hv light

q2 q2

Drot too low

6Drot

q2

6Drot

Even at the highest concentrations, only a few degrees out of alignment.

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 360

50

100

150

200

250

300

Op

tica

l Ro

tatio

n /

arc

-min

ute

s

wt %

Dextran Ficoll

Polarimeters are long for a reason

0 5 10 15 20 25 30 35

0

50

100

150

200

250

300

350

NewFicollRatio_PR

Right way Wrong way

Dro

t / s

-1

wt% ficoll

Slight, but important, improvement.

Improved Drot/Dtrans Ratio Plots

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160

1

2

3

4

5

6

7

8

NewDexConcStudy_PR

Dro

t/Dtr

ans/

109 cm

-2

wt% dextran0 5 10 15 20 25 30 35 40

0

1

2

3

4

5

6

7

8

NewFicollRatio_PR

Dro

t/Dtr

ans/

109 c

m-2

wt% ficoll

Improved Stokes-Einstein PlotsBlack = TMV Translation

Blue = TMV Rotation

0 2 4 6 8 10 12 14 160.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0

0.2

0.4

0.6

0.8

NewDexConcStudy_PR

Dro

t/g-c

m-1s-1

wt% dextranD

trans /10-9g-cm

-s-2

0 5 10 15 20 25 30 350.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0

0.2

0.4

0.6

0.8

NewFicollRatio_PR

Dro

t/g-c

m-1 s

-1

wt% ficoll

Dtrans / 10

-9g-cm-s

-2

Check Dtrans by FPR a.k.a. FRAP

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160

1

2

3

4

5

6

FPRtmvDex_PR

Hv DLS FPR

Dtr

ans/

10-8

cm2 s-1

wt% dextran

Hydrodynamic Ratio—Effect of Matrix M at High Matrix Concentration

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

7

8

9DextranMWStudy_PR

Dro

t/Dtr

ans/

109 cm

-2

dextran MW/ 105 daltons

Effect of Dextran Molecular Weight—High Dextran Concentration (~ 15%)

10000 100000 1000000 1E71

10

100

DextranMWStudy_PR

-0.62 ± 0.04

Dro

t / s

-1

Dextran MW10000 100000 1000000 1E7

0.1

1

10

DextranMWStudy_PR

-0.72 ± 0.01

Dtr

ans/

10-9

cm

2 s-1

Dextran MW

TMV Translation TMV Rotation

1 10 100

0.01

0.1

1

10

100

1000

10000

G' /

Pa

/ Hz

5% w/w 30% w/w 35% w/w 40% w/w

Behavior of Dextran Matrix

Pathological Science?*

The magnitude of the effect is substantially independent of the intensity of the causative agent.

The effect is of a magnitude that remains close to the limits of detectability; or, many measurements are necessary because of the very low statistical significance of the results.

It makes claims of great accuracy.

It puts forth fantastic theories contrary to experience.

Criticisms are met by ad hoc excuses.

The ratio of supporters to critics rises up to somewhere near 50 percent and then falls gradually to oblivion.

LangmuirNobel 1932

*The science of things that aren’t so Lecture December 18, 1953 GE Labs

Studying “entangled” TMV by FPR

Fluorescentlylabeled probe rod

Unlabeled rods

Solvent

Ld

1

1

3

3

3

L

L

L

1

1

2

2

2

dL

dL

dL

1

14

2

2

2

2

A

A

dLA

LC formation = 4/A2 5/dL2

Reduced # Density dL2/5

Doi-Edwards-Onsager Reference Volumes for Rods = number density = # of rods per unit volume

D expected to decrease by half, but at what concentration?

D

D

X

Modulation FPR Device a’la Lanni & Ware

*

*

*

*

AOM

M

M

D

RR

DM

OBJ

S

PMT

PA OS

TA/PVD

L

SCOPE

Measuring Translational Diffusion

0 200 400 600 800 10000

1

2

3

4

DC

Sig

nal

Con

tras

t

t/s

0 2 4 6 8 10 12 140.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

/H

z

K2 / 105cm-2

FPR Data for TMV Solution: very low dye content.

0.1 1 10 1001

2

3

4

5

6

7

Source: Cush Monthly Report (5/1/01)

1/dL21/L3

Dse

lf /

10 -8

cm

2 s

-1

cTMV

/ mg mL-1

Dtracer self of TMV vs. cTMV

TMV vs Helical, Semiflexible Polymer

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

(Dse

lf/Do)

PB

LG /

(D

self/D

o)D

MF

PBLG

TMV

D

self /

Do

/*

Thanks!

Randy CushDavid Neau

Ding Shih

Holly Ricks

Jonathan Strange

Amanda Brown

Zimei Bu

Zuhal & Savas Kucukyavuz—METU

Seth Fraden—Brandeis

Dan DeKee—Tulane

Nancy Thompson—Chapel Hill N$F

THE END

Misalignment from thick polarizer in “active” part of detector train, exacerbated by tiny cells

used to squelch optical rotation & conserve TMV

shifted by thick polarizer element

correctly aligned scattered beam

Ld

1

1

3

3

3

L

L

L

1

1

2

2

2

dL

dL

dL

1

14

2

2

2

2

A

A

dLA

LC formation = 4/A2 5/dL2

Reduced # Density dL2/5

Doi-Edwards-Onsager Reference Volumes for Rods = number density = # of rods per unit volume

Conditions for use as a ProbeConditions for use as a Probe

•Is the TMV Probe Dilute?A TMV concentration of 0.5 mg/mL, well below the

theoretical overlap concentration, was chosen. See Figure 2.•Does dilute TMV overwhelm the matrix scattering?

At 0.5 mg/mL the TMV easily “outscatters” both matrices. See Figure 3.

•Is the probe compatible with the matrix?-Solutions stable months after preparation

-Angle dependent Hv SLS

-Dtrans goes up, not down (Figures 6 & 8)

Effect of Dextran ConcentrationEffect of Dextran Concentration

• The dependence of Drot and Dtrans upon added dextran is shown in Figure 4.

• The quotient Drot/Dtrans is plotted against viscosity in Figure 5. By combining both transport coefficients, each inversely proportional to viscosity in dilute solution, we can remove the effect of solution viscosity. • Figure 6 reveals like positive deviations from the Stokes-Einstein continuum expectation that diffusion be inversely proportional to viscosity (below 6.5%).

•Above 6.5% the deviations become greater for both Drot and Dtrans but in opposite directions

There once was a theorist from Francewho wondered how molecules dance.“They’re like snakes,” he observed, “As they follow a curve, the large onesCan hardly advance.”

D ~ M -2

P.G. de GennesScaling Concepts in Polymer Physics

Cornell University Press, 1979

de Gennes

OutlineOutline• Characterize the TMV

– Is it intact and behaving properly?

• Establish conditions for use of TMV as probe– Can the probe be dilute and still overwhelm the

matrix scattering?– Will the probe stay mixed with the matrix solutions

without aggregating?

• Show the effect of the dextran and ficoll matrices on TMV diffusion

Effect of Ficoll ConcentrationEffect of Ficoll Concentration

• The dependence of Drot and Dtrans upon added dextran is shown in Figure 4.

• The quotient Drot/Dtrans is plotted against viscosity in Figure 7.

• Figure 8 shows slight like positive deviations from the Stokes-Einstein continuum expectation (below 11%).

• Above about 11% ficoll the deviation slowly becomes greater for Drot and slightly greater for Dtrans but in opposite directions

• Figure 9 compares TMV behavior in ficoll to that in dextran.

0 5 10 15 20 25 300

2

4

6D

rot /

Dtr

ans

/109 cm

-2

wt% ficoll

0

20

40

60

80/ cP

0 10 20 30 40 50 60

-1

0

1

2

3

4

5

6

7

8 Ficoll Dextran

Dro

t / D

tran

s/ 1

09 cm-2

/ cP

Too-Good-to-be-True Conclusion?Too-Good-to-be-True Conclusion?

• Below 6.5% dextran the diffusion of the rodlike TMV probe is controlled mostly by viscosity.

• Above 6.5% dextran a sharp transition suggests topological constraint for TMV rotation while translation is not much affected.

• The transition is more gradual in ficoll.• The TMV probe senses something different for

linear vs. highly branched polymers in solution.• Looks good for topological models!

Alternate Conclusion?• The systems studied so far place (impossibly?) strict

demands on geometric & polarization alignment. – Revised polarization placement– Difficult zero angle measurements requiring even more

TMV

• New systems must be studied:– TMV is OK – Dextran/Ficoll must go!

• Depolarized probe diffusion has the potential, as yet unrealized, to assess strength of hydrodynamic vs. topological effects.

To Do

Get Cush to estimate the total number of TMV’s he produced.

Slopes of intrinsic viscosity plot don’t meet the 0.5 rule.

What has Deutch & Pecora to do with Dtrans vs. M?

What does regular viscosity have to say about M-dependence?

At what concentration was that M-dependent stuff done?