nmr diffusion diffraction and diffusion interference from cells

NMR Diffusion Diffraction and Diffusion Interference from Cells

Philip Kuchel & Guilhem Pages

School of Molecular and Microbial Biosciences University of Sydney

Related posters

School of Molecular and Microbial Biosciences University of Sydney

D2 Levitz, P. Intermittent Brownian dynamics over strands

E2 Gratz, M. and Galvasos, P. Methodical aspects of 2D NMRcorrelation spectroscopy under conditions of ultra high pulsedfield gradients

E3 Veil, S., Excoffier, G., Pages, G., Ziarelli, F., Delaurant, C.,and Caldarelli, S. Combined use of pulsed gradient spin echo andhigh resolution magic angle spinning to investigate solute diffusionin the presence of chromatographic stationary phase

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Checking Stasi file!

It says here that yourknowledge is diffusingto the West!

East or West we areall illuminated by sciencedon’t you agree!?

Contents

Red cells…motivation

q-Space analysis

Flow diffraction

Octagon-star model

School of Molecular and Microbial Biosciences University of Sydney

School of Molecular and Microbial Biosciences University of Sydney

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Movie showingred blood cell membrane flickering

Echinocytesunder DIC Microscopy

…showingechinocyteto discocytereversionand backagain

0 min 4 min 16 min

56 min

Echinocytesunder DIC microscopy

Movie showing change in shape ofred blood cell

Discocytes

Spherocytes

Tracking red cell shape transformation

in packed samples over time courses of

minutes

University of Sydney

1E-5

1E-4

1E-3

0.01

0.1

1

E [q

, D] 1st diffraction minimum

pore hopping shoulder

2nd diffraction minimum

3rd diffraction minimum

q (105 x m-1) � �� �

Ht = 58%48%41%

Secondderivative

Fouriertransform

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Unbalanced bipolar pulses in STE…rapid signal acquisition

Pelta et al. (2002) MRChem 40 S147

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q

Movie showing change in shape of the q-spaceplot

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z (μm)

Movie showing change in shape of the mean celldiameter

Flow diffraction

g

sliceδz

sliceFlowa

z

xÕyÕ

z

xÕyÕ

−φ1πy

φ1 xÕyÕ

φ2 −φ1

z

π/2x ...δ

= γδgz

γδg(z + δz) = φ2 ...Δ

B0

Flow rate = 0.834 mm s-1

1.32 mm s-1

2.15 mm s-1

Since the uniform linear flow-velocity is a m s-1 then a = z/ ; and by definition q = (1/2 ) g so the change in phase angle brought about by flow is: = 2 q z = 2 q a

Hence, the normalized signal S[q, ] is proportional to, S[q, ] ∝ sin2[2 q a ]/(2 q a )2

qmin,n = n/(2 a )

a = n/(2 qmin,n )

E[q, Δ] =   ρ[r0]∫∫  P[r

0 | r

0+ R, Δ]  exp[i 2 π  q ⋅ R] dr

0dR

P[R, Δ] =  ρ[r0] P[r

0|∫  r

0 + R , Δ] dr

0 

E[q, Δ] =   P[R, Δ]  exp[i 2 π  q ⋅ R] dR∫P[R, Δ] =   E[q, Δ]  exp[-i 2 π  q ⋅ R] dq∫

E[q, ∞] =   ρ[r0] exp[i 2 π  q ⋅ r

0] dr

0∫    ρ[r] exp[i 2 π  q ⋅ r] dr∫E[q, ∞] =  S*[q] S[q] = | S[q] |2

E[g, Δ] = ∫ρ�r� r Δ� exp�i δ g ·(r - r)� drdrγ

A model of variable packing density

q-space plot results

…octagon-star system

x

z

(b, b)

(0, a)

(a, 0)(0, 0)

Construction element for q-space signal intensityfor octagon-star model

z

x

(a/2, a/2)

(0, 0)

(0, a/2)

(a/2, 0)(b, 0)

(0, b)

Construction element for q-space signal intensityfor octagon-star model…90o rotation

Expression for q-space signal intensity from stars alone

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q-space plot from octagon-star system as Ht increases

Movie showing change in shape of the q-spaceplot-function as Ht is increased

q-space plot from stars only

q-space plot from stars only

School of Molecular and Microbial Biosciences University of Sydney

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Bill Price is my name!

Thanks to past and present students…

Grazie!

School of Molecular and Microbial Biosciences University of Sydney

Bill Bubb NMRBob Chapman NMRTom Eykyn NMRDavid Jacques DICTim Larkin MathematicaGuilhem Pages NMR & fast q-spaceDavid Regan NMR & simulationDavid Szekely DIC & Mathematica

Chris GarveyBill PricePeter Stilbs