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mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
M-A DelsucCentre de Biochimie Structurale
Montpellier
mobilité moléculaire
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
mobilité - mouvement - dynamique - ?
échange chimique étude à l’équilibre
diffusion rotationnelle indispensable pour avoir des signaux fins en RMN
(sauf MAS en RMN du solide - Stefano -)
possible dans les polymères (oligosaccharides, etc.)
échelles de temps “rapides”
sensibles aux interactions
diffusion translationnelle impossibles dans les polymères lourds
échelles de temps “lentes”
sensibles aux interactions
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
rotation
stop flow
échelles de temps
psec nsec µsec msec sec ksec Msecheure mois
relaxation T1-T2relaxation repère
tournant
suivit de diffusionDOSY
sp. d’échangeétudes cinétiqueséchange
translation
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
la mesure d’échange
mesure à l’équilibre accès aux paramètres cinétique
on peut estimer les constantes k et k-1
mesure dynamique il faut “geler” le systèmes à différents instants
temps caractéristiques stop-flow (msec - sec) cinétique dans le spectromètre (sec-ksec) cinétique sur la paillasse (ksec-Msec)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
principe de la mesure d’échange par RMN
échange lent
échange rapidemesure de l’élargissement
mesure de déplacement
Pe =!1P1 + !2P2
!1 + !2
! 1
!a " !bcoalescence
mesure en situation d’échange chimique à l’équilibre
A!" B
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
mesure de relaxation
relaxation longitudinale “T1” retour de l’aimantation à l’équilibre
sensible aux oscillations locales du champs
relaxation transverse “T2” disparation de la cohérence du signal
sensible aux oscillations locales du champs
mais aussi à interactions dipolaires spin-spin anisotropie des interactions (déplacement chimique) échanges chimiques
échange d’aimantation NOE - ROE - échange chimique
T2 ! T1
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
le temps de corrélation
temps caractéristique de réorientation de la molécule dans le champ
NOE - ROE
!c
8–25
shown in (c) above.
Our picture indicates that there are two ways in which the coherence couldbe destroyed. The first is to make the vectors jump to new positions, atrandom. Drawing on our analogy between these vectors and the behaviour ofthe bulk magnetization, we can see that these jumps could be brought about bylocal oscillating fields which have the same effect as pulses.
This is exactly what causes longitudinal relaxation, in which we imagine thelocal fields causing the spins to flip. So, anything that causes longitudinalrelaxation will also cause transverse relaxation.
The second way of destroying the coherence is to make the vectors get out ofstep with one another as a result of them precessing at different Larmorfrequencies. Again, a local field plays the part we need but this time we do notneed it to oscillate; rather, all we need for it to do is to be different at differentlocations in the sample.
This latter contribution is called the secular part of transverse relaxation; thepart which has the same origin as longitudinal relaxation is called the non-secular part.
It turns out that the secular part depends on the spectral density at zerofrequency, J(0). We can see that this makes sense as this part of transverserelaxation requires no transitions, just a field to cause a local variation in themagnetic field. Looking at the result from section 8.5.2 we see that J(0) = 2!c,and so as the correlation time gets longer and longer, so too does the relaxationrate constant. Thus large molecules in the slow motion limit are characterisedby very rapid transverse relaxation; this is in contrast to longitudinal relaxationis most rapid for a particular value of the correlation time.
The plot below compares the behaviour of the longitudinal and transverserelaxation rate constants. As the correlation time increases the longitudinal rateconstant goes through a maximum. However, the transverse rate constantcarries on increasing and shows no such maximum. We can attribute this to thesecular part of transverse relaxation which depends on J(0) and which simplygoes on increasing as the correlation time increases. Detailed calculations showthat in the fast motion limit the two relaxation rate constants are equal.
!c1/"0
W
longitudinal
transverse
Comparison of the longitudinal and transverse relaxation rate constants as a function of the correlation timefor the fixed Larmor frequency. The longitudinal rate constant shows a maximum, but the transverse rateconstant simply goes on increasing.
1/T2
1/T1
Understanding NMR SpectroscopyJames Keeler, (Wiley 2005)
T1 maximum
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
12
Le phénomène de diffusion
C'est en 1827 que le botaniste Robert Brown regarde au microscope le
mouvement erratique de petites particules de pollen immergées dans de l'eau. Les grains
de pollen étant suffisamment gros (de l'ordre du micron) ils ont pus être observés au
microscope optique de l'époque. Ce mouvement erratique des molécules prendra le nom
de cet observateur.
Figure 1 : Le mouvement brownien d'une particule microscopique en suspension dans l'eau. La position de la particule a été repérée toute les 30 secondes [d'après un dessin de Jean Perrin 1912-Document de la revue Pour la Science]
Presque un siècle plus tard, Jean Perrin entreprend une étude plus systématique
du phénomène et formule une description mathématique des trajectoires que suivent les
particules microscopiques en suspension dans l'eau (Figure 1). Il décrit ces trajectoires
comme étant continues et pourtant non différenciables. En effet, si on trace la ligne
entre deux points d'observation correspondant à deux positions consécutives d'une
particule, ce segment[1] "a une direction qui varie follement lorsque l'on fait décroître
la durée qui sépare ces deux instants".
Ce mouvement désordonné, est alors interprêté comme résultant des collisions
entre les particules observées et le fluide dans lequel elles sont immergées. Les
variations de vitesse, de ces particules, réprésentent l'intégration d'un grand nombre de
petits sauts indépendant les uns des autres.
Diffusion translationnelle
Loi de déplacement
Dépendances
d’après un dessin de Jean Perrin (1912)
D =kT
floi de Debye-Einstein
loi de Stokes-EinsteinD =kT
6!"RH
DaDb
!!
MbMa
"13
en pratique
RH
L =!
Dt
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Measuring diffusion coefficient by NMR
z
t
zgradient codeur decoding gradient
diffusion
echo intensity depends on diffusion
coding gradient
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Measuring diffusion coefficient by NMR
- Presence of a gradient permits a coupling between position and time
z
t
zgradient codeur decoding gradient
diffusion
echo intensity depends on diffusion
coding gradient
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Measuring
experiment is repeated for increasing gradient intensities, all delays kept constant.
signal at 3.6 ppmfor increasing gradient intensity
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Least Square fit
Glucose Signal
D = 582 +/- 3 µm2 sec-1
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Spectre DOSY
HOD
glucose
ATP
SDS
ppm
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
un peu de mathématiques
Transformé de Laplace inverse
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
DOSY Spectra by Least Square fit
D µm2/sec
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
DOSY Spectra by Least Square fit
In the absence of spectral superposition, Least Square (LS) fit gives DOSY spectra very well resolved.
D µm2/sec
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
DOSY Spectra by Least Square fit
In the absence of spectral superposition, Least Square (LS) fit gives DOSY spectra very well resolved.
D µm2/sec
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
DOSY Spectra by Least Square fit
In the absence of spectral superposition, Least Square (LS) fit gives DOSY spectra very well resolved.
BUT, LS can hardly be used in the case of spectral superposition
D µm2/sec
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
DOSY Spectra by Least Square fit
In the absence of spectral superposition, Least Square (LS) fit gives DOSY spectra very well resolved.
BUT, LS can hardly be used in the case of spectral superposition
D µm2/sec
superpositions are very common :" Fortuitous spectral superposition (broad lines) " Intense solvent line" Baseline distortion Complex mixtures
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Mono-dispersity and Poly-dispersity
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Mono-dispersity and Poly-dispersity
Mono-dispersity
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Mono-dispersity and Poly-dispersity
Mono-dispersity
δslow fast
D
A
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Mono-dispersity and Poly-dispersity
Mono-dispersity
Laplace Transform
Laplace spectrum
δslow fast
D
A
s
I(s) = A exp (!Ds)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Mono-dispersity and Poly-dispersity
Mono-dispersity • Poly-dispersity
Laplace Transform
δ
Laplace spectrum
δslow fast
D
A
s
I(s) = A exp (!Ds)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Mono-dispersity and Poly-dispersity
Mono-dispersity • Poly-dispersity
δ
Laplace Transform
Laplace spectrum
δslow fast
D
A
s
I(s) = A exp (!Ds)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Mono-dispersity and Poly-dispersity
Mono-dispersity • Poly-dispersity
δ
s
Laplace Transform
Laplace spectrum
δslow fast
D
A
s
I(s) = A exp (!Ds)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Mono-dispersity and Poly-dispersity
Mono-dispersity • Poly-dispersity
δ
s
Laplace Transform Inverse Laplace Transform
Laplace spectrum
δslow fast
D
A
s
I(s) = A exp (!Ds)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
MaxEnt and Inverse Laplace Transform (ILT)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
MaxEnt and Inverse Laplace Transform (ILT)
Direct ILT is not possible, it is an unstable operation
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
MaxEnt and Inverse Laplace Transform (ILT)
Direct ILT is not possible, it is an unstable operation
MaxEnt permits to realize a true ILT with no hypothesis on the size nor the number of constituants
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
MaxEnt and Inverse Laplace Transform (ILT)
Direct ILT is not possible, it is an unstable operation
MaxEnt permits to realize a true ILT with no hypothesis on the size nor the number of constituants
No constraints on gradient intensity values
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
MaxEnt and Inverse Laplace Transform (ILT)
Direct ILT is not possible, it is an unstable operation
MaxEnt permits to realize a true ILT with no hypothesis on the size nor the number of constituants
No constraints on gradient intensity values
some examples : 100 data points 0.1% Gaussian noise 3000 Iterations
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
MaxEnt and Inverse Laplace Transform (ILT)
asymmetric distribution
4 lines
2 close lines
D
D
D
0.01 0.1 1 10
0.01 0.1 1 10 100
0.1 1 10
Direct ILT is not possible, it is an unstable operation
MaxEnt permits to realize a true ILT with no hypothesis on the size nor the number of constituants
No constraints on gradient intensity values
some examples : 100 data points 0.1% Gaussian noise 3000 Iterations
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Comparing with other analysis methods
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Comparing with other analysis methods
3 different techniques
LS Fit (Levenberg Marquardt)
CONTIN (Provencher 1973)
MaxEnt (Gifa 1998)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Comparing with other analysis methods
3 different techniques
LS Fit (Levenberg Marquardt)
CONTIN (Provencher 1973)
MaxEnt (Gifa 1998)
Monte Carlo Test :
100 realisations
Mean and STD analysis
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
0.1 1 10
Fit CONTIN MaxEnt
Comparing with other analysis methods
3 different techniques
LS Fit (Levenberg Marquardt)
CONTIN (Provencher 1973)
MaxEnt (Gifa 1998)
Monte Carlo Test :
100 realisations
Mean and STD analysis
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
0.1 1 10
Fit CONTIN MaxEnt
succes rate
Fit 100%CONTIN 59%MaxEnt 89%
Comparing with other analysis methods
3 different techniques
LS Fit (Levenberg Marquardt)
CONTIN (Provencher 1973)
MaxEnt (Gifa 1998)
Monte Carlo Test :
100 realisations
Mean and STD analysis
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
un peu plus demathématiques
Principes de MaxEnt
(Entropie Maximale)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Maximum Entropy
inverse approach statistical analysis of experimental noise distance to the data : χ2
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Maximum Entropy
inverse approach statistical analysis of experimental noise distance to the data :
statistical analysis of the solution Signal Entropy: Shannon The most probable spectrum
χ2
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Maximum Entropy
inverse approach statistical analysis of experimental noise distance to the data :
statistical analysis of the solution Signal Entropy: Shannon The most probable spectrum
a-priori knowledge on the data
χ2
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Signal Entropy
Among all possible spectra fitted down to the noise, I choose
the less informative(Shannon sense)
the most probable => the one which maximize the signal entropy
with
S = !!
pi log(pi)
pi =fiA
pi =fi!fi
(Mariette 96)
(Delsuc 98)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Optimisation Problem
Complete Problem : maximize find λ such that
fixed point algorithm :
λ control start with λ=0 => i.e. flat spectrum increment λ, until
Q = S ! !"2
!Q = !S ! !!"2
!2 = Nnbexp
!Q = 0at the solution point, we have :
!2 = Nnbexp
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Strengths and pitfalls
No model polydispersité, superposition, off-range signals, etc...
Can easyly adapt non pure-exponential eg. to compensate for gradient non-linearity
Slow heavy processing can take up to several hours
less resolutive than fitting but more accurate...
But...
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
A Complex Mixture
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
A Complex Mixture
Not a mixture made in purpose to show that your technique actually works
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
A Complex Mixture
Not a mixture made in purpose to show that your technique actually works
Large (unknown) number of constituants natural fluids • food
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
A Complex Mixture
Not a mixture made in purpose to show that your technique actually works
Large (unknown) number of constituants natural fluids • food
Very large range of sizes polymers/monomers • gels • micelles
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
A Complex Mixture
Not a mixture made in purpose to show that your technique actually works
Large (unknown) number of constituants natural fluids • food
Very large range of sizes polymers/monomers • gels • micelles
Very large range of concentrations toxics • aroma
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
A Complex Mixture
Not a mixture made in purpose to show that your technique actually works
Large (unknown) number of constituants natural fluids • food
Very large range of sizes polymers/monomers • gels • micelles
Very large range of concentrations toxics • aroma
Interactions protein - ligand
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
A Complex Mixture
Not a mixture made in purpose to show that your technique actually works
Large (unknown) number of constituants natural fluids • food
Very large range of sizes polymers/monomers • gels • micelles
Very large range of concentrations toxics • aroma
Interactions protein - ligand
Low resolution NMR several compartiments
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
quelques exemples
études de cas
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Measuring Mobility - Food industry
flavour - 50 ppm - in food gel
ethyl butyrate in carrageenan matrix
flavour
free oligo-saccharides
carrageenan
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
800
850
900
950
1000
1050
0 0,1 0,2 0,3 0,4 0,5 0,6
[NaCl] % w/w
diff
coef
f µm
2 /se
c
Measuring Mobility...
Evolution of Ethyl Butanoate mobility with gel strength
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
800
850
900
950
1000
1050
0 0,1 0,2 0,3 0,4 0,5 0,6
[NaCl] % w/w
diff
coef
f µm
2 /se
c
Measuring Mobility...
Evolution of Ethyl Butanoate mobility with gel strength
Higher mobility means improved consumer experience !
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
800
850
900
950
1000
1050
0 0,1 0,2 0,3 0,4 0,5 0,6
[NaCl] % w/w
diff
coef
f µm
2 /se
c
Measuring Mobility...
Evolution of Ethyl Butanoate mobility with gel strength
Higher mobility means improved consumer experience !
put salt in your yoghurt !
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
800
850
900
950
1000
1050
0 0,1 0,2 0,3 0,4 0,5 0,6
[NaCl] % w/w
diff
coef
f µm
2 /se
c
Measuring Mobility...
Evolution of Ethyl Butanoate mobility with gel strength
Gostan, T.; C. Moreau; A. Juteau; E. Guichard; M-A, Delsuc Magn.Reson.Chem. 2004.
Higher mobility means improved consumer experience !
ISI TOP 10%most cited article
put salt in your yoghurt !
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and concentration
Diffusion varying with concentration
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and concentration
Diffusion varying with concentration
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and concentration
Diffusion varying with concentration
Detergent : Sodium Dodecyl Sulphate
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and concentration
Diffusion varying with concentration
0
100
200
300
400
500
600
700
800
1 10 100 1000
diffu
sion
µm2 /
sec
concentration mM
S
O
O
O O CH2 CH3( )-11
Na+
Detergent : Sodium Dodecyl Sulphate
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and concentration
Diffusion varying with concentration
0
100
200
300
400
500
600
700
800
1 10 100 1000
diffu
sion
µm2 /
sec
concentration mM
S
O
O
O O CH2 CH3( )-11
Na+
Detergent : Sodium Dodecyl Sulphate
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Model fitting
modeling of the eqeilibrium ( free detergent ⇔ micelle )
Fitted parameters :cmc 8 mMnb de monomer 40Dmono 650 µm2/sec
Dmicelle 37 µm2/sec
n x M Mn
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Various surfactants
cmc N Dmono µm2/sec
Dmic µm2/sec
<χ2> # freedom
SDS 8.29 mM 41 ± 8.5 649 ± 78 36.6 ± 1.0 8.0 7
Triton X100
0.27 mM 34.4 ± 1.7 255 ± 1.6 52.0 ± 0.89 6.4 5
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Various surfactants
cmc N Dmono µm2/sec
Dmic µm2/sec
<χ2> # freedom
SDS 8.29 mM 41 ± 8.5 649 ± 78 36.6 ± 1.0 8.0 7
Triton X100
0.27 mM 34.4 ± 1.7 255 ± 1.6 52.0 ± 0.89 6.4 5
NMRtec Montpellier
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Protein oligomerisation.
AKT Protein, 13.6 kDa, stabilized in 10 mM IP3 and 50 mM Tris
It’s a monomer !
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Protein oligomerisation.
AKT Protein, 13.6 kDa, stabilized in 10 mM IP3 and 50 mM Tris
It’s a monomer !
Auguin, D.; Gostan, T.; MA, D.; Roumestand, C. C.R.A.S. Chimie 2004, 7, 265-271.
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and molecular shape
Diff
usio
n en
µm
2 /s
Masses moléculaire en kD
ChymotrypsinogèneRibonucléase A Myoglobine
LysosymeCytochrome C
Thioredoxine
OvalbumineGST
R=0.99
UbiquitineCarditoxine γ
Neurotoxine αBPTI
charybdotoxine
apo-Myoglobine
10 20 5064
100
200
60
40
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and molecular shape
globular proteins 4kDa to 50kDa
Diff
usio
n en
µm
2 /s
Masses moléculaire en kD
ChymotrypsinogèneRibonucléase A Myoglobine
LysosymeCytochrome C
Thioredoxine
OvalbumineGST
R=0.99
UbiquitineCarditoxine γ
Neurotoxine αBPTI
charybdotoxine
apo-Myoglobine
10 20 5064
100
200
60
40
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and molecular shape
globular proteins 4kDa to 50kDa
standard conditions 23°C
3 mg/ml
1mM Tris, as internal viscosity probe
Diff
usio
n en
µm
2 /s
Masses moléculaire en kD
ChymotrypsinogèneRibonucléase A Myoglobine
LysosymeCytochrome C
Thioredoxine
OvalbumineGST
R=0.99
UbiquitineCarditoxine γ
Neurotoxine αBPTI
charybdotoxine
apo-Myoglobine
10 20 5064
100
200
60
40
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and molecular shape
globular proteins 4kDa to 50kDa
standard conditions 23°C
3 mg/ml
1mM Tris, as internal viscosity probe
Diff
usio
n en
µm
2 /s
Masses moléculaire en kD
ChymotrypsinogèneRibonucléase A Myoglobine
LysosymeCytochrome C
Thioredoxine
OvalbumineGST
R=0.99
UbiquitineCarditoxine γ
Neurotoxine αBPTI
charybdotoxine
apo-Myoglobine
10 20 5064
100
200
60
40
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and molecular shape
globular proteins 4kDa to 50kDa
standard conditions 23°C
3 mg/ml
1mM Tris, as internal viscosity probe
Diff
usio
n en
µm
2 /s
Masses moléculaire en kD
ChymotrypsinogèneRibonucléase A Myoglobine
LysosymeCytochrome C
Thioredoxine
OvalbumineGST
R=0.99
UbiquitineCarditoxine γ
Neurotoxine αBPTI
charybdotoxine
apo-Myoglobine
power law in MW1/3Only one free parameterCheck the hydrodynamic behaviour
Check precision and accuracy 10 20 5064
100
200
60
40
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Diffusion and molecular shape
globular proteins 4kDa to 50kDa
standard conditions 23°C
3 mg/ml
1mM Tris, as internal viscosity probe
Diff
usio
n en
µm
2 /s
Masses moléculaire en kD
ChymotrypsinogèneRibonucléase A Myoglobine
LysosymeCytochrome C
Thioredoxine
OvalbumineGST
R=0.99
UbiquitineCarditoxine γ
Neurotoxine αBPTI
charybdotoxine
apo-Myoglobine
power law in MW1/3Only one free parameterCheck the hydrodynamic behaviour
Check precision and accuracy
S. Arold, F. Hoh, S.Domergue, M-A. Delsuc, M. Jullien & C. Dumas Protein Science 9 p1137-1148 (2000)
10 20 5064
100
200
60
40
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Detecting Traces
Detection, identification and quantification of pollutants
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Detecting Traces
Detecting pollutants ~ 200 ppm
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Detecting Traces
Detecting pollutants ~ 20 ppm
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Detecting Traces
Detecting pollutants ~ 20 ppm
Christine AlbaretC.E.B Vert-le-Petit
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Coffee
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
can be identified :
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
can be identified :0
20
40
60
80
100
120
140
160
180
200
-2-101234567891011ppm
%
Caffeine
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
can be identified :0
20
40
60
80
100
120
140
160
180
200
-2-101234567891011ppm
%0
20
40
60
80
100
120
140
160
-2-101234567891011ppm
%
Caffeine
light sugars
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
can be identified :0
20
40
60
80
100
120
140
160
180
200
-2-101234567891011ppm
%0
20
40
60
80
100
120
140
160
-2-101234567891011ppm
%0
20
40
60
80
100
120
140
160
180
200
220
100 200 300 400 500 600 700 800 900 1 000point
%
Caffeine
light sugars
heavy sugars
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
can be identified :0
20
40
60
80
100
120
140
160
180
200
-2-101234567891011ppm
%0
20
40
60
80
100
120
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160
-2-101234567891011ppm
%0
20
40
60
80
100
120
140
160
180
200
220
100 200 300 400 500 600 700 800 900 1 000point
%
Caffeine
light sugars
heavy sugars
fat and fatty acids
020
40
60
80
100
120
140
160
100 200 300 400 500 600 700 800 900 1 000point
%
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
deca DOSY
DOSY
20
40
60
80
10
01
20
6,46,66,877,27,47,67,888,28,48,68,899,29,49,69,8ppm
po
int
3 5%
Ro
w:
36
8
0,1
0,3
0,5
%
café
comparing deca to regular coffee
aromatic region
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
deca DOSY
DOSY
20
40
60
80
10
01
20
6,46,66,877,27,47,67,888,28,48,68,899,29,49,69,8ppm
po
int
3 5%
Ro
w:
36
8
0,1
0,3
0,5
%
café
comparing deca to regular coffee
deca DOSY
DOSY
20
40
60
80
10
01
20
22,22,42,62,833,23,43,63,844,24,44,64,855,2ppm
po
int
3 5%
Ro
w:
11
3
0,1
0,3
0,5
0,7
%
deca
aromatic region
aliphatic region
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
DOSY as obtained by the fit method
by the way....-3
-2-1
01
2
123456789ppm
Hz
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
DOSY as obtained by the fit method
by the way....-3
-2-1
01
2
123456789ppm
Hz
coffee is fine, but...
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
polyphenols in wines
champagne wine
wine is dessicated
dissolved in DMSO
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
polyphenols in wines
champagne wine
wine is dessicated
dissolved in DMSO
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
polyphenols in wines
champagne wine
wine is dessicated
dissolved in DMSO
0.1% vs glycerol
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
poly-phenol area
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
poly-phenol area
wine artificially aged
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
salivary proteins interaction
A.J. Charlton et aL/FEBS Letters 382 (1996) 289 292 291
+
++ °' ++¢°
t ~ O ~ 1 , r r G ~ e I ser
I
0 0
I
'0 0 Ly, C~ Arg
{ I~ ~ Pro I 00 Pro
,~sn
.0 3.0 2.0 F2 (ppm)
O O A ~ ~y~
~ t
Fig. 2. The aliphatic region of a TOCSY spectrum of the purified PRP. Superscripts for proline and glycine refer to the categories de- fined on the basis of their C~H chemical shift values (Table 1).
studies which became denser on subsequent addi t ions of the
tannin . The precipi ta t ion was found to be reversible, the pre-
cipitate being solubilised by an increase in temperature . F o r
the series of hydrolysable tannins , P e n t a G G , T e t r a G G ,
T r i G G , the precipi tate had become significant by 5, 6, and 9
p.1 of po lyphenol solution, respectively, whereas for ( - ) - ep i ca -
techin, a precipi tate began to form after 59 ~tl of t ann in solu-
tion. Dur ing the later stages of the P R P / t a n n i n t i t rat ions,
b roaden ing of the P R P signals was noted, which is consis tent
with exchange b roaden ing between free and b o u n d chemical
shifts. These results imply s t rong P R P / t a n n i n binding, with
P e n t a G G being the mos t effective ligand.
Least-squares fitt ing o f Eq. 1 to the chemical shift changes
observed on t i t ra t ion of the pro te in with the polyphenols gave
the results listed in Table 2. The quali ty of the fitt ing is illu-
s t ra ted by Fig. 4.
S P P G K
K
P P G K
P Q Q
G K
P Q G G R
Fig. 3. The amino aligned to highlight
P Q G P P
P Q G P P
P Q G P P
P Q A P P
P Q G P P
P P R P A
Q Q E
P P G
A
P P
Q G
G N
G N
Q Q P P Q
acid sequence of basic PRP IB5 (P-D) [11,12] the internal repeat sequences.
4. Discussion
The upfield changes in chemical shift seen on t i t ra t ion of
the prote in with t ann ins can be ascribed to ring current shifts,
caused largely by face-to-face stacking of the prolyl rings of
the prote in with the galloyl rings of the t ann ins [5]. Each
p ro ton within the prote in experiences different upfield shifts
due to local t ann in binding, and therefore the curve fitting
procedure essentially yields individual microscopic dissocia-
t ion cons tants for each site in the protein. As shown in Table
2, for each t ann in studied all of the individual dissociat ion
constants were similar suggesting tha t the b inding interact ions
are of similar strengths. Since a lmost all of the ma jo r chemical
shift changes observed involve prolyl protons , the implicat ion
is tha t each prol ine residue forms an independen t and equiva-
lent b inding site. Similar conclusions were reached in our ear-
lier invest igat ion [5]. We have therefore averaged the indivi-
dual dissociat ion cons tants to obta in a mean cons tan t for
each polyphenol studied.
In our previous s tudy [5] we invest igated the b inding of
P e n t a G G to a single 22-residue repeat of the tandemly re-
peated mouse MP5 P R P sequence. This peptide has the se-
quence G P Q Q R P P Q P G N Q Q G P P P Q G G P Q , which is similar
to tha t of the current ly studied IB5, bu t roughly one th i rd of
the length. Since we have shown tha t the t ann in b inding sites
on b o t h proteins a lmost entirely consist of independent pro-
line residues, we are confident tha t the essential elements of
b inding are c o m m o n to bo th proteins. More recently, we have
studied the b inding of T r iGG, ( - ) - ep i ca t ech in and o ther tan-
nins to the mouse MP5 repeat sequence (Baxter et al., in
Table 2 The dissociation constants (Kd) calculated using Eq. 1 for the interaction of the polyphenols with basic PRP IB5
Proton Kd (M)
PentaGG TetraGG TriGG (-)-Epicatechin
Proline 1 Ca l l 1.85 x 10 -5 * 1.02 x 10 -4 * Proline 2 Ca l l * 1.56x 10 -4 * 1.51 x 10 -4 Proline C~SH a 8.65 x 10 -6 * 1.40 X 10 -4 1.14 X 10 -4 Proline CSH b 1.55x 10 -5 * * 1.37X 10 4 Arginine CSH 4.00 x 10 -5 * 1.89 x 10 -4 1.24 ! 10 -4 Lysine Cel l * 6.51 X 10 -5 2.38x 10 -4 * Proline CI3H ° 1.01 x 10 5 1.92x 10 4 9.97x 10 -5 1.16x 10 -4 Proline CTH 1.11 x 10 -5 3.54x 10 -5 * 1.23x 10 -4
Average 1.73x 10 -5 1.12X 10 4 1.54x 10 -4 1.28x 10 -4 Standard deviation 1.17 x 10 -5 7.39 X 10 -5 5.94x 10 -5 1.41 x 10 5
The initial protein concentration [P]o was treated as a variable during the curve fitting. Proline 1 and Proline 2 correspond to Pro-Pro and Pro-X sequences, respectively (Table 1) and * denotes either that the chemical shift values did not change for the respective proton resonance or that the data obtained were not suitable for fitting against the theoretical curve. aDownfield Proline C~SH. bUpfield Proline CSH. eDownfield Proline C[3H.
IB5 protein
epicatechinegalate
EtOH
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
comparaison sur les spectres TOCSY
tocsysum0eq (1H/1H)
tocsysum12eq (1H/1H)
3,5
44,5
5
1,21,41,61,822,22,42,62,83ppm
ppm
2%
0eq (
1D
1H
)
12
%
0eq (1D 1H)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
cinétique d’oxydation
acide cafféique
oligomérisation en présence d’un oxydant10
20
30
6,877,27,47,6ppm
poin
t
15%
Col: 2
306
40
%
Row: 8
10.8” par mesure
7’
1’
1’
5’
050
100
150
20 40 60 80 100 120 140 160 180point
%0
50
100
150
20 40 60 80 100 120 140 160 180 200point
%
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
DOSY d’un extrait purifié de polyphénol de jus de pomme
1234567ppm
dam
pin
g5
00
50
5
150%
Col: 1
66
7
40
%
au début (1D 1H)
EtOH
divers petites molécules
catéchine
oligomères
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
DOSY d’un extrait purifié de polyphénol de jus de pomme
1234567ppm
dam
pin
g5
00
50
5
150%
Col: 1
66
7
40
%
au début (1D 1H)
EtOH
divers petites molécules
catéchine
oligomères
Véronique CheynierINRA Montpellier
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
localized DOSY 1st trial
1st trial
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
localized DOSY 1st trial
1st trial
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
localized DOSY 1st trial
1st trial
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
2nd trial
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
2nd trial
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
2nd trial
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
2nd trial
J-P Renou; G.BielickiINRA Theix
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
12
Le phénomène de diffusion
C'est en 1827 que le botaniste Robert Brown regarde au microscope le
mouvement erratique de petites particules de pollen immergées dans de l'eau. Les grains
de pollen étant suffisamment gros (de l'ordre du micron) ils ont pus être observés au
microscope optique de l'époque. Ce mouvement erratique des molécules prendra le nom
de cet observateur.
Figure 1 : Le mouvement brownien d'une particule microscopique en suspension dans l'eau. La position de la particule a été repérée toute les 30 secondes [d'après un dessin de Jean Perrin 1912-Document de la revue Pour la Science]
Presque un siècle plus tard, Jean Perrin entreprend une étude plus systématique
du phénomène et formule une description mathématique des trajectoires que suivent les
particules microscopiques en suspension dans l'eau (Figure 1). Il décrit ces trajectoires
comme étant continues et pourtant non différenciables. En effet, si on trace la ligne
entre deux points d'observation correspondant à deux positions consécutives d'une
particule, ce segment[1] "a une direction qui varie follement lorsque l'on fait décroître
la durée qui sépare ces deux instants".
Ce mouvement désordonné, est alors interprêté comme résultant des collisions
entre les particules observées et le fluide dans lequel elles sont immergées. Les
variations de vitesse, de ces particules, réprésentent l'intégration d'un grand nombre de
petits sauts indépendant les uns des autres.
Diffusion Restreinte
transforming the NMR signals amplitudes with
respect to q2. The result is diffusion ordered NMR
spectroscopy (DOSY) [9]. The three basic DOSY
requirements are (1) distortion free absorption mode
data sets acquired with precise gradient encoding, (2)
effective data inversion (transformation) procedures,
and (3) algorithms for the display of the diffusion
spectra. These requirements turn out to be quite severe
because the signal inversion step is extremely sensi-
tive to noise and distortions in the signals. This has
necessitated significant enhancements of the original
PFG-NMR experiments and experimentation with
alternative data inversion methods. Even data display
for DOSY is not straightforward because decisions
must be made about how to generate the spectra.
The contrast with the Fourier transform NMR (FT-
NMR) is striking. With FT-NMR, one has a unique
transformation with an inverse that returns the origi-
nal signal. Also, the resulting spectra are ready for
display.
This review is concerned with the various
implementations of DOSY experiments and with
illustrations of the power of this technique. The imple-
mentations present solutions to the unique problems
of data acquisition, transformation, and display. With
appropriate instrumentation and software, the user can
be offered menu choices for analysis methods and
types of display. The result is a convenient NMR
method for the analysis of mixtures that can reveal
unexpected components and interactions in mixtures
through useful and appealing plots.
2. Previous reviews of DOSY and related topics
Transport ordered NMR [10] and diffusion
measurements by magnetic field gradient methods
including DOSY [11] have previously been reviewed.
Related reviews of MOSY are also available [12,13].
A complete treatment of translational dynamics and
its study by NMR can be found in the book by
Callaghan [14]. Karger et al. [15] have reviewed the
principles and applications of PFG-NMR, and Stilbs
has provided a detailed review of FT diffusion studies
C.S. Johnson / Progress in Nuclear Magnetic Resonance Spectroscopy 34 (1999) 203–256206
Fig. 1. The simple Carr–Purcell spin echo (SE) often called the Hahn echo.
Λ
L
si Λ << L : diffusion libresi Λ >> L : diffusion restreinte
DΔ >> L2
from Stepišnik
from Johnson 99
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Journal of Magnetic Resonance 156, 195–201 (2002)doi:10.1006/jmre.2002.2556
Restricted Self-Diffusion of Water in a Highly Concentrated W/OEmulsion Studied Using Modulated Gradient Spin-Echo NMR
Daniel Topgaard,1 Carin Malmborg, and Olle Soderman
Division of Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
Received September 21, 2001; revised April 4, 2002
Restricted diffusion of water in a highly concentrated w/o emul-sion was studied using pulsed field gradient spin echo techniques.The standard two-pulse version of this technique, suitable for ana-lysis in the time domain, fails to investigate the short time-scalefor diffusion inside a single emulsion droplet with radius 0.7 µm.With a pulse-train technique, originally introduced by Callaghanand Stepisnik, shorter time-scales are accessible. The latter ap-proach is analyzed in the frequency domain and yields frequencydependent diffusion coefficients. Predictions for the outcome ofthe experiment were calculated in the time domain using theGaussian phase distribution and the pore hopping formalism ex-pressions for the echo attenuation. The results of these calcula-tions were transformed to the frequency domain via a numericalinverse integral transform in order to compare with the experimen-tal results. C! 2002 Elsevier Science (USA)
Key Words: self-diffusion; PFG SE NMR; highly concentratedemulsion; diffusion spectrum; modulated gradients.
INTRODUCTION
Pulsed field gradient (PFG) spin echo (SE) or stimulated echo(STE) NMR is a well-established technique to noninvasivelystudy molecular motion. The most widely used methods rely onthe application of two sharp magnetic field gradient pulses whichdefine the beginning and the end of the diffusion time (1, 2).The first pulse labels the position of the diffusing molecules andthe second pulse reads the displacement that has occurred dur-ing the diffusion time. The observed echo intensities are conve-niently analyzed in the time domain with a propagator formalism(2, 3). The molecular displacements can be probed over a widerange of time-scales by varying the distance between the twogradient pulses. The time-dependent diffusion coefficient andmean square displacement of a fluid imbibed in a porous matrixcontain information on the porous structure, such as surface tovolume ratio, pore size, and tortuosity (4–7). The longest diffu-sion time that can be observed is limited by the magnitude ofthe relaxation times. The shortest time accessible is set by in-strumental limitations, i.e., the difficulty of applying strong andmatched magnetic field gradient pulses without generating eddy
1 To whom correspondence should be addressed. Fax: +46 46 222 44 13;E-mail: [email protected].
currents. It is also necessary to keep the gradient pulse lengthmuch shorter than the diffusion time for the standard propa-gator formalism to be valid. An alternative to performing thetwo-pulse experiment as a function of diffusion time is to takeadvantage of diffraction-like effects on plots of echo intensityvs the reciprocal space vector q defined by the strength and du-ration of the gradient pulse (8). The diffraction-like features canbe related to the characteristic distances in the sample, such aspore size and interpore distance.
A different approach to analyze molecular motion is to usea frequency-dependent diffusion coefficient spectrum, whichis the Fourier spectrum of the translational velocity auto-correlation function (9). The diffusion spectrum can be probedwith a train of gradient pulses where the frequency is adjustedby changing the separation between the pulses. In the case ofunrestricted diffusion of small molecules the spectrum is flat forthe frequencies experimentally accessible. For molecules expe-riencing barriers for the diffusive motion, the time between wallcollisions gives rise to additional features of the diffusion spec-trum. This has been demonstrated on a water-saturated packedbed of 15-µm radius polystyrene spheres (10). The use of atrain of gradient pulses has been shown to extend the effectivetime-scale of NMR diffusion measurements to below 1 ms (11).
In this article we examine a system with micrometer-sizewater compartments separated by a thin oil and surfactant film,i.e., a highly concentrated w/o emulsion. With the use of two-pulse and pulse-train experiments the observational time-scalesare adjusted such that both inter- and intracompartment diffu-sion are probed. Previous NMR studies of highly concentratedemulsions include the works of Balinov et al. (12), where theapparent water diffusion coefficient was related to the perme-ability of the oil and surfactant film, and Hakansson et al. (13),where methods to determine the compartment size using q-spacediffusion diffractograms were developed.
THEORY
The PFG STE experiment, shown in Fig. 1, consists of a prepa-ration interval where the first gradient pulse labels the spinswith a positionally dependent phase shift and a read intervalwhere the second gradient pulse reverses the phase shift with the
195 1090-7807/02 $35.00C! 2002 Elsevier Science (USA)
All rights reserved.
MODULATED GRADIENT STUDY OF WATER IN EMULSIONS 199
FIG. 6. Diffusion diffractogram with water signal intensity vs the reciprocalspace vector q for a fresh (squares) and aged (triangles) highly concentratedemulsion. The droplet size is determined from the position of the first localmaximum.
and the characteristic time for diffusion between the droplets !b
!b = b2
2Dp. [13]
For the gradient calibration we used Db = 2.3 · 10!9 m2/s (17)and from Fig. 4 we get Dp " 1.4 · 10!10 m2/s for the fresh andDp " 2.4 · 10!10 m2/s for the aged emulsion. Inserting thesevalues in Eqs. [12] and [13] gives estimates of !a and !b. Thevalues are summarized in Table 1. In analogy with the reasoningabove the regime of unrestricted diffusion is then observed att # !a and the long-time limit is reached when t $ !b. Restricteddiffusion inside a droplet occurs when t is on the order of 0.1 msand the water molecules sample a limited number of dropletswhen t is on the order of 10 ms. Since !b $ !a the pore hopping(PH) formalism of Callaghan (8) can be used to describe theregime of t around 10 ms. With this approach it is assumedthat each molecule entering a pore stays there long enough tohave equal probability of being anywhere within the pore, beforemigrating to the next pore.
There exists expressions for Dt(t) in the short-time (4) andlong-time limit (7). An interpolation between the two limits hasbeen used to describe the full range of t (6). For certain simplepore geometries, i.e., planar, cylindrical, and spherical geometry,
TABLE 1Structural Parameters for the Fresh and Aged
Emulsions Estimated from the Diffractogramand PFG STE Experiments
Fresh Aged
a/µm 0.71 1.7b/µm 1.4 3.4Dp/m2/s 1.4 · 10!10 2.4 · 10!10
!a/ms 0.11 0.60!b/ms 7.3 23
FIG. 7. Calculated %Z2& and Dt(t) using the GPD approximation (solidline) and the PH formalism (broken line) using parameters relevant for the freshemulsion.
there exist expressions for the echo attenuation at all values of t(18). The initial slope of a calculated echo-attenuation curve canbe used to numerically evaluate %Z2& and Dt(t) through Eqs. [2]and [3]. An example of such a calculation is displayed in Fig. 7for spherical pores with radius 0.71 µm. For the calculation weused the Gaussian phase distribution (GPD) approximation formolecules diffusing in a spherical cavity with reflecting walls(19)
ln E = !2" 2G2
Db
'!
m=1
#!4m
#2ma2 ! 2
[14](
"
#
#
#
$
#
#
#
%
2$!
2+ exp&
!#2m Db(%!$)
'
!2 exp(
!#2m Db$
)
! 2 exp(
!#2m Db%
)
+ exp&
!#2m Db(%+$)
'
#2m Db
*
#
#
#
+
#
#
#
,
,
where #m is the mth root of the Bessel equation 1/(#a)J3/2(#a) = J5/2(#a). As can be seen in Fig. 7, Dt(t) starts todrop from Db for t orders of magnitude smaller than !a. Whent = !a, Dt(t) is slightly less than Db/2 and %Z2&1/2 reaches aconstant value
)2/5a. At longer t , Dt (t) goes toward zero. To
account for the permeability of the film separating the dropletswe use the PH formalism (16) to calculate Dt (t) in an analogous
198 TOPGAARD, MELANDER, AND SODERMAN
FIG. 4. The time-dependent diffusion coefficient Dt(t) for free water (cir-cles) and water confined within emulsion droplets in a highly concentrated fresh(squares) and aged (triangles) emulsion. The two lower lines are calculated us-ing the GPD approximation for short times and the PH formalism for long times(see text for details). The upper line is the value of D for free water.
frequencies as high as 500 Hz, corresponding to a diffusiontime of 2 ms. Callaghan and Stepisnik (11) used frequencies upto 1667 Hz. Our attempts with such high frequencies resulted ina dramatic signal loss due to eddy currents after the pulse. Theresidual gradients lead to a slice selection with the subsequent180! pulse.
For the free water both methods yield a constant value for thewater self-diffusion coefficient D as expected. A closer inspec-tion of Fig. 5 reveals a slight decrease of D!(!) at the highestfrequencies. This was also observed by Callaghan and Stepisnik(11) who attributed it to the finite rise time of the gradient leadingto a slightly smaller value of G" at higher frequencies. By usinga fixed value of D!(!) for free water it is possible to calculate aneffective G" for each frequency. Since the effect is minor no suchcorrection was made. For lower frequencies the experiment isless accurate because of the increasing influence of T2 relaxation.This is more severe for the emulsion, not because of differentT2, but because of the order of magnitude slower long-rangediffusion. Increasing the gradient strength and decreasing N
FIG. 5. The frequency-dependent diffusion coefficient D!(!) for free water(circles) and water confined within emulsion droplets in a highly concentratedfresh (squares) and aged (triangles) emulsion. The two lower lines are calculatedaccording to the flow-scheme in Fig. 9. The upper line is the value of D for freewater.
is not a solution to this problem since N must be above acertain level if the sampling of D!(!) should occur at a suf-ficiently narrow range of frequencies (cf. Eq. [7]). The largescatter for all samples at 50 Hz we attribute to disturbances fromthe power supply. For the emulsions Dt(t) is almost constantwith the two-pulse method. At the shorter time-scales accessi-ble with the pulse-train method a significant increase of D!(!)is observable.
At this stage we want to relate the experimental results to thecharacteristic length- and time-scales for water diffusion in theemulsion. As discussed by Callaghan and Coy (16), the effectof restrictions for the diffusing molecules is conveniently han-dled with a propagator formalism. Due to the limitations of thetwo-pulse method we were forced to use the pulse-train methodto access the shorter time-scales. We will first calculate Dt(t),using a reasonable model for the structure of and water diffu-sion in a concentrated emulsion, and then convert it to D!(!)and compare both quantities with the experimental data.
Calculation of Dt (t)
For molecules diffusing in a porous medium different time-scales can be distinguished. First we consider an isolated porewith size a. At short t, "Z2#1/2 $ a and few molecules are influ-enced by the restrictions implying that Dt(t) % Db, where Db isthe bulk diffusion coefficient in the absence of barriers. At inter-mediate t, "Z2#1/2 % a and Dt(t) is decreasing with increasingt due to the increasing number of molecules that reach the bar-riers. In the case of nonpermeable pore walls "Z2#1/2 reachesa constant value at long t . This value is related to a and thepore shape. For spherical pores the long-time limit of "Z2#1/2
is&
2/5a, where a is the pore radius (16). In the case of per-meable walls or connections between the pores, the diffusioncoefficient reaches a constant value Dp reflecting the long rangepermeability. For discrete pores separated with a distance b thereexists an intermediate diffusion time regime where the diffusingmolecules sample a limited number of pores. At this time-scalediffraction-like effects can be observed in the echo-attenuationplots of intensity vs the reciprocal space vector q = # G"/2$
(13). The position of the first maximum is inversely related tothe distance between the center of neighboring pores b. Thewater droplets in a highly concentrated emulsion have a poly-hedral shape but can be approximated as a sphere with radiusa. Due to the limited size of the film separating the dropletswe may write b = 2a. In Fig. 6 we display experimental echo-attenuation plots. The first maximum occurs at q % 7 · 105 m'1
for the fresh and q % 3 · 105 m'1 for the aged emulsion. In-verting these values we obtain an estimate of b,from which a iscalculated. The values can be found in Table 1. To proceed wedefine the characteristic time for restricted diffusion inside thedroplets %a
%a = a2
2Db[12]
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Lipid Transfer Protein
protéine marquée 15N
spectre HSQC
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
(T1)!1 =
!2H!2
N!2
4r6NH
!J("H ! "N) + 3J("N) + 6J("H + "N)
"+
!2"2N
3J("N)
(T2)!1 =!2
H!2N!2
8r6NH
!4J(0) + J(!H ! !N) + 3J(!N) + 6J(!H) + 6J(!H + !N)
"+
!2"2N
3
!2/3J(0) + 1/2J(!N)
"
(nOe)!1 =!2
H!2N!2
4r6NH
!6J("H + "N)! J("H ! "N)
"
(!H ! !N) " (!H + !N) " !H
Mesure des relaxations T1 T2 NOE en 1H et 15N (~nsec)
Lipari-Szabo Model
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
(T1)!1 =
!2H!2
N!2
4r6NH
!J("H ! "N) + 3J("N) + 6J("H + "N)
"+
!2"2N
3J("N)
(T2)!1 =!2
H!2N!2
8r6NH
!4J(0) + J(!H ! !N) + 3J(!N) + 6J(!H) + 6J(!H + !N)
"+
!2"2N
3
!2/3J(0) + 1/2J(!N)
"
(nOe)!1 =!2
H!2N!2
4r6NH
!6J("H + "N)! J("H ! "N)
"
(!H ! !N) " (!H + !N) " !H
Mesure des relaxations T1 T2 NOE en 1H et 15N (~nsec)
Lipari-Szabo Model
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
(T1)!1 =
!2H!2
N!2
4r6NH
!J("H ! "N) + 3J("N) + 6J("H + "N)
"+
!2"2N
3J("N)
(T2)!1 =!2
H!2N!2
8r6NH
!4J(0) + J(!H ! !N) + 3J(!N) + 6J(!H) + 6J(!H + !N)
"+
!2"2N
3
!2/3J(0) + 1/2J(!N)
"
(nOe)!1 =!2
H!2N!2
4r6NH
!6J("H + "N)! J("H ! "N)
"
(!H ! !N) " (!H + !N) " !H
Mesure des relaxations T1 T2 NOE en 1H et 15N (~nsec)
Lipari-Szabo Model
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
(T1)!1 =
!2H!2
N!2
4r6NH
!J("H ! "N) + 3J("N) + 6J("H + "N)
"+
!2"2N
3J("N)
(T2)!1 =!2
H!2N!2
8r6NH
!4J(0) + J(!H ! !N) + 3J(!N) + 6J(!H) + 6J(!H + !N)
"+
!2"2N
3
!2/3J(0) + 1/2J(!N)
"
(nOe)!1 =!2
H!2N!2
4r6NH
!6J("H + "N)! J("H ! "N)
"
(!H ! !N) " (!H + !N) " !H
Mesure des relaxations T1 T2 NOE en 1H et 15N (~nsec)
Lys 19
Lipari-Szabo Model
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Ala 8
Gly 33
Mouvement moléculaire d’ “échange” (~100 µsec)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Échange Deuterium (~heure-semaine)
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Échange Deuterium (~heure-semaine)
(1) de Lamotte, F.; Vagner, F.; Pons, J.-L.; M.-F.Gautier; Delsuc, M.-A. CR Acad. des Sci. Chimie/Chemistry 2001, 4, 839-843.(2) Pons, J.-L.; Lamotte, F. d.; Gautier, M.-F.; Delsuc, M.-A. J Biol Chem 2003, 16, 14249-14256.
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
UCRL-JRNL-210010
Characterization of the restricted rotation of thedimethyl groups in chemically N-terminal 13Clabeled Antifreeze Glycoproteins: A temperaturedependent study in water to ice through thesupercooled state.
V. V. Krishnan, E. Y. Lau, N. M.Tsvetkova, R. E.Feeney, W. H. Fink, Y. Yeh
February 25, 2005
Journal of Chemical Physics
Temperature (C)
Lin
ew
idth
R2
* (H
z)
Figure 3
-20.0 -10.0 0.0 10.0 20.0 30.00.0
2.0
4.0
6.0
8.0
10.0
Figure Captions
!"#$%&'()'*+,&-./"+'0".#%.-'12'/,&'34/&%-"5.6'-10"2"&0'7!89:';-<7!89:=>'?.+,'12'/,&'
@,%&&'.-"514.+"0'%&A&./B';77@'1%'97@=C'D"/,'/,&'/,%&15"5&B';B,1D5'EF'6.%#&%'
6&//&%B='#6F+1BF6./&0'./'/,&'G!'A1B"/"15B'D"/,'/,&'0"B.++,.%"0&>'@,&'/D14(HG'6.E&6&0'
-&/,F6'#%1$AB'.50'/,&'%1/./"15'12'/,&'0"4-&/,F6'#%1$A'"B'.6B1'A1"5/&0'1$/>''7/1-'
5.-&B'$B&0'21%'0&B+%"E"5#'/,&'3C340"-&/,F6.6.5"5&'.%&'B,1D5>'
!"#$%&'I)'*16$/"15'B/./&'3JK'0./.>';.='L5&40"-&5B"15.6'(HG43JK';
(M40&+1$A6&0='BA&+/%.'
12'-<7!89:''.B'.'2$5+/"15'12'/&-A&%./$%&'/,%1$#,'/,&'B$A&%+116&0'B/./&>'NOP'.50'
NKP'.%E"/%.%"6F'%&2&%'/1'/,&'/D1'+.%E15B>';E='G15B/.5/'/"-&'M*QG';G@4M*QG='
BA&+/%.'12'-<7!89:'"5'/,&'B$A&%+116&0'.50'%11-'/&-A&%./$%&>''
!"#$%&'H)'961/'12'/,&'&22&+/"R&'6"5&'D"0/,';,.624D"0/,'./',.624-.S"-$-='12'/,&'NOP'.50'NKP'
+.%E15B'"5'-<7!89:C'B,1D5'EF'+"%+6&B'.50'BT$.%&B'%&BA&+/"R&6F>'@,&'&%%1%'E.%B'
.%&'1E/."5&0'2%1-'/,&'0"#"/.6'%&B16$/"15'12'/,&'/"-&'01-."540./.>'U&%/"+.6'0.B,&04
6"5&'"B'0%.D5'./'V"'G>'
!"#$%&'W)'3JK'BA&+/%.'12'-<7!89:'.B'.'2$5+/"15'12'/,&'A1B/4"5R&%B"15'%&+1R&%F'0&6.F'"5'
/,&'@('-&.B$%&-&5/B'./'%11-'/&-A&%./$%&';.='.50'"5'/,&'B$A&%+116&0'/&-A&%./$%&'
;E=>'@,&'A61/'12'/,&'%&+1R&%F'+$%R&B'$B&0'/1'-&.B$%&'/,&'@('R.6$&B'"B'B,1D5'"5';+=>'
@,&'&%%1%'E.%B'.%&'1E/."5&0'2%1-'0$A6"+./&'-&.B$%&-&5/B>''
!"#$%&'X)'961/'12'/,&'&SA&%"-&5/.6'BA"546.//"+&'%&6.S./"15'%./&'+15B/.5/B';K(='.B'.'2$5+/"15'12'
/&-A&%./$%&'21%'/,&'NOP';+"%+6&B='.50'NKP';BT$.%&B='+.%E15B'12'-<7!89:>'''K('
R.6$&B'D&%&'1E/."5&0'.B'0&B+%"E&0'"5'/,&'-./&%".6B'.50'-&/,10B>'
' 9.#&'(:'12'IX' '
-20.0 -10.0 0.0 10.0 20.0 30.0
0.0
1.0
2.0
3.0
4.0
Temperature (C)
Sp
in L
att
ice
Re
lax
ati
o R
ate
R
1 (
s-1
)
Figure 5
Figure Captions
!"#$%&'()'*+,&-./"+'0".#%.-'12'/,&'34/&%-"5.6'-10"2"&0'7!89:';-<7!89:=>'?.+,'12'/,&'
@,%&&'.-"514.+"0'%&A&./B';77@'1%'97@=C'D"/,'/,&'/,%&15"5&B';B,1D5'EF'6.%#&%'
6&//&%B='#6F+1BF6./&0'./'/,&'G!'A1B"/"15B'D"/,'/,&'0"B.++,.%"0&>'@,&'/D14(HG'6.E&6&0'
-&/,F6'#%1$AB'.50'/,&'%1/./"15'12'/,&'0"4-&/,F6'#%1$A'"B'.6B1'A1"5/&0'1$/>''7/1-'
5.-&B'$B&0'21%'0&B+%"E"5#'/,&'3C340"-&/,F6.6.5"5&'.%&'B,1D5>'
!"#$%&'I)'*16$/"15'B/./&'3JK'0./.>';.='L5&40"-&5B"15.6'(HG43JK';
(M40&+1$A6&0='BA&+/%.'
12'-<7!89:''.B'.'2$5+/"15'12'/&-A&%./$%&'/,%1$#,'/,&'B$A&%+116&0'B/./&>'NOP'.50'
NKP'.%E"/%.%"6F'%&2&%'/1'/,&'/D1'+.%E15B>';E='G15B/.5/'/"-&'M*QG';G@4M*QG='
BA&+/%.'12'-<7!89:'"5'/,&'B$A&%+116&0'.50'%11-'/&-A&%./$%&>''
!"#$%&'H)'961/'12'/,&'&22&+/"R&'6"5&'D"0/,';,.624D"0/,'./',.624-.S"-$-='12'/,&'NOP'.50'NKP'
+.%E15B'"5'-<7!89:C'B,1D5'EF'+"%+6&B'.50'BT$.%&B'%&BA&+/"R&6F>'@,&'&%%1%'E.%B'
.%&'1E/."5&0'2%1-'/,&'0"#"/.6'%&B16$/"15'12'/,&'/"-&'01-."540./.>'U&%/"+.6'0.B,&04
6"5&'"B'0%.D5'./'V"'G>'
!"#$%&'W)'3JK'BA&+/%.'12'-<7!89:'.B'.'2$5+/"15'12'/,&'A1B/4"5R&%B"15'%&+1R&%F'0&6.F'"5'
/,&'@('-&.B$%&-&5/B'./'%11-'/&-A&%./$%&';.='.50'"5'/,&'B$A&%+116&0'/&-A&%./$%&'
;E=>'@,&'A61/'12'/,&'%&+1R&%F'+$%R&B'$B&0'/1'-&.B$%&'/,&'@('R.6$&B'"B'B,1D5'"5';+=>'
@,&'&%%1%'E.%B'.%&'1E/."5&0'2%1-'0$A6"+./&'-&.B$%&-&5/B>''
!"#$%&'X)'961/'12'/,&'&SA&%"-&5/.6'BA"546.//"+&'%&6.S./"15'%./&'+15B/.5/B';K(='.B'.'2$5+/"15'12'
/&-A&%./$%&'21%'/,&'NOP';+"%+6&B='.50'NKP';BT$.%&B='+.%E15B'12'-<7!89:>'''K('
R.6$&B'D&%&'1E/."5&0'.B'0&B+%"E&0'"5'/,&'-./&%".6B'.50'-&/,10B>'
' 9.#&'(:'12'IX' '
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
The di!usion coe"cients were obtained using:
I d;D; g; T2; T1; 2s;TR! "
# I0 exp!$ 2s
T2
"1
!$ exp
!$ TR
T1
""
% exp
#$ c2g2d2 D
!$ d
3
"D$; !1"
where I!d;D; g; T2; T1; 2s;TR" and I0 are the echo inten-sities of NMR signal in the presence of gradient pulsesof strength g and in absence of gradient pulses, re-spectively. c is the gyromagnetic constant for 1H(c # 2:6752% 108 radT$1 s$1 for protons), d is the du-ration of the z gradient pulse, and D is the time intervalbetween the gradient pulses. The delay between the first90! pulse and the first gradient pulse t1, was fixed at1ms. s is the time interval between the successive RFpulses and TR the recuperation time. T2 and T1 were,respectively, the spin–spin and spin–lattice relaxationtimes. To eliminate the e!ect of spin relaxation, thedi!usion coe"cient determination was performed bykeeping d and D constant and varying g. In our exper-iments, g was incremented from 0.4 to 3.3 Tm$1. Thenthe echo intensity in the presence of gradients dividedby the echo intensity without application of gradients,i.e., the attenuation of the NMR spin-echo signalintensity, became:
IgI0# exp & $ kD'; !2"
where k is defined as k # $c2g2d2!D$ !d=3"". As aresult, the self-di!usion coe"cient of H2O (Dwater) wasequal to the slope calculated from a regression analysisof the data sets (ln!Ig=I0"; k) using Eq. (2). This ap-proach is valid when the echo intensity could be at-tributed to the water proton relaxation only. If theecho intensity became dependent on both water and fatrelaxation, the relaxation parameters of each compo-nent should be considered in the equation given the
self-di!usion coe"cient. In the study of multiple com-ponent di!usion, the echo attenuation observed isdependent on c2g2d2D!2". So, for a fixed s;TR; T2water;T2fat; T1water; T1fat; c, the echo intensity was given bythe equation:
I d;D; g! " # I(water exp & $ kDwater ' ) I(fat exp & $ kDfat '; !3"
where, for TR * T1fat and T1water, one has:
I(water # exp
!$ 2sT2water
"and I(fat # exp
!$ 2sT2fat
"; !4"
where T2water; T1water; T2fat; and T1fat were, respectively,the spin–spin and the spin–lattice relaxation times ofwater and fat and Dwater and Dfat were the respectivewater and fat self-di!usion coe"cients.
Finally,
IgI0# %Pwater exp & $ kDwater ' )%Pfat exp & $ kDfat ' !5"
with %Pwater # I(water=!I(water ) I(fat", the relative water echosignal intensity weighted by the water relaxationparameters and %Pfat # I(fat=!I(water ) I(fat", the relative fatecho signal intensity weighted by the fat relaxationparameters.
The calculation of the water self-di!usion coe"cientfrom Eq. (5) could be performed using a bi-exponentialfitting.
However, if only water self-di!usion coe"cient isrequired, an appropriate choice of the sequenceparameters should be used. In this work, a T1-nullinversion recovery sequence was evaluated.
So, for the implementation of the T1-weighed spin-echo sequence, a 180!x pulse was added before thefirst 90! pulse (Fig. 1). The delay between the 180!and the 90! pulse was defined by ti, the inversiontime.
For this specific sequence, Eq. (4) could be modifiedto include the signals arising from each fat and watercomponent, and became:
Fig. 1. The standard spin-echo and the T1-weighted spin-echo sequences. A spin-echo NMR signal is generated from a sequence consisting of 90!xand 180!y radio-frequency pulses and its intensity is modulated by two-field gradient pulses g. TE is the echo time and corresponding to 2s.Recuperation time TR # 5 s, inter-pulse spacing time s # 7:5ms, di!usion time D # 7:5ms, width of the field gradient pulses d # 0:5ms and the delay(t1) between the first pulse RF and the first gradient pulse was fixed at 1ms. In the experiments, g was incremented from 0.4 to 3.3Tm$1. For the T1-weighted spin-echo sequence, an additional 180!x radio-frequency pulse was included (diagonally shaded) and the parameters are identical to thespin-echo sequence. The pre-delay ti is experimentally defined for each temperature.
268 A. M!eetais, F. Mariette / Journal of Magnetic Resonance 165 (2003) 265–275
Determination of water self-di!usion coe"cient in complexfood products by low field 1H PFG-NMR: comparison between
the standard spin-echo sequence and the T1-weightedspin-echo sequence
Ang!eelique M!eetais and Franc!ois Mariette*
Cemagref, UR Technologie des Equipements Agro-alimentaires, CS 64426, 17 Avenue de Cucill!ee, 35044 Rennes Cedex, France
Received 23 April 2003; revised 26 August 2003
Communicated by Joseph Ackerman
Abstract
In 1990, Van Den Enden et al. proposed a method for the determination of water droplet size distributions in emulsions using apulsed-field-gradient nuclear magnetic resonance (PFG-NMR) T1-weighted stimulated-echo technique. This paper describes boththe T1-weighted spin-echo sequence, an improved method based on this earlier work, and, the standard PFG spin-echo sequence.These two methods were compared for water self-di!usion coe"cient measurement in the fatty protein concentrate sample used as a!cheese model." The transversal and longitudinal relaxation parameters T1 and T2 were determined according to the temperature andinvestigated for each sample; fat-free protein concentrate sample, pure anhydrous milk fat, and fatty protein concentrate sample.The water self-di!usion in fat-free protein concentrate samples followed a linear behavior. Consequently, the water self-di!usioncoe"cient could be easily characterized for fat-free protein concentrate samples. However, it seemed more complicated to obtainaccurate water self-di!usion in fatty protein concentrate samples since the di!usion-attenuation data were fitted by a bi-exponentialfunction. This paper demonstrates that the implementation of the T1-weighted spin-echo sequence, using the di!erent T1 propertiesof water and fat phases, allows the accurate determination of water self-di!usion coe"cient in a food product. To minimize thecontribution of the 1H nuclei in the fat phase on the NMR echo signal, the fat protons were selectively eliminated by an additional180! pulse. This new method reduces the standard errors of di!usion data obtained with a basic spin-echo technique, by a factor of10. The e!ectiveness of the use of the T1-weighted spin-echo sequence to perform accurate water self-di!usion coe"cients mea-surement in fatty products is thus demonstrated." 2003 Elsevier Inc. All rights reserved.
Keywords: 1H NMR; Low-field NMR; Self-di!usion; Relaxation; Food products
1. Introduction
Pulsed-field-gradient spin-echo NMR (PFG-NMR) isa powerful method for studying molecular di!usion[1–3]. The NMR pulsed-field gradient technique repre-sents a versatile tool for studying transport phenomenaof molecules such as water, lipids or sugars in porousmedia such as food gels, wheat starch gels [4–6], gellangum gels [7], cheeses [8], and bread matrixes [9]. More-
over, structural information can be obtained from acareful analysis of the system in which the water is dif-fusing such as a micro-emulsion [10].
The classic method for self-di!usion coe"cient de-termination was firstly proposed by Stejskal and Tanner[11]. The determination is carried out by the acquisitionof an echo, either of spin or stimulated. If acquisition isdone with a high field NMR spectrometer, then theacquisition of the echo is followed by the FourierTransform in order to identify the molecule according tothe chemical shift. The self-di!usion coe"cient is thendirectly estimated from the variation of the surface (orthe intensity) of the peak according to the gradient
*Corresponding author. Fax: +02-23-48-21-15.E-mail addresses: [email protected] (A. M!eetais), franc-
[email protected] (F. Mariette).
1090-7807/$ - see front matter " 2003 Elsevier Inc. All rights reserved.doi:10.1016/j.jmr.2003.09.001
Journal of Magnetic Resonance 165 (2003) 265–275
www.elsevier.com/locate/jmr
Determination of water self-di!usion coe"cient in complexfood products by low field 1H PFG-NMR: comparison between
the standard spin-echo sequence and the T1-weightedspin-echo sequence
Ang!eelique M!eetais and Franc!ois Mariette*
Cemagref, UR Technologie des Equipements Agro-alimentaires, CS 64426, 17 Avenue de Cucill!ee, 35044 Rennes Cedex, France
Received 23 April 2003; revised 26 August 2003
Communicated by Joseph Ackerman
Abstract
In 1990, Van Den Enden et al. proposed a method for the determination of water droplet size distributions in emulsions using apulsed-field-gradient nuclear magnetic resonance (PFG-NMR) T1-weighted stimulated-echo technique. This paper describes boththe T1-weighted spin-echo sequence, an improved method based on this earlier work, and, the standard PFG spin-echo sequence.These two methods were compared for water self-di!usion coe"cient measurement in the fatty protein concentrate sample used as a!cheese model." The transversal and longitudinal relaxation parameters T1 and T2 were determined according to the temperature andinvestigated for each sample; fat-free protein concentrate sample, pure anhydrous milk fat, and fatty protein concentrate sample.The water self-di!usion in fat-free protein concentrate samples followed a linear behavior. Consequently, the water self-di!usioncoe"cient could be easily characterized for fat-free protein concentrate samples. However, it seemed more complicated to obtainaccurate water self-di!usion in fatty protein concentrate samples since the di!usion-attenuation data were fitted by a bi-exponentialfunction. This paper demonstrates that the implementation of the T1-weighted spin-echo sequence, using the di!erent T1 propertiesof water and fat phases, allows the accurate determination of water self-di!usion coe"cient in a food product. To minimize thecontribution of the 1H nuclei in the fat phase on the NMR echo signal, the fat protons were selectively eliminated by an additional180! pulse. This new method reduces the standard errors of di!usion data obtained with a basic spin-echo technique, by a factor of10. The e!ectiveness of the use of the T1-weighted spin-echo sequence to perform accurate water self-di!usion coe"cients mea-surement in fatty products is thus demonstrated." 2003 Elsevier Inc. All rights reserved.
Keywords: 1H NMR; Low-field NMR; Self-di!usion; Relaxation; Food products
1. Introduction
Pulsed-field-gradient spin-echo NMR (PFG-NMR) isa powerful method for studying molecular di!usion[1–3]. The NMR pulsed-field gradient technique repre-sents a versatile tool for studying transport phenomenaof molecules such as water, lipids or sugars in porousmedia such as food gels, wheat starch gels [4–6], gellangum gels [7], cheeses [8], and bread matrixes [9]. More-
over, structural information can be obtained from acareful analysis of the system in which the water is dif-fusing such as a micro-emulsion [10].
The classic method for self-di!usion coe"cient de-termination was firstly proposed by Stejskal and Tanner[11]. The determination is carried out by the acquisitionof an echo, either of spin or stimulated. If acquisition isdone with a high field NMR spectrometer, then theacquisition of the echo is followed by the FourierTransform in order to identify the molecule according tothe chemical shift. The self-di!usion coe"cient is thendirectly estimated from the variation of the surface (orthe intensity) of the peak according to the gradient
*Corresponding author. Fax: +02-23-48-21-15.E-mail addresses: [email protected] (A. M!eetais), franc-
[email protected] (F. Mariette).
1090-7807/$ - see front matter " 2003 Elsevier Inc. All rights reserved.doi:10.1016/j.jmr.2003.09.001
Journal of Magnetic Resonance 165 (2003) 265–275
www.elsevier.com/locate/jmr
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Consequently, whatever the value of the echo time inthe standard PFG spin-echo sequence, the echo intensitywas always dependent on fat and water proteins content.So, water self-di!usion coe"cient would not be mea-sured without any perturbations from fat protons.
Because of the larger di!erence between T1 relaxationsof water in fat-free protein concentrate and of AMF, abetter discrimination was possible at any temperature.The T1 distribution was bimodal (Fig. 2D). The first T1value corresponded to the fat relaxation and the secondT1 value corresponded to the water relaxation. As al-ready explained when considering T2, the T1 changes forwater between fat-free and fatty protein concentratewere explained by the water content variation.
3.2. Di!usion results
3.2.1. Water self-di!usion determination from standardspin-echo sequence for fat-free protein concentrates
The logarithmic plot of the echo attenuation as afunction of k is given in Fig. 3 for the fat-free proteinconcentrate. A straight line was observed whatever thetemperature. This demonstrates that the water mole-cules are not confined or restricted in compartments.So they can di!use freely over a length, given by the
relationship: hr2z i ! 6DD. According to the water self-di!usion coe"cients (Table 2), the length in three-di-mensional di!usion corresponded to a traveled distanceof between " 6 and 10 lm by the water molecule for atemperature range between 5 and 40 !C. A di!erencewas observed between the pure water self-di!usionand the water self-di!usion in the fat-free protein con-centrate. This reduction of the water self-di!usion infat-free protein concentrate compared to pure water self-di!usion has been already observed in dairy productssuch as casein dispersions and gels [26] and cheese [8].The decrease of the water di!usion was explained by theobstruction e!ect induced by the dairy protein as mainlycasein micelle [26].
3.2.2. Water and fat self-di!usion determination fromstandard spin-echo sequence for fatty protein concentrates
The self-di!usion coe"cient in the pure anhydrousmilk fat (DAMF) for each temperature is given in Table 3.As expected the fat self-di!usion was very low comparedto the water self-di!usion and increased with tempera-ture. The fat self-di!usion coe"cient value, we obtainedat 30 !C, was of the same order as the one measured forthe fat di!usion in bulk milk fat by Callaghan et al. [8],i.e., "1.1# 10$11 m2 s$1. However, it appeared that the
A
0,01
0,02
0,03
0,04
0,05
100 200 300 400 500 600 700 800 900 1 000 1 100
Am
pli
tud
e(a
rb
itra
ryu
nit
)
0,02
0,04
0,06
0,08
0,10
50 100 150 200 250
T2 (ms) T1 (ms)
T1 (ms)T2 (ms)
Am
pli
tud
e(a
rbit
rary
un
it)
0,02
0,04
0,06
0,08
0,10
100 200 300 400 500 600
Am
pli
tud
e(a
rbit
rary
un
it)
0,1
0,2
0,3
0,4
0,5
10 20 30 40 50 60 70 80 90 100
Am
pli
tud
e(a
rb
itrary
un
it)
B
C D
Fig. 2. Spin–spin (A) and spin–lattice (B) relaxation time distribution obtained by MEM for the anhydrous milk fat sample at 20 !C. Spin–spin (C)and spin–lattice (D) relaxation time distribution obtained by MEM for the fatty protein concentrate samples at 20 !C.
270 A. M!eetais, F. Mariette / Journal of Magnetic Resonance 165 (2003) 265–275
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
bi-exponential fitting, with the basic sequence were notsignificantly di!erent (Fig. 6). In comparison to thesedi!usion values, previously determined, a mono-expo-nential adjustment for di!usion data obtained with theclassical sequence have given lower values of water self-di!usion coe"cient. This could be explained by theinterference of the fat proton contribution on the esti-mation of the water di!usion coe"cient. The advantageof this T1-weighted spin-echo sequence is that the ac-curacy of the water di!usion coe"cient can be improvedsignificantly. Indeed, the di!usion coe"cient accuracycan be increased up to a factor of 10 without changingthe water di!usion coe"cient values between the basicsequence and the T1-weighted spin-echo sequence(Fig. 6). So, this latter one allows a more confident in-terpretation of the self-di!usion, and avoids confusionwith anomalous di!usion behavior. Moreover, the e!ectof the di!usion time D on the water self-di!usion couldbe studied without any perturbations from the echo-in-tensity from the fat protons. Nevertheless, the T1-weighted spin-echo sequence required a preliminarydetermination of the T1 or the ti and thus increased theexperimental time. Moreover, when the T1 relaxationdoes not behave as a single mono-exponential, the fatproton relaxation could not be totally suppressed withsingle ti value. Residual signal from fat protons couldbe detected for higher k values whereas the echoattenuation became non-linear for k values above1! 109 rad2 m s"2 as observed at 30 and 40 !C (Figs. 5Cand D). In that latter case, a mono-exponential was notenough accurate and a bi-exponential fitting should be
used as the classical spin-echo sequence (Fig. 6). Con-sequently, the use of the T1-weighted spin-echo sequencefor suppression of the fat signal was limited to sampleswith small amounts of liquid fat or with fat character-ized by a small distribution of spin–lattice relaxationtimes, at any temperature.
4. Conclusion
In this paper, we explored the application of thePFG-NMR 1H to the water phase of a complex recon-stituted fatty product. The results clearly show that thecharacterization of the water self-di!usion coe"cient ina complex dairy product is possible using a bi-expo-nential fitting adjustment. However, we had to pay at-tention to the accuracy and precision of the values.Indeed, this required constraining the measurement timeas well as taking a large number of measurements and ahigh ratio signal/noise for a precise estimation of thewater self-di!usion coe"cient Dwater.
Therefore, the use of the T1-weighted spin-echo se-quence is one solution for improving the precision of theresults and to make it possible to demonstrate the ex-istence of particular di!usion behavior. Moreover,compared to the use of high field NMR spectrometers,for which the generally expected errors are about 5%; weobtained standard errors lower than 0.5%. This clearlyshows the interest of this type of low-field bench topNMR equipment for self-di!usion studies on foodproducts.
0,7
0,9
1,1
1,3
1,5
1,7
1,9
2,1
2,3
0 5 10 15 20 25 30 35 40 45
Temperature (˚C)
Wate
rself
-dif
fus
ion
co
eff
icie
nt
(10
-9m
2s
-1)
Fig. 6. Water self-di!usion coe"cients versus the temperature for fatty protein concentrate samples measured with the two di!usion sequences. Thedi!usion data are fitted with a mono-exponential for the classical spin-echo sequence (}# and T1-weighted spin-echo sequence (!# and with a bi-exponential model for the classical spin-echo sequence (m) and for the data at 30 and 40 !C obtained with the T1-weighted spin-echo sequence (s#.
274 A. M!eetais, F. Mariette / Journal of Magnetic Resonance 165 (2003) 265–275
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Di!usion–relaxation correlation in simple pore structures
P.T. Callaghan,* S. Godefroy, and B.N. Ryland
MacDiarmid Institute for Advanced Materials and Nanotechnology, School of Chemical and Physical Sciences,Victoria University of Wellington, Wellington, New Zealand
Received 8 October 2002; revised 10 February 2003
Abstract
The e!ects of independent encoding for relaxation and for di!usion using separate time and gradient dimensions are calculated forspins di!using in plane parallel and spherical pores with relaxing walls. Two-dimensional inverse Laplace transformation is used toobtain computed !D; T2"maps for both geometries, in the regime in which the dimensionless di!usion coe"cient is less than unity andthe dimensionless relaxation parameter of order unity or greater. It is shown that there exist two distinct branches on the !D; T2"maps,onewith di!usion and relaxation strongly correlated andone inwhich the di!usion coe"cients varywidely independently of relaxation.! 2003 Elsevier Science (USA). All rights reserved.
Keywords: Di!usion; Relaxation; Two-dimensional; Laplace; Porous media
1. Introduction
The problem of restricted di!usion in simple porestructures forms a paradigm for many practical appli-cations of NMR in porous media, for example in oil welllogging, separation science, reactor technology, micro-filtration, plant physiology, and biomedicine. The ori-ginal platform for NMR analysis was provided in aclassic paper by Brownstein and Tarr [1] in which theypredicted multi-exponential relaxation for spins carriedby molecules undergoing restricted di!usion in a porewith relaxing walls. In particular they solved this re-laxation–di!usion problem for planar, cylindrical, andspherical pores using eigen-mode expansions and ob-tained exact analytic expressions for the amplitudes andtime constants of the multi-exponential relaxation. Thedimensionless parameter which defines the problem isthe ratio Ma=D0, where M is the wall relaxivity, acharacterizes the pore dimension, and D0 is the (unre-stricted) self-di!usion coe"cient of the fluid within thepore. Brownstein and Tarr showed that the dominantterm in the spin relaxation was associated with a relax-ation time which depends on the pore dimension as a=Mfor Ma=D0 small and a2=D0 for Ma=D0 large. This
behavior forms the basis of pore size analysis throughNMR relaxivity measurement. The primary mathemat-ical tool for deriving a distribution of relaxation times(and hence pore sizes) from multi-exponential signaldecay is inverse Laplace transformation [2–4].
During the last decade the e!ects of di!usion re-striction in porous media have been studied using an-other NMR method, the Pulsed Gradient Spin Echotechnique [5–10] in which the echo attenuation is mea-sured as a function of gradient wavevector q and thedi!usive observation time D. At values of D su"cientlylarge that many spin-bearing molecules reach the walls!D0D=a2 > 1" this ‘‘signal’’, E!q;D", exhibits coherencephenomena in the q-domain reminiscent of di!raction[10–16]. The problem is amenable to exact analytic so-lution in the case of planar, cylindrical, and sphericalpores and expressions have been published [17] whichalso take into account wall relaxation during the di!u-sion encoding period.
In principle the relaxation response and the q-vectorresponse of the system are separable using an experi-ment in which relaxation and di!usive e!ects are en-coded in two independent dimensions on the sameNMR magnetization using classical two-dimensionalNMR methodology. The experiment consists in apply-ing a Carr–Purcell–Meiboom–Gill pulse train (or aninversion recovery period) in which the time over which
Journal of Magnetic Resonance 162 (2003) 320–327
www.elsevier.com/locate/jmr
*Corresponding author. Fax: +646-350-5164.E-mail address: [email protected] (P.T. Callaghan).
1090-7807/03/$ - see front matter ! 2003 Elsevier Science (USA). All rights reserved.doi:10.1016/S1090-7807(03)00056-9
D0nn !r0Ps "MPs # 0; $2%
where nn is the outward surface normal. Eqs. (1) and (2)may be tackled via the standard eigenmode expansion
Ps$rjr0; t% #X
1
n#0
exp$&knt%un$r%u'n$r0%; $3%
where the un$r0% are an orthonormal set of solutions to theHelmholtz equation parameterized by the eigenvalue kn.
We choose here to investigate the case of the planarand spherical pore in the narrow gradient pulse ap-proximation. The e!ect of finite width gradient pulsesmay be easily incorporated using the matrix methodoutlined in an earlier paper [26]. For the moment, and inthe interests of simplicity, we seek to elucidate thissimplest of all problems for two classical geometries.
Eigenfunctions for the case of the planar and sphericalboundaries have been given earlier [17].
The echo attenuation expression derived from thepulse sequence of Fig. 1 may be written
ED$q; t% #Z Z
q$r; t%Ps$rjr0;D% exp(i2pq ! $r0 & r%)drdr0;
$4%
where q$r; t% reflects the spin relaxation taking placeover the relaxation encoding time, t and is given by
q$r0; t% #Z
q$r; 0%Ps$rjr0; t%dr $5%
with Ps$rjr0; t% subject to Eq. (2). In general the two-di-mensional experiment will allow for one q direction,which we shall define by spatial coordinate z, so that Eq.(4) is rewritten
ED$q; t% #Z Z
q$z; t%Ps$zjz0;D% exp(i2pq ! $z0 & z%)dzdz0:
$6%
Note that the PGSE encode time, D, is considered fixed.Of course, varying D and q while keeping t fixed orvarying D and t while keeping q fixed leads to di!erent,alternative, two-dimensional experiments. The expres-sions that we derive are general and allow for analysis ofall three sets of experiments. For the planar pore casethe gradient is applied along the z-direction normal to apair of bounding planes and these relaxing planes areseparated by a distance 2a and placed at z # *a. For thespherical case the gradient of magnitude q is appliedalong the polar axis of the spherical polar coordinateframe. The relaxing boundary is at a radial distancer # a from the sphere center. The resulting expressionsfor ED$q; t% are:
ED$q; t% # 2X
k;n
exp
!
&D0n2k t
a2
"
exp
!
&D0n2nD
a2
"
sinc$nk%(1" sinc$2nk%)&1(1
" sinc$2nn%)&1 2pqa sin$2pqa% cos$nk " nn% & $nk " nn% cos$2pqa% sin$nk " nn%
($2pqa%2 & $nk " nn%2)
(
" 2pqa sin$2pqa% cos$nk & nn% & $nk & nn% cos$2pqa% sin$nk & nn%($2pqa%2 & $nk & nn%
2)
)
2pqa sin$2pqa% cos$nn% & nn cos$2pqa% sin$nn%($2pqa%2 & n2n)
" 2X
k;m
exp
!
&D0n2kt
a2
"
exp
!
&D0f2mD
a2
"
sinc$nk%(1& sinc$2nk%)&1(1
" sinc$2fm%)&1 2pqa cos$2pqa% sin$nk " fm% & $nk " fm% sin$2pqa% cos$nk " fm%
($2pqa%2 & $nk " fm%2)
(
" 2pqa cos$2pqa% sin$fm & nk% & $fm & nk% sin$2pqa% cos$fm & nk%($2pqa%2 & $fm & nk%
2)
)
2pqa cos$2pqa% sin$fm% & fm sin$2pqa% cos$fm%($2pqa%2 & f2m)
;
$7a%
Fig. 1. NMR pulse sequence for two-dimensional encoding for relax-ation and di!usion. The relaxation period is t # 2ns for the precedingCPMG sequence.
322 P.T. Callaghan et al. / Journal of Magnetic Resonance 162 (2003) 320–327
D0nn !r0Ps "MPs # 0; $2%
where nn is the outward surface normal. Eqs. (1) and (2)may be tackled via the standard eigenmode expansion
Ps$rjr0; t% #X
1
n#0
exp$&knt%un$r%u'n$r0%; $3%
where the un$r0% are an orthonormal set of solutions to theHelmholtz equation parameterized by the eigenvalue kn.
We choose here to investigate the case of the planarand spherical pore in the narrow gradient pulse ap-proximation. The e!ect of finite width gradient pulsesmay be easily incorporated using the matrix methodoutlined in an earlier paper [26]. For the moment, and inthe interests of simplicity, we seek to elucidate thissimplest of all problems for two classical geometries.
Eigenfunctions for the case of the planar and sphericalboundaries have been given earlier [17].
The echo attenuation expression derived from thepulse sequence of Fig. 1 may be written
ED$q; t% #Z Z
q$r; t%Ps$rjr0;D% exp(i2pq ! $r0 & r%)drdr0;
$4%
where q$r; t% reflects the spin relaxation taking placeover the relaxation encoding time, t and is given by
q$r0; t% #Z
q$r; 0%Ps$rjr0; t%dr $5%
with Ps$rjr0; t% subject to Eq. (2). In general the two-di-mensional experiment will allow for one q direction,which we shall define by spatial coordinate z, so that Eq.(4) is rewritten
ED$q; t% #Z Z
q$z; t%Ps$zjz0;D% exp(i2pq ! $z0 & z%)dzdz0:
$6%
Note that the PGSE encode time, D, is considered fixed.Of course, varying D and q while keeping t fixed orvarying D and t while keeping q fixed leads to di!erent,alternative, two-dimensional experiments. The expres-sions that we derive are general and allow for analysis ofall three sets of experiments. For the planar pore casethe gradient is applied along the z-direction normal to apair of bounding planes and these relaxing planes areseparated by a distance 2a and placed at z # *a. For thespherical case the gradient of magnitude q is appliedalong the polar axis of the spherical polar coordinateframe. The relaxing boundary is at a radial distancer # a from the sphere center. The resulting expressionsfor ED$q; t% are:
ED$q; t% # 2X
k;n
exp
!
&D0n2k t
a2
"
exp
!
&D0n2nD
a2
"
sinc$nk%(1" sinc$2nk%)&1(1
" sinc$2nn%)&1 2pqa sin$2pqa% cos$nk " nn% & $nk " nn% cos$2pqa% sin$nk " nn%
($2pqa%2 & $nk " nn%2)
(
" 2pqa sin$2pqa% cos$nk & nn% & $nk & nn% cos$2pqa% sin$nk & nn%($2pqa%2 & $nk & nn%
2)
)
2pqa sin$2pqa% cos$nn% & nn cos$2pqa% sin$nn%($2pqa%2 & n2n)
" 2X
k;m
exp
!
&D0n2kt
a2
"
exp
!
&D0f2mD
a2
"
sinc$nk%(1& sinc$2nk%)&1(1
" sinc$2fm%)&1 2pqa cos$2pqa% sin$nk " fm% & $nk " fm% sin$2pqa% cos$nk " fm%
($2pqa%2 & $nk " fm%2)
(
" 2pqa cos$2pqa% sin$fm & nk% & $fm & nk% sin$2pqa% cos$fm & nk%($2pqa%2 & $fm & nk%
2)
)
2pqa cos$2pqa% sin$fm% & fm sin$2pqa% cos$fm%($2pqa%2 & f2m)
;
$7a%
Fig. 1. NMR pulse sequence for two-dimensional encoding for relax-ation and di!usion. The relaxation period is t # 2ns for the precedingCPMG sequence.
322 P.T. Callaghan et al. / Journal of Magnetic Resonance 162 (2003) 320–327
here are robust under variations in eigenvalue trunca-tion or stepsize e!ects. In carrying out a two-dimen-sional inverse Laplace analysis of the ED!q; t" data, wehave chosen to deliberately de-emphasize the principaldi!usion–relaxation mode by using a lower !qa"2 cuto!value of approximately 0:15a2=!D0D" The choice ofcuto! is not significant. It a!ects the relative amplitudesof the modes, but not their corresponding !D; T2" co-ordinates in the 2-D plots that result from two-dimen-sional inverse Laplace transformation.
Fig. 4 shows an example of a !D; T2" map for theplane parallel pore case, obtained for Ma=D0 # 2 andD0D=a2 # 0:2. This was calculated using a 4012!q2; t"input data set and a 50$ 40!D; T2" domain. In accor-dance with standard practice (3), regularisation wasadjusted to minimize v2 with maximum smoothing. As aguide to Fig. 4, a number of arrows are used to indicate!D; T2" reference features. The diagonal arrow indicatesthe position of the principal relaxation–di!usion featurewhich dominates as qa > 0. The principal (slow) relax-ation mode, T2 # a2=D0n
20 is shown with a horizontal
arrow. Also shown, using a vertical arrow, is the freedi!usion value, D0.
Fig. 5 shows a set of !D; T2" maps for the planeparallel pore case, for values of Ma=D ranging from0.5 to 10 and for D0D=a2 # 0:1, 0.2, and 0.3. The samedata transformation conditions were used as for Fig.4. Again the diagonal arrows indicate the position ofthe relaxation–di!usion feature which dominates asqa > 0 while the principal (slow) relaxation value,T2 # a2=D0n
20 is shown with a horizontal arrow, and a
vertical arrow, is used to indicate the free di!usionvalues, D0. Also shown, using a horizontal arrow onthe right hand side of the graph, is the high Ma=D0
relaxation limit, T2 # a2=D0!p=2"2. These maps areremarkably rich in features and show a wide spread of
di!usion and relaxation values, despite the simple ge-ometry of the pore. Note that the restriction ofD0D=a2 to values less than 0.5 ensure that the curva-ture of the echo attenuation data in q2-space remainsconsistent with apparent multi-exponential decay. Wewould emphasise that the choice of the maximumvalue of q2 does not influence the position of the peaksfound in the D% T2 domain, but only their relativeamplitude.
In interpreting these two-dimensional patterns, it isimportant to recognize that these are maps in which!D; T2" features are separated in a wave-number do-main, rather than in a spatial domain. The echo at-tenuation data arise from a superposition of modes. Inconverting the echo attenuation data to the Laplacedomain these modes tend to become separated andidentifiable. Note that the relaxation behavior at shortt and the di!usion behavior at short D are completemode sums, while the principal relaxation and di!usionmodes, with eigen-value n0, dominate in the long timelimits.
In the !D; T2" maps the following features are ap-parent:(i) There exists a concentration of intensity in the region
where the di!usion value takes its unrestricted valueD0, and the relaxation has the principal (slow) modevalue a2=D0n
20. This feature moves to slower di!usion
as D0D=a2 increases, due to greater influence of wallcollisions. This region also corresponds to the posi-
Fig. 4. Two-dimensional !D; T2" map for the plane parallel pore, forthe case Ma=D0 # 2 and D0D=a2 # 0:2. Dvalues are expressed in unitsof a2=D and T2 values in units of a2=D0. These maps were obtained bysuppressing the amplitude of the primary relaxation–di!usion mode ofby using a lower cuto! of !qa"2 # 0:15a2=D0D. The diagonal arrowindicates the position of the primary relaxation–di!usion mode ob-tained from the low-q data. The vertical arrow indicates D0 while thehorizontal arrow on the left indicates the position of the primary re-laxation mode T2 # a2=D0n
2k .
Fig. 3. Ratio of the secondary and primary modes for relaxation, as afunction of 2pqa for two values of Ma=D0 # 5 and Ma=D0 # 0:5, forthe case D0D=a2 # 0:2. Note the enhancement for the secondary re-laxation mode as qa increases.
324 P.T. Callaghan et al. / Journal of Magnetic Resonance 162 (2003) 320–327
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Journal of Colloid and Interface Science 297 (2006) 303–311www.elsevier.com/locate/jcis
Quantitative characterization of food products by two-dimensional D–T2and T1–T2 distribution functions in a static gradient
Martin D. Hürlimann !, Lauren Burcaw, Yi-Qiao Song
Schlumberger-Doll Research, 36 Old Quarry Road, Ridgefield, CT 06877, USA
Received 16 September 2005; accepted 22 October 2005
Available online 21 November 2005
Abstract
We present new NMR techniques to characterize food products that are based on the measurement of two-dimensional diffusion–T2 relaxationand T1–T2 relaxation distribution functions. These measurements can be performed in magnets of modest strength and low homogeneity anddo not require pulsed gradients. As an illustration, we present measurements on a range of dairy products that include milks, yogurt, cream,and cheeses. The two-dimensional distribution functions generally exhibit two distinct components that correspond to the aqueous phase and theliquid fat content. The aqueous phase exhibits a relatively sharp peak, characterized by a large T1/T2 ratio of around 4. The diffusion coefficientand relaxation times are reduced from the values for bulk water by an amount that is sample specific. The fat signal has a similar signature inall samples. It is characterized by a wide T2 distribution and a diffusion coefficient of 10"11 m2/s for a diffusion time of 40 ms, determined bybounded diffusion in the fat globules of 3 µm diameter.! 2005 Elsevier Inc. All rights reserved.
Keywords: Food product; Diffusion; Relaxation; Globule size
1. Introduction
Nuclear magnetic resonance has long played an importantrole in the analysis and characterization of food products [1]. Itis noninvasive and a large number of specific techniques havebeen developed that are sensitive to chemical composition andto the structural arrangement or texture of the various com-ponents. These techniques include high resolution spectrosco-py [2], magic angle spinning [3], imaging [4], pulsed field gra-dient diffusometry [5–7], field cycling relaxometry [8], and lowfield relaxometry [9,10].
The purpose of this paper is to demonstrate that recently in-troduced 2D NMR techniques of relaxation and diffusion [11,12] in static gradients can be usefully applied to the characteri-zation of food products. The techniques were originally devel-oped to characterize fluid filled porous media and are currentlyused routinely in well-logging applications [13,14]. A key ad-vantage of the techniques is that they can be implemented in
* Corresponding author. Fax: +1 (203) 438 3819.E-mail address: [email protected] (M.D. Hürlimann).
an inhomogeneous magnet at low field without pulsed fieldgradient [12,15]. This greatly simplifies the required instru-mentation: a permanent magnet with a static gradient and abasic NMR spectrometer are sufficient. There is no need fora high field superconducting magnet of high homogeneity orpulsed gradient systems with gradient amplifiers. For this rea-son, this new approach might be well suited for applicationsof process monitoring and quality control. We demonstrate thenew approach with diffusion–T2 and T1–T2 distribution func-tions measured on a range of dairy products, including milk,cream, and various cheeses. Métais and Mariette [16] showedthat T2 measurements alone are generally insufficient to distin-guish quantitatively the fat and water proton signals. Godefroyet al. previously reported high field measurements on two sam-ples of cheese using the pulsed gradient method [17,18].
Dairy products can be considered to be emulsions of milk fatin a continuous aqueous phase. In bovine milk, the most abun-dant components of the aqueous phase after water are caseinproteins and lactose [19]. Depending on the preparation of thedairy products, the casein proteins can be present in the form ofmicelles (milk) or a continuous porous network (cheese), andare therefore a key parameter to control the consistency and
0021-9797/$ – see front matter ! 2005 Elsevier Inc. All rights reserved.doi:10.1016/j.jcis.2005.10.047
Journal of Colloid and Interface Science 297 (2006) 303–311www.elsevier.com/locate/jcis
Quantitative characterization of food products by two-dimensional D–T2and T1–T2 distribution functions in a static gradient
Martin D. Hürlimann !, Lauren Burcaw, Yi-Qiao Song
Schlumberger-Doll Research, 36 Old Quarry Road, Ridgefield, CT 06877, USA
Received 16 September 2005; accepted 22 October 2005
Available online 21 November 2005
Abstract
We present new NMR techniques to characterize food products that are based on the measurement of two-dimensional diffusion–T2 relaxationand T1–T2 relaxation distribution functions. These measurements can be performed in magnets of modest strength and low homogeneity anddo not require pulsed gradients. As an illustration, we present measurements on a range of dairy products that include milks, yogurt, cream,and cheeses. The two-dimensional distribution functions generally exhibit two distinct components that correspond to the aqueous phase and theliquid fat content. The aqueous phase exhibits a relatively sharp peak, characterized by a large T1/T2 ratio of around 4. The diffusion coefficientand relaxation times are reduced from the values for bulk water by an amount that is sample specific. The fat signal has a similar signature inall samples. It is characterized by a wide T2 distribution and a diffusion coefficient of 10"11 m2/s for a diffusion time of 40 ms, determined bybounded diffusion in the fat globules of 3 µm diameter.! 2005 Elsevier Inc. All rights reserved.
Keywords: Food product; Diffusion; Relaxation; Globule size
1. Introduction
Nuclear magnetic resonance has long played an importantrole in the analysis and characterization of food products [1]. Itis noninvasive and a large number of specific techniques havebeen developed that are sensitive to chemical composition andto the structural arrangement or texture of the various com-ponents. These techniques include high resolution spectrosco-py [2], magic angle spinning [3], imaging [4], pulsed field gra-dient diffusometry [5–7], field cycling relaxometry [8], and lowfield relaxometry [9,10].
The purpose of this paper is to demonstrate that recently in-troduced 2D NMR techniques of relaxation and diffusion [11,12] in static gradients can be usefully applied to the characteri-zation of food products. The techniques were originally devel-oped to characterize fluid filled porous media and are currentlyused routinely in well-logging applications [13,14]. A key ad-vantage of the techniques is that they can be implemented in
* Corresponding author. Fax: +1 (203) 438 3819.E-mail address: [email protected] (M.D. Hürlimann).
an inhomogeneous magnet at low field without pulsed fieldgradient [12,15]. This greatly simplifies the required instru-mentation: a permanent magnet with a static gradient and abasic NMR spectrometer are sufficient. There is no need fora high field superconducting magnet of high homogeneity orpulsed gradient systems with gradient amplifiers. For this rea-son, this new approach might be well suited for applicationsof process monitoring and quality control. We demonstrate thenew approach with diffusion–T2 and T1–T2 distribution func-tions measured on a range of dairy products, including milk,cream, and various cheeses. Métais and Mariette [16] showedthat T2 measurements alone are generally insufficient to distin-guish quantitatively the fat and water proton signals. Godefroyet al. previously reported high field measurements on two sam-ples of cheese using the pulsed gradient method [17,18].
Dairy products can be considered to be emulsions of milk fatin a continuous aqueous phase. In bovine milk, the most abun-dant components of the aqueous phase after water are caseinproteins and lactose [19]. Depending on the preparation of thedairy products, the casein proteins can be present in the form ofmicelles (milk) or a continuous porous network (cheese), andare therefore a key parameter to control the consistency and
0021-9797/$ – see front matter ! 2005 Elsevier Inc. All rights reserved.doi:10.1016/j.jcis.2005.10.047
M.D. Hürlimann et al. / Journal of Colloid and Interface Science 297 (2006) 303–311 307
Fig. 4. Comparison of T1–T2 distribution functions (left) and D–T2 distrib-ution functions (right) measured on four different dairy products: skim milk,heavy cream, a soft cheese (Brie), and a hard cheese (Emmentaler). The dashedlines in the T1–T2 distribution functions indicate T1 = T2, whereas in the D–T2distribution functions, they indicate the diffusion coefficient of water. Contourlines are shown at 10, 30, 50, 70, and 90% of maximum values in each panel.For the samples of heavy cream and Brie, we show in addition the 5% line.
sociated with proteins and free water. The T1/T2 ratio is muchlarger than 1, which is shown as dashed line in the T1–T2 plots.This implies the presence of slow motion and a frequency de-pendence of T1. The measured diffusion coefficient is close tothe molecular diffusion coefficient of water, shown as dashedline in the D–T2 plots. In contrast to the relaxation properties,diffusion is much less affected by the minor components, in thiscase proteins.
The D–T2 distributions of the other three samples show twocomponents. The upper component is still relatively sharp andits diffusion coefficient is within a decade of water. Therefore,we associate it with the aqueous phase. The lower component
Fig. 5. T1–T2 distribution functions for undiluted and 50% diluted heavy cream(shaded). The dashed line indicates T1 = T2. The contour lines are at 2, 5, 10,15, 25, 35, 55, 75, and 95% of the maximum level for each distribution function.
has a T2 distribution that is about 1.5 decades wide and at amuch lower diffusion coefficient. This component is associatedwith the liquid fat. Additional components due to solid fat andproteins have relaxation times less than 100 µs [9] are not de-tected here.
In the T1–T2 distributions, the two components do not sep-arate as clearly as in the D–T2 distributions, but the results arefully consistent with a superposition of a relatively sharp peakassociated with the aqueous phase with a large T1/T2 ratio anda broader feature due to the liquid fat with a T1/T2 ratio closeto 1. From both distribution functions, it is clear that 1D re-laxation measurements alone may be insufficient to distinguishunambiguously the water and fat signal, as the relaxation timeof the aqueous phase can be both longer or shorter than of thefat signal, in agreement with the conclusions by Métais and Ma-riette [16]. On the other hand, diffusion can be used to separatethe two phases and can therefore be used to quantify the contentof liquid fat in the food product [22].
4.2. T1–T2 relaxation
To further support our interpretation of the fat and water sig-nal in T1–T2 distributions, we performed dilution experiments.In Fig. 5 results for undiluted heavy cream (open) and heavycream diluted 50% with water (shaded) are superimposed. Asthe sample is diluted, the intensity of the fat signal decreases,but its position in the T1–T2 plane is largely unaffected. In con-trast, the water signal of the diluted sample moves to longerrelaxation times, as the protein concentration decreases. Thisconfirms the identification of the two signals.
T2 relaxation in model milk systems has been studied re-cently in detail by le Dean et al. [10] and Gottwald et al. [23].They showed that it is mainly controlled by the concentrationof casein micelles and that the dominant mechanisms are pro-ton exchange between labile protein protons and the exchange
mobilité moléculaireM-A Delsuc - INRA - 18-10-2006
Acknowledgments
ILT Thérèse Malliavin
Diffusion Sophie Augé
Emmanuel Brun
Thierry Gostand
Yann Prigent
NPK Vincent Catherinot
Dominique Tramesel
Studies NMRtec
Christian Roumestand
Stefan Arold
Christian Dumas
Anja Bockmann
Frédéric de Lamotte
Céline Morau
Véronique Cheynier
Carine Mané
Christine Pascal
JP Renou
G. Bielicki