Mesures de diffusion et de relaxation pour l'étude de l ... · The Horse in motion Eadweard Muybridge:- 1878 Eadweard Muybridge mardi 3 juillet 2012 2 • GERM - St Hilaire- mai

Mesures de diffusion et de relaxation pour l'étude de l'oligomérisation et de

la polydispersité,quelques exemples d'applications.

Marc-André DelsucGERM 2012

St Hilaire

1mardi 3 juillet 2012

• GERM - St Hilaire- mai 2012 •

space and time separation

The Horse in motionEadweard Muybridge:- 1878

Eadweard Muybridge


http://en.wikipedia.org/wiki/Eadweard_Muybridge





space and time separation

• How to measure dynamics ?• couple space and time

Woman Walking DownstairsEadweard Muybridge:- 1887

Nu descendant un escalier no 2Marcel Duchamp - 1912





short considerations on measure

• optical (IR, UV, SAXS, ME)• many motion-less molecules : ensemble mean

hν

l

X = �Xi�E



electron microscopyThe EMBO Journal (2012) 31, 291–300IIgor Orlov, Natacha Rochel, Dino Moras and Bruno P Klaholz



mesuring dynamics

N Fischer, A L Konevega, W Wintermeyer, M V Rodnina & H StarkRibosome dynamics and tRNA movement by time-resolved electron cryomicroscopyNature (2010) 466 15





• correlation spectroscopy (FCS, FCCS)• unique mobile molecule : temporal mean

Sako Yasushi, Hiroshima Michio, Pack Chan‐Gi, Okamoto Kenji, Hibino Kayo, Yamamoto Akihiro. WIREs Syst Biol Med 2012, 4: 183-192

temporal CorrelationCross-correlation

X = �Xi�T

X = �Xi�E






• Ergodicity• equivalence of both means

• implies a stationary system

• usually assumed (not possible to do otherwise)

X = �Xi�T

X = �Xi�E

�Xi�T = �Xi�E






• Ergodicity

• Variants• QENS - DLS - fluorescence anisotropy

temporal response of ensemble mean

mean ensemble correlation

X = �Xi�T

X = �Xi�E







• Ergodicity

• Variants• QENS - DLS - fluorescence anisotropy

• ls-NMR• many motion-less molecules

• !!

X = �Xi�T

X = �Xi�E


X = � �Xi�T �E



NMR

• ensemble AND time mean

• What saves us :• caracteristic time of measure

time over which the measure is performed

• weighted statistics

in length

in angle

other ...



Time scale

fs ns µs ms s hps

NMR relaxometryB1relaxation exchange

stop-flow

T-jump

dielectic resonance

moleculartumblingtime



Space scale

pm nm µm mm m

microscopySTED

ME /AFM

NMR

SAXS-SANS

Xray

atomicresolution

MRIdiffusion



Measuring Diffusion by NMR

q = γGδ

I

Io= exp(−Dq2(∆− δ/3))

q : pitch of the magnetization helix

x y

z

O

90° 180°

! "

Laplace analysisby MaxEnt

variation - of q - of Δ

G G

DOSY spectrum



polynucleosomes

http://www.humans.be/images/biocell/chromatine.jpg

Cell260

Figure 1. The Atomic Structure of the Nucleosome Core Particle

Each strand of DNA is shown in different shade of blue. The DNA makes 1.7 turns around the histone octamer to form an overall particle witha disk-like structure. Histones are colored as in (A) and (B) of Figure 2.

karyote, appearing in some cases directly adjacent to assembled (Figures 1, 2A, and 2B). Each histone usesa protein fold, the histone fold, consisting of a three-the centromeres. A 73 base pair unit from the !-satellite

region of the human X chromosome has successfully helix core domain. These domains form “handshake”arrangements (see Figure 2B) to give rise to the hetero-been used to produce a 2-fold symmetric DNA palin-

drome that could then be reconstituted with separately dimer H2A-H2B and the heterodimer H3-H4 (Arents etal., 1991). Biochemical studies have shown that in solu-prepared histone octamers for high resolution structure

determination (Harp et al., 1996). tions of moderate salt and in the absence of DNA, theH3-H4 complex forms a tetramer whereas H2A-H2BThere are currently a handful of high-resolution struc-

tures of the nucleosome core particles available all of complex remains a stable dimer (Figures 2A and 2B).These components then associate together further towhich contain the DNA palindrome derived from the

human !-satellite DNA (Figure 1). A 2.8 A resolution form the histone octamer in the presence of DNA or inbuffered solutions containing more than 1 M NaCl. H3structure contains the DNA palindrome bound to recom-

binant Xenopus laevis histones prepared in E. coli (Luger has a unique role within the nucleosome, as there is a2-fold symmetry in the nucleosome organized directlyet al., 1997); a related structure has also been deter-

mined at 1.9 A resolution (Richmond and Davey, 2003; along the dimer interface of the two H3 histones. Apartfrom heterodimerization with H4, H3 also forms directDavey et al., 2002). A 2.5 A resolution structure contains

the DNA palindrome complexed to histones purified contacts with histone H2A. The H2A-H2B dimers posi-tion themselves such that two H2A molecules interactfrom chicken erythrocyte nuclei (Harp et al., 2000). The

E. coli-produced Xenopus histones do not get post- with each other in the nucleosome.In addition to the structured histone fold core, each his-translational modifications. By contrast, the histones

obtained from chicken erythrocytes carry numerous tone forms extensions consisting of disordered N-terminaland or C-terminal tails that protrude from the nucleo-posttranslational modifications, and transcription is to

a large extent blocked in these cells. Analysis of the some. The histone tails are only partially visible in allthese structures and show no secondary structures.chicken erythrocyte histone H3 has shown that lysines

4, 9, 14, 27, 36, and 79 are methylated, whereas lysines However, the tail segments of H3 and H2B protrudefrom the DNA gyres through the minor-groove channels.18 and 23 are acetylated; the significance of methylation

and acetylation is discussed below (Zhang et al., 2002). By extending beyond the disk-shaped nucleosome sur-face, the tails form ideal surfaces for covalent modifica-Nevertheless, the nucleosome core particle structure

containing posttranslationally modified histones shows tions by enzyme machineries (see below).Within the core particle, the DNA is wrapped so thatnear identical structure to the structure obtained from

recombinant histones that are free of such modifica- it forms 1.7 turns of a left-handed superhelix within thenucleosome core particle (Figure 1). Where the DNAtions. This finding implies that these modifications do

not exert their biological function by significantly re- enters and leaves the nucleosome, there are contactswith the N-terminal tail of the histone H3. The helicalshaping the nucleosome structure, but rather act as

marks for the specific recruitment of proteins that bring periodicity around the nucleosome core is 10.2 basepair as compared to 10.6 base pair for the helical period-additional regulatory functions to these units.

We have also now learned a great deal about how the icity of a free B-DNA. This small adjustment betweenfree and nucleosomal DNA is largely a result of the tor-histone octamer within the nucleosome is organized and

Khorasanizadeh. The nucleosome: from genomic organization to genomic regulation. Cell (2004) vol. 116 (2) pp. 259-72





polynucleosomes

CHO cell polynucleosomes, mild digestion - overnight acquisition on a 600MHz with DOTY probe

withBruno KiefferChristian KoehlerLionel Allouche

Valine signal

Poster 22



polynucleosomes

CHO cell polynucleosomes, stronger digestion -



nucleosomes

CHO cell polynucleosomes, harsh digestion



Relating Molecular Size and Diffusion

• Hydrodynamic Radius• hypotheses

-molecules freely diffusing in a continuous medium

- constant density

- non interacting (diluted)

• But..• mixed model !

atomic / continuous

• Expressed as a radius

But Not really a measure of the size.

D =kT

6πηrh

RH

Stokes-Einstein Equation

rh



GPC calibration kits from Fluka



sum (DOSY 1H/1H) D2O 600MHz 10

e0.5

10e1

10e1

.510

e210

e2.5

3.43.453.53.553.63.653.7ppm

dam

ping

20 40 60%

Mea

n

050

100

150

%

Row 1 (DOSY 1H)

GPC calibration kits from Fluka

withLionel Allouche

D=539 µm2/s

D=65 µm2/s

D=14 µm2/s

238 Da

12.1 kDa

209 kDa



MEAN F1 (DOSY 1H) D2O 600MHz

020

4060

8010

012

014

0

10e0,5 10e1 10e1,5 10e2 10e2,5 10e3damping

%GPC calibration kits from Fluka



PolyEthyleneOxide in D2O

• series of PEO• from monomer to Md

• 4 orders of magnitude !

0,001

0,01

0,1

1

100 1000 104

105

106

y = 5,0133 * x^(-0,5388) R= 0,99889

Diffu

sio

n r

ela

tive t

o D

2O

Molecular Mass

1 / 1.86

D ∝M−α

• very different from 1 / 3

S Augé, PO Schmit, CA Crutchfield, MT Islam, DJ Harris, E Durand, M Clemancey, AA Quoineaud, JM Lancelin, Y Prigent, F Taulelle, MA DelsucJ.Phys.Chem 113 p1914-18 (2009)

( )n



some Theory

• Flory theory of soluble polymers• Rg Radius of Gyration

Rg = kM δ dF =1

δ

Flory, P. University Press (1953). Schimmel, P. R. & Flory, P. J. (1967) PNAS 58, 52–59.

dF

1.0 2.0 3.0

rigid rodpolymer in poor solvent

polymer in Theta solvent

1.67



Da

Db≈

�Mb

Ma

�α

fractal dimension

3.0

2.5

2.0

1.5

1.0

Flor

y-pr

edict

ed zo

ne3.0

2.0

1.0

α =1

dF

dF

Globular proteins

PolySaccharides

DNAdenatured peptides

PS in toluene

PS in acetone

PS in THF

PEO in water

POMs clusters



sugar mixture

MW = 201 +/- 43

MW = 357 +/- 76

MW = 500 +/- 105

MW = 1040 +/- 219

1 - 180

2 - 342

3 - 504

4 - 666

5 - 828

6 - 990

7 - 1152

Glucose

10e2,3

10e2,4

10e2,5

10e2,6

10e2,7

10e2,8

44,24,44,64,855,2ppm

damping

Sucrose

Raffinose

ß-cyclodextrine (MW =1135)

Assemat, Coutouly, Hajjar, Delsuc Cr Chim (2010) 13 pp. 412-415

Da

Db≈

�Mb

Ma

�α



Determining polydispersity

• typical PEO 1H spectrum

are weighted by the number of molecules, while signals measuredon the whole polymer chain, extremities included, are weighted bymass of the molecules. Thus, the two different weightings used fordefining Mn and Mw can be observed in NMR, depending on themeasure being performed either on the extremities or on thewhole polymer chain.

This property applies also to PFGNMRmeasurement of diffusioncoefficients. From Eqs. (1) and (2), it is thus possible to express PDIas follows:

PDI ! hDwihDni

! ""df#5$

where hDni is the mean diffusion coefficient measured from the ILTanalysis of the PFGNMR signal of the extremity units, and hDwi themean diffusion coefficient measured for the whole polymer.

From this theoretical presentation, it appears that the polydis-persity index can be determined from a simple PFGNMR measure-ment, by comparing the signals originated from the main chain tothe signal of the extremities, and applying Eq. (5), given the preli-minary knowledge of fractal dimension of the chain.

To confirm this hypothesis, 2D-DOSY spectra were registeredfor different mixes of poly-ethyleneoxide (PEO) in water with cal-ibrated chain lengths and PDIs. Experimental values were con-fronted to theoretical ones.

2. Results and discussion

2.1. 1D NMR

The 1D-1H NMR spectrum of mix L is shown in Fig. 1. Very fewpeaks are observed and are easily assigned. Besides the resonanceat 3.7 ppm of the principal chain, other resonances are observed.Four different spin systems can be identified. The signal A corre-sponds to the chain methylene group, and the signal B to the pen-

ultimate methylene. The signal C corresponds to the signalassigned to the terminal methylene group bearing the hydroxyfunction, and last signals D and E show the 13C-satellites of thechain protons. As one can see on this example, protons on the PEO’sextremities are clearly identified. It is the case for all the mixeswhich makes the calculation of the average chain length N alwayspossible.

2.2. The DOSY experiment

Fig. 2 shows the NMR signal decay for signals A and C from PEOmix L versus the square of the gradient strength. Both curves arecolumns extracted respectively at 3.69 ppm and 3.63 ppm, fromthe diffusion experiment performed on mix L after Fourier trans-form and baseline correction. As expected, being obtained from aquite polydisperse sample (here PDI = 2.51) both curves present astrong non-exponential decay, as can be seen from the non-linear-ity of the log-plot. The ILT analysis of the decays produces a DOSYspectra with peaks broaden along the diffusion axis. However, de-spite this broadening, this experiment reveals two different diffu-sion regimes. Due to marked difference in the diffusioncoefficients, the 2D-DOSY spectrum displayed in Fig. 3 unequivo-cally confirms that two different diffusion profiles can be ex-tracted. In this example, the DOSY peak summit measured forthe extremity was found to be D = 1.83 % 103 lm2 s"1, whereasthe DOSY peak summit measured for the chain was found to beD = 1.11 % 103 lm2 s"1.

It should be noted that the measure relies on the complete mea-surement of all the different polymers present in the sample. Inconsequence, the PFG experiment should be designed to allow asignal attenuation from the longest chains, sufficient for a correctmeasurement of their diffusion coefficient. In the present case, allexperiments have been performed in the same conditions, opti-mized on the largest monodisperse polymer studied. However,

Fig. 1. 1D-1H NMR spectrum of a poly-ethyleneoxide in D2O, mix L. Assignment is given in inset, D and E are the 13C satellites of A.

170 J. Viéville et al. / Journal of Magnetic Resonance 212 (2011) 169–173

13C satelites13C satelites

J Viéville, M Tanty, MA DelsucPolydispersity index of polymers revealed by DOSY NMR. J Magn Reson (2011) 212 pp169

mixture of controlled polydispersity

Here PDI = 2.12

integral ratio provides mean chain length



looking to diffusion profiles

What’s going on ?



difference in behaviour

• all signal evolutions are non-linear

• end groups appear lighter!

when the composition of the mix is unknown, one should use largeenough PFG intensities to ensure the signal attenuation of theheaviest polymers. As a rule of thumb, a final attenuation around10% on a monodisperse species is usually required to permit a pre-cise determination of the diffusion coefficient. Thus, when study-ing an unknown polydisperse polymer, one should try to reach atleast a 1% attenuation for the main signal.

Mega-dalton polymers have already been precisely measuredon standard spectrometers [3]. So, the main size limitation forthe application of this technique is the possibility to reliably detectsignals from the chain extremities. Of course, this is more difficultto achieve on large polymers, as the extremity signals might be toofaint to be observed. This was done here for PEO polymers up to10 kDa, despite the fact that this signal only integrates as a CH2.

The method requires that the extremity of the polymer presentsan isolated signal in the NMR spectrum. This condition is not really

Fig. 2. Log-plot of the observed decays for varying gradient values squared for mixL. Diamonds are from the signal of the main chain (signal A Fig. 1), dots are from thesignal of the extremity (signal C).

Fig. 3. 2D-DOSY spectrum of mix L. The black rectangle on the right is the region over which the integration is made to determine hDni. hDwi is determined by integration overthe whole spectral range shown by outer red rectangle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of thisarticle.)

Table 1Experimental results compared to theoretical values.

N PDI Mn (g mol!1) Mw (g mol!1)

PEOmix

Theo Exp Theo Exp Theo Exp Theo Exp

Mix A 36.3 36.1 1.04 1.06 1615 1588.4 1679.6 1683.7Mix B 49.4 53.7 1.07 1.08 2190 2362.8 2343.3 2551.8Mix C 107.5 120 1.11 1.12 4750 5280 5272.5 5913.6Mix D 8.7 8.7 1.12 1.12 400.6 382.8 447.5 428.7Mix E 8.8 9.5 1.14 1.17 403.4 418 459.7 489.1Mix F 23 23.8 1.26 1.31 1021 1047.2 1268.3 1371.8Mix G 71.5 85.3 1.28 1.28 3165 3753.2 4051.2 4804.1Mix H 44.8 47.5 1.34 1.15 1989.3 2090 2518 2403.5Mix I 34.7 37 1.54 1.5 1544.3 1628 2382.7 2442Mix J 38.1 39.8 2.01 2.2 1696.9 1751.2 3238.5 3852.6Mix K 15.7 15.9 2.12 1.89 710.3 699.6 1332.1 1322.2Mix L 19.1 19.4 2.51 2.24 858.5 853.6 2008.2 1912.1Mix M 21.4 24.8 3.3 2.41 961.7 1091.2 3062.8 2629.8Mix N 22.4 23.8 3.41 2.75 1001.7 1047.2 3328 2879.8Mix O 13.5 13.9 5.23 4.48 611.3 611.6 3099.6 2740

J. Viéville et al. / Journal of Magnetic Resonance 212 (2011) 169–173 171

Main chain

End groups

when the composition of the mix is unknown, one should use largeenough PFG intensities to ensure the signal attenuation of theheaviest polymers. As a rule of thumb, a final attenuation around10% on a monodisperse species is usually required to permit a pre-cise determination of the diffusion coefficient. Thus, when study-ing an unknown polydisperse polymer, one should try to reach atleast a 1% attenuation for the main signal.

Mega-dalton polymers have already been precisely measuredon standard spectrometers [3]. So, the main size limitation forthe application of this technique is the possibility to reliably detectsignals from the chain extremities. Of course, this is more difficultto achieve on large polymers, as the extremity signals might be toofaint to be observed. This was done here for PEO polymers up to10 kDa, despite the fact that this signal only integrates as a CH2.

The method requires that the extremity of the polymer presentsan isolated signal in the NMR spectrum. This condition is not really

Fig. 2. Log-plot of the observed decays for varying gradient values squared for mixL. Diamonds are from the signal of the main chain (signal A Fig. 1), dots are from thesignal of the extremity (signal C).

Fig. 3. 2D-DOSY spectrum of mix L. The black rectangle on the right is the region over which the integration is made to determine hDni. hDwi is determined by integration overthe whole spectral range shown by outer red rectangle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of thisarticle.)

Table 1Experimental results compared to theoretical values.

N PDI Mn (g mol!1) Mw (g mol!1)

PEOmix

Theo Exp Theo Exp Theo Exp Theo Exp

Mix A 36.3 36.1 1.04 1.06 1615 1588.4 1679.6 1683.7Mix B 49.4 53.7 1.07 1.08 2190 2362.8 2343.3 2551.8Mix C 107.5 120 1.11 1.12 4750 5280 5272.5 5913.6Mix D 8.7 8.7 1.12 1.12 400.6 382.8 447.5 428.7Mix E 8.8 9.5 1.14 1.17 403.4 418 459.7 489.1Mix F 23 23.8 1.26 1.31 1021 1047.2 1268.3 1371.8Mix G 71.5 85.3 1.28 1.28 3165 3753.2 4051.2 4804.1Mix H 44.8 47.5 1.34 1.15 1989.3 2090 2518 2403.5Mix I 34.7 37 1.54 1.5 1544.3 1628 2382.7 2442Mix J 38.1 39.8 2.01 2.2 1696.9 1751.2 3238.5 3852.6Mix K 15.7 15.9 2.12 1.89 710.3 699.6 1332.1 1322.2Mix L 19.1 19.4 2.51 2.24 858.5 853.6 2008.2 1912.1Mix M 21.4 24.8 3.3 2.41 961.7 1091.2 3062.8 2629.8Mix N 22.4 23.8 3.41 2.75 1001.7 1047.2 3328 2879.8Mix O 13.5 13.9 5.23 4.48 611.3 611.6 3099.6 2740

J. Viéville et al. / Journal of Magnetic Resonance 212 (2011) 169–173 171



polydispersity index

Polydispersity index of polymers revealed by DOSY NMR

Justine Viéville a,b, Matthieu Tanty a,b, Marc-André Delsuc a,b,!a Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), UMR 7104, 1 rue Laurent Fries, BP 10142, 67404 Illkirch cedex, FrancebNMRTEC, Bioparc B, boulevard Sébastien Brant, 67400 Illkirch, France

a r t i c l e i n f o

Article history:Received 17 May 2011Revised 22 June 2011Available online 1 July 2011

Keywords:PolymerPolydispersityDOSYFractal dimensionInverse Laplace transform

a b s t r a c t

The polydispersity of a polymer chain is usually measured by its polydispersity index (PDI). In this studywe present a method which allows to estimate the PDI of linear polymers from a simple diffusion exper-iment.The approach is based on the differential diffusion profile observed for the main polymer chain signal

versus the extremity signal. From this difference, a statistical analysis of the DOSY spectrum allows thePDI to be estimated accurately, to the condition that the Flory coefficient of the polymer chain is known.Alternatively, the mass average molar mass Mw and the number average molar mass Mn can be extractedseparately from the same spectrum.Results on PEO mixes reveal that, using this new method, PDI can be estimated with a very good accu-

racy. This method can easily be applied to almost any kind of linear polymers.! 2011 Elsevier Inc. All rights reserved.

1. Introduction

Polymers are characterized by a distribution of molecularmasses. For linear polymers this distribution can be expressed interms of average chain length and polydispersity of the chainlength. The average chain length is routinely measured by NMRspectroscopy by measuring the ratio of the integrals of the mainchain signal to the extremity signals.

Self-diffusion, measured by pulsed field gradient NMR(PFGNMR) is sensitive to molecular size and provides an approachto the determination of the distribution of molecular mass. In thecase of linear polymer chains, the diffusion coefficient is linkedto the molecular mass through the following equation:

M / D!df "1#

where D is the diffusion coefficient of the molecule, M its mass anddf its fractal dimension [1–3]. The fractal dimension is a measure ofthe way the chain extends into the solvent, and is equal to the in-verse of the Flory coefficient m: df = 1/m. It is comprised between5/3 and 3 [4].

The effect of polydispersity on PFGNMR measurements has al-ready been well studied [5–7] and is known to lead to non expo-nential decays, even for weak polydispersity [8]. The analysis ofnon exponential decays requires the use of Inverse Laplace Trans-

form (ILT) in order to estimate the molecular mass distribution.This is an ill-posed mathematical problem, to which an approxi-mate solution can only be constructed. This was investigated byChen et al. using the CONTIN algorithm [1], but due to the approx-imate reconstruction, it is not possible to extract a useful value ofthe polydispersity index from this approach.

Polydispersity is commonly measured by the polydispersity in-dex (PDI). For a given polymer sample, it is defined as the ratio ofthe mass average molar mass (Mw) to its number averaged molarmass (Mn)

PDI $ Mw

Mn"2#

For a homopolymer linear chain, assuming that the mass of thechain is equal to the product of its length by the mass of the mono-meric unit M, the average molecular massesMn and Mw expressionsare given in Eqs. (3) and (4),

Mn $P

niMiPni

$ NM "3#

Mw $P

miMiPmi

$P

niM2iP

niMi"4#

where ni is the number of molecules of massMi,mi the mass of mol-ecules of mass Mi, and N the averaged chain length.

Mn andMw are statistical features of the same polymer distribu-tion but with different weightings. Because of this difference,Mw isalways greater than or equal to Mn, and PDI is always greater thanor equal to 1.

NMR parameters are also obtained as statistical average on thewhole sample. Signals measured from the extremity of the chain

1090-7807/$ - see front matter ! 2011 Elsevier Inc. All rights reserved.doi:10.1016/j.jmr.2011.06.020

! Corresponding author at: Institut de Génétique et de Biologie Moléculaire etCellulaire (IGBMC), UMR 7104, 1 rue Laurent Fries, BP 10142, 67404 Illkirch cedex,France. Fax: +33 (0)3 68 85 47 18.

E-mail addresses: [email protected], [email protected] (J. Viéville),[email protected] (M. Tanty), [email protected] (M.-A. Delsuc).

Journal of Magnetic Resonance 212 (2011) 169–173

Contents lists available at ScienceDirect

Journal of Magnetic Resonance

journal homepage: www.elsevier .com/locate / jmr

Mn averages by the number of moleculesMw averages by the amount of matter

So does the DOSY measure End groups averages by the number of molecules => DnMain chain averages by the number of monomer => Dw

PDI =Mw

Mn=

�< Dw >

< Dn >

�−dF

PDI =Mw

Mn



let’s take an example

n M D

12 12 0.5

10 10 0.6

8 8 0.7

6 6 0.8

<Mn> = (12+10+8+6)/4 = 9.0<Mw> = (122+102+82+62)/36 = 9.56

<Dn> = (0.5+0.6+0.7+0.8)/4 = 0.65<Dw> = (10*0.5+8*0.6+6*0.7+4*0.8)/28 = 0.614

PDI = 1.06

a polydisperse mixture of four polymers



experimental results

stringent. On the PEO samples, the small shift of 0.08 ppm ob-served between the chain and the extremity signals, is sufficientfor the study. Given this shift difference, two different diffusioncoefficient distributions can be extracted by ILT from one 2D-DOSYspectrum. By integrating over the regions displayed in Fig. 3, thebarycenters of these distributions are calculated to estimate thePDI.

2.3. Comparison to theoretical values

Table 1 gathers the expected and measured values of N and PDIfor all the different analyzed PEO mixes and Fig. 4 shows the com-parison between the theoretical and measured values of N and PDI.The very good correlation between theory and measurement indi-cates that the quality of the method.

The value of the fractal dimension df is the only free parameterwhich is needed to extract the PDI for the 2D-DOSY spectrum.From the Flory theory, it is predicted to be 5/3 and 3 for fullysolvated and collapsed polymer chains, respectively [4]. In a hsolvent, where polymer–polymer interactions are equal topolymer–solvent and solvent–solvent interactions, the polymerbehaves as a Gaussian chain and the exponent df is predicted tobe 2.

Results presented here have been obtained with a df value of1.86, as was determined by several studies [3,9]. Are also addedin Fig. 4, points showing the impact of varying the df values. Itcan be observed that while an error on this value may have an im-pact on the PDI accuracy, this impact is not very important.

3. Conclusion

We have shown that DOSY NMR can bring valuable informationon polydisperse polymers. With the proposed approach the poly-dispersity index as well as average chain length can readily bedetermined for linear polymers. To assess the polydispersity indexfrom the 2D-DOSY spectra, the barycenter of diffusion peak is cal-culated, this is made possible here thanks to the ILT analysis of theDOSY signal, which conserves the properties of the polymer distri-bution [7]. With this approach, results are independent of the aver-age chain length and only the fractal dimension of the polymerchain df must be known. Experimental average chain length andpolydispersity index did not indicate significative difference whencompared to supplier data. This technique was shown to equallyreliable and accurate for both high (5.23) and low (1.04) polydis-persity indexes. This method requires a separate NMR proton sig-

nal for the extremity of the studied polymer to be observed.However this condition is not stringent, as it was easily fulfilledhere in the case of PEO, where only 0.08 ppm separates both sig-nals. It will be easily extended to polymers with different extrem-ity chemical patterns (for example, a methyl- or amide-group).Moreover, in the case of very large polymers with low extremitiessignals, a chemical modification of the extremities will allow theuse of the method presented here.

Compared to other PDI determination technique such as MassSpectrometry or Size Exclusion Chromatography, this approachpresents the unique advantage of a direct measure which doesnot require any interaction with a static phase, separation, ioniza-tion or dilution of the polymer. It does not require any special cal-ibration, equipment, or preparation and is a rapidly obtained witha diluted polymer sample. NMR as always been a powerful spec-troscopy for the study of polymers, with DOSY NMR and the pro-posed procedure, the range of the physico-chemical parameterswhich can be accessed by NMR is further extended.

4. Experimental

4.1. Sample preparation

A set of 17 PEO standards, with masses ranging from 106 Da to10,730 Da were purchased from American Polymer Standards Cor-poration (Mentor, OH, USA). Each standard has been dissolved inMilli-Q water to 10% (w/v) solutions. These solutions were usedto create 15 mixes with controlled PDI from 1.04 to 5.23 and a con-centration range from 0.05% to 1% (w/v). Each mix contains 10%D2O (v/v) and 1% (v/v) of a 1 mM DSS (4,4-dimethyl-4-silapen-tane-1-sulfonic acid) aqueous solution. The details of the 17 stan-dard PEO as well as the 15 mixes are given in the Supplementarymaterials.

4.2. NMR spectroscopy

1D-1H and 2D-DOSY experiments were carried out on each PEOmix at 298 K on a 500 MHz Bruker Avance I NMR spectrometeremploying a 5 mm TXI probe equipped with z-gradients deliveringup to 53 G/cm.

1D-1H experiments were obtained with presaturation of water,128 scans of 16k data points, and recycle time of 6.1 s. Fouriertransform was applied with zerofilling and 0.5 Hz exponentialbroadening. Careful spline polynomial correction was applied toeach 1D-1H spectra before integration.

Fig. 4. Correlations curves for the average chain length N (left) and the PDI (right). Red lines correspond to theo = exp. The PDI was computed with the fractal dimension valuedf = 1.86 (blue square); df = 1.96 (upper bar); and df = 1.76 (lower bar). (For interpretation of the references to color in this figure legend, the reader is referred to the webversion of this article.)

172 J. Viéville et al. / Journal of Magnetic Resonance 212 (2011) 169–173

from integrals from DOSY

dF = 1.96dF = 1.86dF = 1.76



remark

results. Furthermore, both FlFFF and DLS are best suited foranalysis of macromolecules and large molecular aggregates. Thesetwo techniques have been used to characterize higher molecularweight soil humic substances;14,15 however, many of the samplesanalyzed in the current work are aquatic humic substances withconsiderably lower molecular weights. Finally, while FCS is highlysensitive it is limited to compounds that contain fluorophores, i.e.,those with aromatic moieties. On the other hand, PFG-NMR canyield diffusion coefficients for all of the 1H resonances in the NMRspectrum of a compound. However, measurements are limited torelatively concentrated solutions, because of the low sensitivityof NMR.PFG-NMR is also attractive because it can be used for mixture

analysis even in regions of the spectrum where resonances fromdifferent components overlap. Because of the complexity of thehumic samples, a typical humic NMR spectrum is relativelyfeatureless compared to that of a pure compound. Figure 1 showsthe broad overlapping resonances in the one-dimensional 1H NMRspectra of Suwannee River fulvic and humic acid standards. Atbest, only gross spectral assignments can be made,7 as sum-marized in Table 1. However, the PFG-NMR experiment allowsfor the integrated intensity of these broad spectral regions to beanalyzed, yielding a diffusion coefficient for each region. Thisillustrates the power of the PFG-NMR technique, in that aseemingly featureless 1D spectrum can be expanded into a seconddimension to provide useful molecular size information.In a PFG-NMR experiment using the bipolar pulse pair

longitudinal encode-decode (BPPLED) pulse sequence,16 theintensity of a resonance, I, is related to the diffusion coefficientof the molecule, D, by eqs 1 and 2,16 where Io is the resonance

intensity in the absence of a gradient pulse, ! is the time during

which diffusion occurs, ! and G are the duration and amplitudeof the bipolar magnetic field gradient, respectively, " is the delayfollowing each gradient pulse, and # is the magnetogyric ratio.From these equations, it can be seen that the signals for smallmolecules decay more rapidly with increasing gradient strengththan the signals for large molecules. Typically, a series of spectraare collected with increasing K values, and a simple linear least-squares regression is performed to obtain D. In addition, the PFG-NMR data set can be inverted to yield a two-dimensional diffusion-ordered spectrum (DOSY) in which 1H chemical shifts aredisplayed in one dimension and diffusion coefficients are displayedin the other.17-21Previous work on fulvic acid samples has shown that, unlike

single-component systems, different spectral regions can yielddifferent diffusion coefficients.22 Therefore, a single diffusioncoefficient calculated from a linear regression may not fullydescribe the system. Considering the fact that the humic sub-stances are complex mixtures, it is reasonable to hypothesize thatthere are numerous molecules of varying shapes and sizes, whichgive rise to a distribution of diffusion coefficients. Thus, theobjectives of this work were (1) to analyze PFG-NMR data forseveral standard humic materials using the computer programCONTIN to obtain diffusion coefficient distributions and 2D DOSYspectra for these samples, (2) to determine number average, DN,weight average, DW, and most probable, DP, diffusion coefficientsfrom the distributions, and (3) to explore the use of the ratio,DW/ DN, as an indication of the polydispersity of the humicsubstances.

EXPERIMENTAL SECTIONMaterials . The Suwannee River humic acid reference (SRHA),

fulvic acid standard (SRFA), Nordic Aquatic humic acid (NAHA),and Peat humic acid (PHA) reference samples were obtained fromthe International Humic Substances Society (IHSS, St. Paul, MN,June 1998). All samples were used without further purificationand were prepared at a concentration of 5 mg/ mL in deuteriumoxide (D2O 99.9 atom %D), obtained from Cambridge IsotopeLaboratories, Inc. (Andover, MA). Solutions were first acidifiedand lyophilized before being reconstituted in D2O, 100.0 atom %D, obtained from either Aldrich (Milwaukee, WI) or Sigma (St.Louis, MO) to reduce the overall intensity of the HOD resonancein the final spectra. Concentrated solutions of DCl and NaODobtained from Isotec (Miamisburg, OH) and diluted in D2O wereused to adjust the acidity of the SRHA, SRFA, NAHA, and PHAsolutions to pD 6.5, 4.0, 6.3, and 8.0, respectively. All pHmeasurements were made with a Fisher Scientific Acumet 10 pHmeter equipped with a 3-mm Ingold combination pH microelec-trode calibrated daily with aqueous pH buffers. The pH measure-ments were corrected for the deuterium isotope effect, pD, byadding 0.40 to the pH meter readings.23

(14) Pinheiro, J. P.; Mota, A. M.; d’Oliveira, J. M. R.; Martinho, J. M. G. Anal.Chim . Acta 1 9 9 6 , 329, 15-24.

(15) Schimpf, M. E.; Petteys, M. P. Colloids Surf., A 1 9 9 7 , 120, 87-100.(16) Wu, D.; Chen, A.; Johnson, C. S., Jr. J. Magn. Reson. Ser. A 1 9 9 5 , 115,

260-264.

(17) Morris, K. F.; Johnson, C. S., Jr. J. Am . Chem . Soc. 1 9 9 2 , 114, 3139-3141.(18) Morris, K. F.; Johnson, C. S., Jr. J. Am . Chem . Soc. 1 9 9 3 , 115, 4291-4299.(19) Morris, K. F.; Stilbs, P.; Johnson, C. S., Jr. Anal. Chem . 1 9 9 4 , 66, 211-

215.(20) Chen, A.; Wu, D.; Johnson, C. S., Jr. J. Phys. Chem . 1 9 9 5 , 99, 828-834.(21) Jayawickrama, D. A.; Larive, C. K.; McCord, E. F.; Roe, D. C. Magn. Reson.

Chem . 1 9 9 8 , 36, 755-760.(22) Dixon, A. M.; Larive, C. K. Anal. Chem . 1 9 9 7 , 69, 2122-2128.(23) Bates, R. G. Determination of pH: Theory and Practice; Wiley: New York,

1964; pp 219-220.

Figure 1. One-dimensional 1H NMR spectra of the Suwannee River(a) fulvic acid and (b) humic acid.

I ) Io exp[-D(! - !/ 3 - "/ 2)K2] (1)

K ) G#! (2)

5316 Analytical Chemistry, Vol. 71, No. 23, December 1, 1999

Two-Dimens ional CONTIN Analyses . A complimentaryCONTIN analysis was also carried out to generate 2D DOSYspectra for each of the samples. A DOSY spectrum displays 1Hchemical shifts along one axis and diffusion coefficients along theother, thus resolving the individual components in a complexmixture on the basis of their overall molecular size. An exampleDOSY spectrum for the SRFA sample is shown in Figure 4. Thefull 2D DOSY spectrum complements the information obtainedfrom the one-dimensional diffusion distributions discussed previ-ously. By performing the CONTIN analysis at each chemical shiftin the 1H spectrum, subtle differences in the diffusion rate atdifferent chemical shifts can be readily visualized. For example,the SRFADOSYspectrum shows the resonances in proton regions3 and 4 pulled down to slightly lower diffusion coefficient valuesthan those of regions 1 and 2. This effect was also seen in the 1Ddiffusion distributions.Furthermore, since the 2D DOSYanalyses allow small, rapidly

diffusing species to be readily identified, it is preferable to carryout the full two-dimensional analysis before the one-dimensional

integrations. In this manner, the 2D spectrum can be closelyinspected to ensure that no small-molecule impurities are presentin the spectral regions to be analyzed. Integrals can then becalculated and used to generate the 1D diffusion distributions.This ability to see “at a glance” all of the different components ina complex mixture is the main advantage of the 2D DOSY analy-sis. Finally, we note that in the 2D spectrum the placement ofthe contour level threshold does distort somewhat the relativewidths of the distributions at different chemical shifts. There-fore, quantitative comparisons of the distribution width for dif-ferent spectral regions should be made only with the 1D CONTINplots.Interpretation of CONTIN Results . Molecular weight de-

terminations of humic materials also show evidence of polydis-persity, and the average molecular weight measured for humicsubstances is governed in part by the analytical technique used.For example, methods based on measurement of colligativeproperties yield a number-average molecular weight, MN, whichemphasizes the lower molecular weight components; whiledynamic light scattering produces weight average molecularweights, MW, which emphasize the higher molecular weightspecies.37 Values of MN and MW for several of the humicsubstances examined in this work have been previously re-ported: SRHA, 1580 and 4390;35 SRFA, 1150 and 1910;35 andNAHA, 2272 and 3264,8 respectively. The ratio MW/MN is also awell-accepted measure of the polydispersity of the sample.33,35,38Using an analogous argument, we examined the use of the ratioDW/ DN as an indication of the polydispersity of the humic samples.As shown in Table 2, the ratio DW/ DN was greater than 1 for allsamples studied. This result suggests that on average the humicand fulvic samples are made up of a larger fraction of small, rapidlydiffusing molecules. Although they are in relatively good agree-ment, the DW/ DN values were less than the reported MW/MN

values for similar humic substances, which ranged from 1.66 to5.89.2,35 The lower ratios of DW/ DN may reflect the lack ofsensitivity of diffusion coefficients to molecular weight, scalingroughly as the cube root of the molecular weight. Furthermore,although DW and DN are conceptually similar to MW and MN, theyare determined by fundamentally different measurements. Thus,the DW/ DN ratio can be at least a qualitative, and at best asemiquantitative, indication of the polydispersity of the sample,but should not be used as a quantitative measure of polydis-persity.There are several important trends in the data presented in

Table 2. First, the SRFA DN values agree reasonably well withthose reported by a linear regression analysis.22 This is expectedbecause DN values are weighted by the faster diffusing compo-nents for this sample. The DP values, however, paint a differentpicture. These values tend to cluster in two groups of about 3.6! 10-10 and 2.8 ! 10-10 m2 s-1. This difference is significant andis corroborated by the 2D DOSY plot for the same sample; seeFigure 4. Furthermore, all DN, DW, and DP values for the SRFAare greater than the corresponding values of the SRHA. This resultis expected, because the HA fraction is normally larger with

(36) Lead, J. R.; Wilkinson, K. J.; Balnois, E.; Cutak, B. J.; Larive, C. K.; Assemi,S.; Beckett, R. Unpublished work; University of Geneva, Geneva, Switzerland;University of Kansas, Lawrence, KS.; and Monash University, Clayton,Victoria, Australia, 1998.

(37) Wershaw, R. L.; Aiken, G. R. In Humic Substances in Soil, Sediment, andWater: Geochemistry, Isolation, and Characterization; Aiken, G. R., McKnight,D. M., Wershaw, R. L., MacCarthy, P., Eds.; John Wiley & Sons: New York,1985; Chapter 19.

(38) Posner, A. M.; Creeth, J. M. J. Soil Sci. 1 9 7 2 , 23, 333-341.

Figure 3. Normalized CONTIN diffusion coefficient distributions forregion 2 (a) Suwannee River fulvic acid, pD 4.0, (b) Suwannee Riverhumic acid, pD 6.5, (c) Nordic Aquatic humic acid, pD 6.3, and (d)Peat humic acid, pD 8.0.

Figure 4. Two-dimensional DOSY spectrum of the Suwannee Riverfulvic acid. The narrow HOD distribution is somewhat oversmoothedby the CONTIN analysis.

Analytical Chemistry, Vol. 71, No. 23, December 1, 1999 5319

KF Morris and BJ Cutak and AM Dixon and CK Larive. Anal Chem (1999) 71 pp. 5315-21

In 1999, Cynthia Larive working on humic acid, defines Dn and Dw.But she fails in relating them to measurement



A more complex example

withSandrine Denis-Quanquin Cyrille Monnereau



PDI = 1.10

Determination of Polydispersity Index by DOSY-NMR: application to polycationic polymers

S. Denis-Quanquina, C. Monnereaua, V. Appukuttana, J. Vievilleb and M.A. Delsucb

a UMR 5182, Laboratoire de Chimie, ENS Lyon (ENS/CNRS/UCBL),46 allée d’Italie, 69364 Lyon7 b NMRTEC, Bioparc, boulevard S. Brant, 67400 Illkirch, France

As chain polymerisation methods suffer from a low control over chain elongation they lead to a mixture of polymers of various length. In the case of a linear homopolymer, the polymer and the mixture’s homogeneity are described by the average molecular chain length and the mass dispersion around the average mass. Polydispersity is expressed by the polydispersity index (PDI) which is the ratio of the mass average molar mass to the number averaged molar mass (Mw/Mn).

with and

E.g. homopolymer mixture with a unit of mass= 4,5

Mn= (1*67,5+2*54+1*40,5)/4 ! Mn= 54 Mw= (1*67,52+2*542+1*40,52)/(1*67,5+2*54+1*40,5) ! Mw=55,69

PDI= 55,69/54 ! PDI= 1,03

!

PDI =Mw

Mn

The average chain length is given by the ratio of the integrals of extremities signals to main chain signals from a 1H spectrum. The PDI is determined by DOSY1: for a linear polymer the diffusion coefficient and the molecular mass are proportional

with dF the fractal dimension i.e. a measure of the way the chain extends into the solvent.The PDI may then be expressed as a ratio of diffusion coefficients

!

M " D#dF

!

PDI =Dw

Dn

"

#

$ $

%

&

' '

(dF

Notion of polydispersity index (PDI) NMR determination of PDI

NMR signals reflect a statistical average on the sample: - signals from the extremities are weighted by the number of molecules (whatever the chain lenght, ALWAYS 2 extremities) -  signals from the whole chain are weighted by the mass of the molecules (the longer the chain, the stronger the signals)

Why a different diffusion coefficient for the extremities?

Coupled poly(hydroxyl)acrylate

* * * 1H spectrum shows an integration default of the aromatic signals while DOSY shows a mixture of the expected polymer, the uncoupled molecule and another polymer a little heavier. The coupling is thus estimated to 25%.

N

N

N

HN

O

S

S

O

HO

SS

OH

O

OO

OH

O

O

P

O

OH

OHn

Example: poly(hydroxyl)acrylate

n (average) = 22 from 1H 1D spectrum PDI=1,27 from GPC PDI=1,23 from DOSY

* * *

log(

D)

Br

OO

OH

O

O

P

O

OH

OHn

Application: polycationic polyacrylates

Br

OO

OH

O

On

Br

OO

N+

O

On

N

Br-

Br

OO

N+

O

On

Br-

Br

OO

P+

O

On

Br-

NMR vs GPC PDI=1,12 from GPC PDI=1,11 from DOSY

The following cationic polymers cannot be analysed by GPC.

PDI=1,01 from DOSY

Partial hydrolysis of the chains (CH2O and CH2OH signals *)

* *

PDI=1,04 from DOSY

Sharp signals can be assigned to hydrolysed pyridine OH

N+

Br-

PDI cannot be measured for there is no isolated signal from the extremities.

NMR analysis GPC analysis

average chain length

Integration of 1D proton signals

- quantitative conditions - all signals should be sharp enough to be integrated

Size exclusion chromatography

followed by 3 different detection

- M is estimated from the measured gyration radius Rg - calibration of the system is needed - no interactions between the molecules and between the system and the molecules - purity - homopolymer

PDI Mn Mw

Integration of DOSY signals

- M is estimated from the measured gyration radius Rg - Rg depends on dF: ! solvent - homopolymer

i (nb of units) M (mass of a chain) n (nb of chains) 15 67,5 1 12 54 2 9 40,5 1

!

Mn =niMii"nii"

!

Mw =miMii"mii"

=niMi

2i"niMii"

Signals from the extremities show a slightly higher diffusion coefficient...

Comparison of the two methods shows less sources of error for the DOSY NMR analysis. Furthermore, ionic polymers cannot be analysed by GPC as they may interact with the system, whereas this is not an issue with NMR.

1. Viéville J., Tanty M. and Delsuc M.A., J. Magn. Reson., 212, 169-173 (2011)

Poster 5



pseudodesmin-A• pseudodesmins A is a lipodepsipeptide isolated from

Pseudomonas bacteria collected from the mucus layer in the skin of the black belly salamander. It show moderate antibacterial activity against Gram positive bacteria.

withBruno KiefferJosé MartinsDavy SinnaeveFX Coudert



semi-log plot

x-y plot

diffusion in CHCl3



oligomerization

M + M � M2

M + M2 � M3

M + M3 � M4

...

fitting the experiment requires :• computing Dn : diffusion coefficient of Mn• modeling the oligomerization equilibrium• computing Dmix from all Dn

⇒ Dexp = f(conc.)



• Master equation• Augé et al. NMR Measure of Translational Diffusion and Fractal

Dimension. Application to Molecular Mass Measurement. J Phys Chem B (2009) 113 (7) pp. 1914-1918

• fractal dimension

computing Dn

α =1

dF

Dn

D1= n−α



modeling the oligomerization equilibrium

• assuming K independent on n

M + Mn � Mn+1

Kn =[Mn+1][M ][Mn]

M + M � M2

M + M2 � M3

M + M3 � M4

...

[Mn] = 21−n

�1 + 2MoK −

√1 + 4MoK

MoK

�−1+n �1− 1 + 2MoK −

√1 + 4MoK

2MoK

�



Summary of simple fits

Performed only on diffusion data provided by MAD ; D = f(C)

0.1 1 10C (mmol/L)

100

200

300

400

500

D (

µm

2/s

)

To relate diffusion to concentrations, we use:

!

D"

n2cnDn

n

#

n2cn

n

#"

n2+$cn

n

#

n2cn

n

#

with cn the concentration and ! between -1 and -1/3 (-1 = rod; -1/2 = random walk; -1/3 = sphere)

Model #1: simple equilibrium M + Mn-1 ! Mn, constant K

This model has an analytical expression for cn, and has a complicated by analytical expression for

D(C):

D = Dmax

PolyLog�−2− α, 1+2CK−

√1+4CK

2CK

�

CK√

1 + 4CK

Using this functional form to fit the experimental data gives poor results (graph of D vs C):

0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

150

200

250

300

350

400

450

(blue: ! = –1; green: ! = –1/2; black: ! = -1/3)

Summary of simple fits

Performed only on diffusion data provided by MAD ; D = f(C)

0.1 1 10C (mmol/L)

100

200

300

400

500

D (

µm

2/s

)

To relate diffusion to concentrations, we use:

!

D"

n2cnDn

n

#

n2cn

n

#"

n2+$cn

n

#

n2cn

n

#

with cn the concentration and ! between -1 and -1/3 (-1 = rod; -1/2 = random walk; -1/3 = sphere)

Model #1: simple equilibrium M + Mn-1 ! Mn, constant K

This model has an analytical expression for cn, and has a complicated by analytical expression for

D(C):

D = Dmax

PolyLog�−2− α, 1+2CK−

√1+4CK

2CK

�

CK√

1 + 4CK

Using this functional form to fit the experimental data gives poor results (graph of D vs C):

0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

150

200

250

300

350

400

450

(blue: ! = –1; green: ! = –1/2; black: ! = -1/3)

modeling the oligomerization equilibrium (2)



But, if we remove the first 5 points, which may belong to a different regime, we get a much better

fit for ! = –1:

0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

150

200

250

300

350

400

450

! = –1, Dmax = 347 "m2/s, K = 0.109 L/mmol

The two other values of ! are clearly not giving decent fits:

0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

150

200

250

300

350

400

450

If we try to also fit the value of !, along with Dmax and K, we get:

0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

150

200

250

300

350

400

450

! = –0.85 = –1/1.17, Dmax = 356 "m2/s, K = 0.155 L/mmol

If we remove the first 5 points, which may belong to a different regime, we get a much better fit

modeling the oligomerization equilibrium



1

Insight into peptide self-assembly from anisotropic rotational diffusion derived from 13C NMR relaxation

Davy Sinnaeve,*† Marc-André Delsuc,‡ José C. Martins† and Bruno Kieffer*‡

† NMR and Structure Analysis Unit, Ghent University, Krijgslaan 281 S4, B-9000 Gent, Belgium ‡ IGBMC, 1 rue Laurent Fries, BP 10142, 67404 Illkirch, France

ABSTRACT: The NMR heteronuclear relaxation rate’s dependency on the anisotropy of rotational diffusion motions can be exploited to investigate the supramolecular organization that results from reversible peptide self-assembly in solution. The measurement of longitudinal (R1) and transverse (R2)

13C relaxation rates for several peptide concentrations provides insight both into the orientation of individual molecules within the supramolecular assembly and its growth. The methodology was applied on the pore forming cyclic lipodepsipeptide pseudodesmin A, which reversibly assembles into supramolecular structures of indefinite size in non-polar organic solvents. The information extracted by correlating the 13C R1 and R2 relaxation rates ! obtained at natural abundance and at multiple peptide concentrations ! with the orientation of the C!H bonds in the monomer conformation demonstrates the existence of an axially symmetric assembly that exhibits a unidimensional growth upon increased peptide concentrations. The orientation of the pseudodesmin A peptide within this assembly could be determined accurately and is consistent with the suggested model for the pore forming function and the peptide-peptide interactions within the oligomer.

Introduction

In nature, molecular self-assembly is a ubiquitous process wherein intermolecular forces drive individual molecules to organize themselves spontaneously into supramolecular structures1,2. The occurrence and functional relevance of self-assembly in many biological systems has received wide-spread attention and continues to inspire many new strategies and technologies in chemical synthesis, nanotechnology, polymer science, materials and engineering research and drug delivery2-4. Compared to classical macromolecular polymers, materials based on self-assembly, exploit the dynamic and reversible nature of supramolecular polymerization5.

The self-assembly of peptides (natural, designed or peptide analogues) or proteins into larger, structured aggregates also receives increased attention due to its relation with several neurodegenerative amyloid diseases, such as Alzheimer3. Other examples include the design of peptide nanotubes3,6-9, hydrogel materials4,10 and electronic conducting materials11,12. Molecular self-assembly is also essential for the biological activity of various classes of natural antimicrobial peptides, where individual molecules assemble into larger, often pore-like structures within the non-polar environment of the cellular membrane13. To understand the mechanism that governs their self-assembly and ultimately their biological function, it is important to gain a detailed insight of the supramolecular structure at a molecular level. This is often a challenging task, requiring a multidisciplinary approach. An example of such a successful study is the self-assembly of the octapeptide lanreotide14,15, where a combination of FT-IR, EM, SAXS and WAXS among others was used to elucidate the mechanism and hierarchy of the supramolecular structures. Additional

approaches and techniques that allow detailed information regarding the structure and dynamics of the individual building blocks and their mutual interactions are therefore highly desirable.

Figure 1. (a) Acetonitrile solution conformation of pseudodesmin A, showing only the backbone atoms. (b) Model for the self-assembly of pseudodesmin A as proposed previously16, where " monomer units first assemble to the disc-like #-state before these states stack upon each other to supramolecular structures of indefinite size.

This study investigates the self-assembly of pseudodesmin A16, a cyclic lipodepsipeptide (CLP) with potential antimicrobial activity17 and belonging to the viscosin

Page 1 of 16

ACS Paragon Plus Environment

Journal of the American Chemical Society

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960



fitting results

best with 3 parameters

best with 5 parameters



determining ß

• green and red curve are not significantly different yet they differ only on the fit at high concentration



1

Insight into peptide self-assembly from anisotropic rotational diffusion derived from 13C NMR relaxation

Davy Sinnaeve,*† Marc-André Delsuc,‡ José C. Martins† and Bruno Kieffer*‡

† NMR and Structure Analysis Unit, Ghent University, Krijgslaan 281 S4, B-9000 Gent, Belgium ‡ IGBMC, 1 rue Laurent Fries, BP 10142, 67404 Illkirch, France

ABSTRACT: The NMR heteronuclear relaxation rate’s dependency on the anisotropy of rotational diffusion motions can be exploited to investigate the supramolecular organization that results from reversible peptide self-assembly in solution. The measurement of longitudinal (R1) and transverse (R2)

13C relaxation rates for several peptide concentrations provides insight both into the orientation of individual molecules within the supramolecular assembly and its growth. The methodology was applied on the pore forming cyclic lipodepsipeptide pseudodesmin A, which reversibly assembles into supramolecular structures of indefinite size in non-polar organic solvents. The information extracted by correlating the 13C R1 and R2 relaxation rates ! obtained at natural abundance and at multiple peptide concentrations ! with the orientation of the C!H bonds in the monomer conformation demonstrates the existence of an axially symmetric assembly that exhibits a unidimensional growth upon increased peptide concentrations. The orientation of the pseudodesmin A peptide within this assembly could be determined accurately and is consistent with the suggested model for the pore forming function and the peptide-peptide interactions within the oligomer.

Introduction

In nature, molecular self-assembly is a ubiquitous process wherein intermolecular forces drive individual molecules to organize themselves spontaneously into supramolecular structures1,2. The occurrence and functional relevance of self-assembly in many biological systems has received wide-spread attention and continues to inspire many new strategies and technologies in chemical synthesis, nanotechnology, polymer science, materials and engineering research and drug delivery2-4. Compared to classical macromolecular polymers, materials based on self-assembly, exploit the dynamic and reversible nature of supramolecular polymerization5.

The self-assembly of peptides (natural, designed or peptide analogues) or proteins into larger, structured aggregates also receives increased attention due to its relation with several neurodegenerative amyloid diseases, such as Alzheimer3. Other examples include the design of peptide nanotubes3,6-9, hydrogel materials4,10 and electronic conducting materials11,12. Molecular self-assembly is also essential for the biological activity of various classes of natural antimicrobial peptides, where individual molecules assemble into larger, often pore-like structures within the non-polar environment of the cellular membrane13. To understand the mechanism that governs their self-assembly and ultimately their biological function, it is important to gain a detailed insight of the supramolecular structure at a molecular level. This is often a challenging task, requiring a multidisciplinary approach. An example of such a successful study is the self-assembly of the octapeptide lanreotide14,15, where a combination of FT-IR, EM, SAXS and WAXS among others was used to elucidate the mechanism and hierarchy of the supramolecular structures. Additional

approaches and techniques that allow detailed information regarding the structure and dynamics of the individual building blocks and their mutual interactions are therefore highly desirable.

Figure 1. (a) Acetonitrile solution conformation of pseudodesmin A, showing only the backbone atoms. (b) Model for the self-assembly of pseudodesmin A as proposed previously16, where " monomer units first assemble to the disc-like #-state before these states stack upon each other to supramolecular structures of indefinite size.

This study investigates the self-assembly of pseudodesmin A16, a cyclic lipodepsipeptide (CLP) with potential antimicrobial activity17 and belonging to the viscosin

Page 1 of 16



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

D. Sinnaeve, M-A.Delsuc, J.C. Martins and B.Kieffer - Chemical Science (2012) vol. in-press pp. 1-9



Relaxation measure

2

group of CLPs18,19 produced by Pseudomonas bacteria. It consists of a nonapeptide part (L-Leu1-D-Gln2-D-aThr3-D-Val4-D-Leu5-D-Ser6-L-Leu7-D-Ser8-L-Ile9) that forms a left-handed !-helix spanning five to six residues, followed by a three-residue loop that covalently connects the end of the helix with its middle. The N-terminal end of the oligopeptide is bound to a 3-hydroxydecanoic acid (HDA) moiety (Figure 1a). Overall, the conformation is amphipathic and found to be quite rigid in solution16. Besides their antagonistic function, the diverse Pseudomonas produced CLPs play a role in various bacterial functions such as biofilm formation, cell motility and plant pathogenesis virulence20.

An often proposed mechanism to account for their physiological effects is the formation of pores in cellular membranes, allowing passive influx and efflux of ions to the cell. In this light, pseudodesmin A has been found to undergo reversible, indefinite self-association when dissolved in non-polar solvents such as chloroform. This self-association occurs fast on the NMR frequency time-scale and was previously studied using translational diffusion NMR studies, which showed that the oligomerization degree can be controlled by varying the peptide concentration or the solvent polarity16. Based on these findings, the solution conformation of the monomer and the identification of intermolecular rOes, a model was proposed for the structure of the supramolecular assembly16. This model assumes two levels of interaction, as illustrated in Figure 1b. In a first step, the peptide monomers aggregate through their hydrophilic side chains, minimizing their interactions with the non-polar environment. This nucleation step leads to the formation of a disc-like structure, here referred to as the "-state. Second, an interaction at the level of the oligopeptide main chain between the electrostatic oppositely charged ends of the molecule triggers the stacking of "-states upon each other. This results in populations of discrete and cylindrically shaped supramolecular structures that grow in length as the degree of self-association increases. Within a cellular membrane, these structures could be able to function as transmembrane ion-pores, as the hydrophilic inside would facilitate the passive transport of ions and their maximum size would be restricted by the dimensions of the phospholipid bilayer. In an organic solvent however, the structures are able to expand without limit, creating a concentration dependent distribution of oligomer sizes.

It is the suspected cylindrical and thus anisotropic shape associated with the self-assembly model of pseudodesmin A that led to the application of heteronuclear relaxation measurements to extract structural information about the supramolecular assembly. Analysis of heteronuclear relaxation rates has proven to be an invaluable tool to provide accurate insights into the anisotropic nature of rotational diffusion motions in proteins21-25. Measurements of 15N relaxation rates for backbone amide nitrogens, whose relaxation is dominated by the dipolar interaction with its bound amide proton, allows the components of the rotational diffusion tensor to be defined, even when only small differences exist between the different rotational diffusion coefficients. In the case of axially symmetric objects, such as the suspected cylindrically shaped pseudodesmin A assembly, the rotational diffusion is described by two of these diffusion coefficients, D|| and D#, whose ratio determines the degree of anisotropy (Figure 2).

The heteronuclear relaxation rates R1 and R2 are not only dependent on the values of these coefficients, but also on the orientation of the N$H bond relative to the main axis of the rotational diffusion tensor frame, represented here by the angle %. Therefore, defining the rotational diffusion tensor frame through the experimental relaxation rates delivers structural information by revealing the orientation of individual N$H vectors relative to the molecular frame.

Here, 13C relaxation rates measured at natural abundance are used in a similar fashion to define the components of the rotational diffusion tensor of the pseudodesmin A assemblies. By increasing the peptide concentration and thus shifting the oligomer size distribution, it is shown that the orientation of the tensor remains constant so that the evolution of the average rotational diffusion coefficients can be evaluated. By using a cylindrical model, the average dimensions of the assemblies were calculated and found to be consistent with the proposed unidirectional self-assembly model. Moreover, the definition of the rotational diffusion tensor frame identifies the orientation of the monomer in the assembly and thus the direction of growth. This study therefore significantly contributes to the structure-function relationship of pseudodesmin A, while simultaneously illustrating the potential of heteronuclear relaxation measurements for studying self-assembly.

Figure 2. (a) Rotational diffusion tensor frame of axial anisotropic objects, with D|| and D# the diffusion coefficients for rotation around respectively the symmetric axis and any axes perpendicular to the symmetric axis. Heteronuclear relaxation rates are dependent on the angle ! between the symmetric axis of this frame and the bond between the heteronucleus and the directly attached proton nucleus. (b) Dependence of 13C R2/R1 on the angle !, simulated for isotropic (D|| = D# = 40 µs-1) (black), prolate anisotropic (D|| = 50 µs-1, D# = 27 µs-1) red) and oblate anisotropic objects (D|| = 29 µs-1, D# = 36 µs-1) (blue).

Experimental section

Pseudodesmin A was obtained as described earlier17. 13C relaxation experiments (R1 and R2) in chloroform-d solution were performed at natural abundance and four separate concentrations as determined by the ERETIC26 or PULCON27 methods: 0.5 mM, 6.6 mM, 16.4 mM and 44.8 mM. A layer of water (H2O) was placed on top of the chloroform solution in each sample to seal the solution and avoid evaporation

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• 13C T1 and T2

• on a rigid object, relaxation depend on bond orientation

• in particular T1 / T2 has a robust dependance on orientation.



Relaxation measure

3

(ELISE)28. Due to the limited material available, the 44.8 mM sample was prepared in a 3 mm tube but measured using a 5 mm probe head. The measurements at 0.5 mM were performed on a Bruker 16.4 T Avance III spectrometer equipped with a 5mm 1H-13C-15N TCI cryoprobe with Z-gradients, while those at higher concentration were performed on a Bruker 16.4 T Avance II spectrometer equipped with a 1H-13C-15N TXI-Z probe. In addition, 13C R2 relaxation measurements were repeated on the 16.4 mM sample with a Bruker 11.7 T DRX spectrometer equipped with a 1H-13C-15N TXI-Z probe. The sample temperature was set at 283.0 K throughout. Pulse sequences used were similar to those described for 15N relaxation experiments29,30. All spectra were recorded with a spectral width of 4 ppm in the direct 1H dimension and 24 ppm in the indirect 13C dimension. The 0.5 mM, 6.6 mM and 44.8 mM samples were sampled by 1024 complex time domain points in the direct dimension and 64 complex time domain points in the indirect dimension. The 16.4 mM sample was sampled by 2048 complex time domain points in the direct dimension at both field strengths, while the number of indirect complex time domain points was 64 in the 16.4 T experiments and 112 in the 11.7 T experiments. The delay for 1H-13C polarization transfer was set to 2.94 ms, the interscan delay was 2 s and the delay between the 180° 13C pulses in the CPMG sequences was 900 µs. Prior to Fourier transform, only the first 512 complex time domain points in the direct dimension were retained to increase the signal-to-noise ratio. The FIDs were multiplied with a squared cosine bell window function in both dimensions. They were subsequently zero filled to a real data matrix size of 1024!1024, 2048!256, 1024!512, 2048!512 and 2048!1024 for respectively the measurements at 0.5 mM, 6.6 mM, 44.8 mM, 16.4 mM at 16.4 T and 16.4 mM at 11.7 T. The inversion recovery delay during the R1 measurements was varied from 8.36 ms to 1.045 s, 12.6 ms to 1.68 s, from 12.6 ms to 2.51 s and from 12.6 ms to 1.68 s for respectively the 0.5 mM, 6.6 mM, 44.8 mM and 16.4 mM samples at 16.4 T. The total CPMG time during the R2 measurements was varied from 0 ms to 236.40 ms, 5.92 ms to 118.3 ms, 0 ms to 59.0 ms, 5.91 ms to 65.05 ms and 5.85 ms to 64.4 ms for respectively 6.6 mM, 44.8 mM, 16.4 mM at 16.4 T and 16.4 mM at 11.7 T. The sampling always occurred randomly over at least 14 experiments, including at least one repeated experiment. The R1 and R2 relaxation rates were fitted to the obtained data point intensities of each cross-peak, while a Monte Carlo error analysis was performed using 200 simulations to obtain 95% confidence intervals31, both using in-house MatLab 7.5 routines (2007, The MathWorks Inc.).

The simulation of the 13C R1 and R2 values from rotational diffusion coefficients during the anisotropy analysis were calculated using the Woessner model for the spectral density function24,32 and expressions and parameters for the relaxation rates as described by Tjandra et al

33. The grid search was performed by placing the monomer solution structure within an axially symmetric rotational diffusion tensor frame and subsequently rotating it to sample all possible spherical orientations. At each orientation, the angles " between the main axis of the diffusion tensor frame and the C#H bond vectors were calculated. These were then used to fit the rotational diffusion coefficients D|| and D$ to the experimental

R2/R1 values at each concentration. Leu1 C% and HDA C& were excluded from the fitting, as these nuclei lie close to the more flexible, exocyclic N-terminal end of the peptide. Even if within the supramolecular assembly this part of the oligopeptide would turn out to adopt a rigid structure, the solution structure would not necessarily represent a correct orientation of their C#H bonds within this assembly, as the precise conformation that was adopted at this position remains elusive16. The Thr3 C& nucleus was also excluded for the 0.5 mM data as it turned out to be a strong outlier. The sum-total E of the sum of squared differences at each concentration of these fittings, divided by the number of data points N (35) minus the number n of estimated parameters (10), was calculated at each orientation and used to evaluate the optimal orientation of the pseudodesmin A monomer within the supramolecular assembly. Further depiction concerning the anisotropy analysis and the calculation of the cylinder dimensions are presented in the supporting information.

Figure 3. Experimental R2 values for several 13C nuclei within pseudodesmin A, measured at a magnetic field strength of 16.4 T and a concentration in chloroform of 0.5 mM (orange), 6.6 mM (black), 16.4 mM (red) and 44.8 mM (green), and at a magnetic field strength of 11.7 T and a concentration of 16.4 mM (blue). Error bars represent 95% confidence intervals.

Results

Relaxation rates

The experimental 13C R2 relaxation rates, measured at four concentrations in chloroform solution at 16.4 T, are shown in Figure 3. It is clear that R2 is strongly concentration dependent, increasing by a factor of 2.9 to 4.7 when values from the lowest and the highest concentrations are compared. Since for molecules in the spin-diffusion limit R2 is proportional to the correlation time constant, this reflects the strong increase in average size of the assemblies. At 16.4 mM, the R2 values were also measured at a lower magnetic field strength (11.7 T) to assess whether any contribution from exchange processes is present. Since it has been established that the self-assembly is fast on the frequency time scale16, the apparent R2 should decrease with decreasing magnetic field if this exchange would contribute to the line-width34. No significant difference was found at 11.7 T with the values measured at 16.4 T, except for Leu1 C%. The R2 of this nucleus appears to increase with the magnetic field strength, in any case ruling out exchange to be the cause of its apparent magnetic field dependence. A second observation is that at each concentration significant variation can be observed over the different 13C nuclei. Moreover, these variations are

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3

(ELISE)28. Due to the limited material available, the 44.8 mM sample was prepared in a 3 mm tube but measured using a 5 mm probe head. The measurements at 0.5 mM were performed on a Bruker 16.4 T Avance III spectrometer equipped with a 5mm 1H-13C-15N TCI cryoprobe with Z-gradients, while those at higher concentration were performed on a Bruker 16.4 T Avance II spectrometer equipped with a 1H-13C-15N TXI-Z probe. In addition, 13C R2 relaxation measurements were repeated on the 16.4 mM sample with a Bruker 11.7 T DRX spectrometer equipped with a 1H-13C-15N TXI-Z probe. The sample temperature was set at 283.0 K throughout. Pulse sequences used were similar to those described for 15N relaxation experiments29,30. All spectra were recorded with a spectral width of 4 ppm in the direct 1H dimension and 24 ppm in the indirect 13C dimension. The 0.5 mM, 6.6 mM and 44.8 mM samples were sampled by 1024 complex time domain points in the direct dimension and 64 complex time domain points in the indirect dimension. The 16.4 mM sample was sampled by 2048 complex time domain points in the direct dimension at both field strengths, while the number of indirect complex time domain points was 64 in the 16.4 T experiments and 112 in the 11.7 T experiments. The delay for 1H-13C polarization transfer was set to 2.94 ms, the interscan delay was 2 s and the delay between the 180° 13C pulses in the CPMG sequences was 900 µs. Prior to Fourier transform, only the first 512 complex time domain points in the direct dimension were retained to increase the signal-to-noise ratio. The FIDs were multiplied with a squared cosine bell window function in both dimensions. They were subsequently zero filled to a real data matrix size of 1024!1024, 2048!256, 1024!512, 2048!512 and 2048!1024 for respectively the measurements at 0.5 mM, 6.6 mM, 44.8 mM, 16.4 mM at 16.4 T and 16.4 mM at 11.7 T. The inversion recovery delay during the R1 measurements was varied from 8.36 ms to 1.045 s, 12.6 ms to 1.68 s, from 12.6 ms to 2.51 s and from 12.6 ms to 1.68 s for respectively the 0.5 mM, 6.6 mM, 44.8 mM and 16.4 mM samples at 16.4 T. The total CPMG time during the R2 measurements was varied from 0 ms to 236.40 ms, 5.92 ms to 118.3 ms, 0 ms to 59.0 ms, 5.91 ms to 65.05 ms and 5.85 ms to 64.4 ms for respectively 6.6 mM, 44.8 mM, 16.4 mM at 16.4 T and 16.4 mM at 11.7 T. The sampling always occurred randomly over at least 14 experiments, including at least one repeated experiment. The R1 and R2 relaxation rates were fitted to the obtained data point intensities of each cross-peak, while a Monte Carlo error analysis was performed using 200 simulations to obtain 95% confidence intervals31, both using in-house MatLab 7.5 routines (2007, The MathWorks Inc.).

The simulation of the 13C R1 and R2 values from rotational diffusion coefficients during the anisotropy analysis were calculated using the Woessner model for the spectral density function24,32 and expressions and parameters for the relaxation rates as described by Tjandra et al

33. The grid search was performed by placing the monomer solution structure within an axially symmetric rotational diffusion tensor frame and subsequently rotating it to sample all possible spherical orientations. At each orientation, the angles " between the main axis of the diffusion tensor frame and the C#H bond vectors were calculated. These were then used to fit the rotational diffusion coefficients D|| and D$ to the experimental

R2/R1 values at each concentration. Leu1 C% and HDA C& were excluded from the fitting, as these nuclei lie close to the more flexible, exocyclic N-terminal end of the peptide. Even if within the supramolecular assembly this part of the oligopeptide would turn out to adopt a rigid structure, the solution structure would not necessarily represent a correct orientation of their C#H bonds within this assembly, as the precise conformation that was adopted at this position remains elusive16. The Thr3 C& nucleus was also excluded for the 0.5 mM data as it turned out to be a strong outlier. The sum-total E of the sum of squared differences at each concentration of these fittings, divided by the number of data points N (35) minus the number n of estimated parameters (10), was calculated at each orientation and used to evaluate the optimal orientation of the pseudodesmin A monomer within the supramolecular assembly. Further depiction concerning the anisotropy analysis and the calculation of the cylinder dimensions are presented in the supporting information.

Figure 3. Experimental R2 values for several 13C nuclei within pseudodesmin A, measured at a magnetic field strength of 16.4 T and a concentration in chloroform of 0.5 mM (orange), 6.6 mM (black), 16.4 mM (red) and 44.8 mM (green), and at a magnetic field strength of 11.7 T and a concentration of 16.4 mM (blue). Error bars represent 95% confidence intervals.

Results

Relaxation rates

The experimental 13C R2 relaxation rates, measured at four concentrations in chloroform solution at 16.4 T, are shown in Figure 3. It is clear that R2 is strongly concentration dependent, increasing by a factor of 2.9 to 4.7 when values from the lowest and the highest concentrations are compared. Since for molecules in the spin-diffusion limit R2 is proportional to the correlation time constant, this reflects the strong increase in average size of the assemblies. At 16.4 mM, the R2 values were also measured at a lower magnetic field strength (11.7 T) to assess whether any contribution from exchange processes is present. Since it has been established that the self-assembly is fast on the frequency time scale16, the apparent R2 should decrease with decreasing magnetic field if this exchange would contribute to the line-width34. No significant difference was found at 11.7 T with the values measured at 16.4 T, except for Leu1 C%. The R2 of this nucleus appears to increase with the magnetic field strength, in any case ruling out exchange to be the cause of its apparent magnetic field dependence. A second observation is that at each concentration significant variation can be observed over the different 13C nuclei. Moreover, these variations are

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orienting the peptide in the diffusion frame

5

Figure 4. (a) The E/(N ! n) value of the grid search projected upon the surface of a sphere. (b) Pseudodesmin A monomer conformation with all C!H bonds exemplified, with the relative orientation to the rotational diffusion tensor frame corresponding to the orientation with the lowest E/(N ! n) value. (c) Experimental 13C R2/R1 values with 95% error bars at 16.4 T at 0.5 mM (orange), 6.6 mM (black), 16.4 mM (red) and 44.8 mM (green). Data points represented as a triangle were not used in the grid search. The R2/R1 values are plotted against the ! angles of the corresponding C!H bonds within the orientation with the lowest E/(N ! n) value.

single supramolecular assembly of a well-defined size, as they are obtained from relaxation rates that result from an average over a distribution of oligomer sizes.

The calculated lengths increase with concentration, varying from 32.6 Å to 60.9 Å between 0.5 mM and 44.8 mM. However, the calculated diameter remains constant at about

26.4 Å, except at the lowest concentration, where it is somewhat reduced to 21.9 Å. This observed asymptotic behavior of the diameter value supports the proposed supramolecular model of a self-assembly occurring along a single direction aligned with the main axis of the diffusion tensor. Indeed, the increased contribution of higher oligomer

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5

Figure 4. (a) The E/(N ! n) value of the grid search projected upon the surface of a sphere. (b) Pseudodesmin A monomer conformation with all C!H bonds exemplified, with the relative orientation to the rotational diffusion tensor frame corresponding to the orientation with the lowest E/(N ! n) value. (c) Experimental 13C R2/R1 values with 95% error bars at 16.4 T at 0.5 mM (orange), 6.6 mM (black), 16.4 mM (red) and 44.8 mM (green). Data points represented as a triangle were not used in the grid search. The R2/R1 values are plotted against the ! angles of the corresponding C!H bonds within the orientation with the lowest E/(N ! n) value.

single supramolecular assembly of a well-defined size, as they are obtained from relaxation rates that result from an average over a distribution of oligomer sizes.

The calculated lengths increase with concentration, varying from 32.6 Å to 60.9 Å between 0.5 mM and 44.8 mM. However, the calculated diameter remains constant at about

26.4 Å, except at the lowest concentration, where it is somewhat reduced to 21.9 Å. This observed asymptotic behavior of the diameter value supports the proposed supramolecular model of a self-assembly occurring along a single direction aligned with the main axis of the diffusion tensor. Indeed, the increased contribution of higher oligomer

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molecular model

6

sizes to the average relaxation rates does not impact the calculated diameter for peptide concentrations above 6.6 mM. The asymptotic value for the diameter corresponds to about three times the size of the pseudodesmin A solution structure (8-10 Å), revealing that the assemblies are not just single strands of molecules. This therefore provides additional support for the existence of the !-state. The slightly lower value for the diameter obtained at the lowest concentration can be rationalized by the presence of an increasing population of single monomer units in the distribution, arising from the dissociation of "!-states.

Figure 5. Obtained rotational diffusion coefficients D|| and D# (a), their ratio D||/D# (b) and the corresponding calculated dimensions of a cylindrical object (c) as a function of pseudodesmin A concentration. The increasing length and constant diameter at high concentration is explained by the stacking of !-states, while at low concentration the decreasing diameter can be explained by the !-state$monomer equilibrium becoming more significant (d).

Discussion

The analysis of heteronuclear relaxation data at multiple concentrations of pseudodesmin A in chloroform solution exposes important geometric information of the supramolecular assemblies. First, an estimate of the average dimensions of the anisotropic supramolecular assembly was obtained, information that is unavailable from the translational diffusion studies performed before16. Second, the relaxation data supported a unidirectional and infinite growth of the molecular assembly, in good agreement with the previously proposed model where it is assumed that the disc-like !-states stack upon each other, forming cylinder structures. It should be emphasized that the dimensions acquired at each concentration are obtained from relaxation rates that result from population weighted averages of all oligomers present and thus cannot be interpreted as those from a single molecular complex. However, since only the average length of the assemblies varies with concentration, it can be concluded

that only this parameter is averaged, while the diameter does not vary among the oligomers dominating the size distribution above 6.6 mM and thus corresponds closely to the calculated value.

Figure 6. Three copies of the pseudodesmin A solution conformation translated by an arbitrary distance along the direction of the main axis of the rotational diffusion tensor frame, corresponding to the direction of growth. The left image shows only the main chain of the oligopeptide, with the helix structure accentuated by a rectangle, while the right image shows only the side chain atoms as spheres. In the latter, hydrophobic side chains are shown in a green tint, the hydrophilic ones in a red tint and the Thr3 side chain in a pink or violet tint.

The third piece of structural information obtained from this study is the orientation of the monomer within the rotational diffusion tensor frame, which also remains constant with concentration. The main axis of this frame corresponds to the direction along which the assemblies grow with concentration. In Figure 6, several individual molecules of pseudodesmin A are shown translated along this direction, revealing the contact surfaces that instigates this molecular interaction. The axis of the helix structure is not exactly parallel to the direction of growth, but makes an angle of about 15° % 2°. The free amide groups of Leu1 and Gln2 at the N-terminus of the helix are positioned near the free carbonyl groups of Ser6 and Leu7,

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6

sizes to the average relaxation rates does not impact the calculated diameter for peptide concentrations above 6.6 mM. The asymptotic value for the diameter corresponds to about three times the size of the pseudodesmin A solution structure (8-10 Å), revealing that the assemblies are not just single strands of molecules. This therefore provides additional support for the existence of the !-state. The slightly lower value for the diameter obtained at the lowest concentration can be rationalized by the presence of an increasing population of single monomer units in the distribution, arising from the dissociation of "!-states.

Figure 5. Obtained rotational diffusion coefficients D|| and D# (a), their ratio D||/D# (b) and the corresponding calculated dimensions of a cylindrical object (c) as a function of pseudodesmin A concentration. The increasing length and constant diameter at high concentration is explained by the stacking of !-states, while at low concentration the decreasing diameter can be explained by the !-state$monomer equilibrium becoming more significant (d).

Discussion

The analysis of heteronuclear relaxation data at multiple concentrations of pseudodesmin A in chloroform solution exposes important geometric information of the supramolecular assemblies. First, an estimate of the average dimensions of the anisotropic supramolecular assembly was obtained, information that is unavailable from the translational diffusion studies performed before16. Second, the relaxation data supported a unidirectional and infinite growth of the molecular assembly, in good agreement with the previously proposed model where it is assumed that the disc-like !-states stack upon each other, forming cylinder structures. It should be emphasized that the dimensions acquired at each concentration are obtained from relaxation rates that result from population weighted averages of all oligomers present and thus cannot be interpreted as those from a single molecular complex. However, since only the average length of the assemblies varies with concentration, it can be concluded

that only this parameter is averaged, while the diameter does not vary among the oligomers dominating the size distribution above 6.6 mM and thus corresponds closely to the calculated value.

Figure 6. Three copies of the pseudodesmin A solution conformation translated by an arbitrary distance along the direction of the main axis of the rotational diffusion tensor frame, corresponding to the direction of growth. The left image shows only the main chain of the oligopeptide, with the helix structure accentuated by a rectangle, while the right image shows only the side chain atoms as spheres. In the latter, hydrophobic side chains are shown in a green tint, the hydrophilic ones in a red tint and the Thr3 side chain in a pink or violet tint.

The third piece of structural information obtained from this study is the orientation of the monomer within the rotational diffusion tensor frame, which also remains constant with concentration. The main axis of this frame corresponds to the direction along which the assemblies grow with concentration. In Figure 6, several individual molecules of pseudodesmin A are shown translated along this direction, revealing the contact surfaces that instigates this molecular interaction. The axis of the helix structure is not exactly parallel to the direction of growth, but makes an angle of about 15° % 2°. The free amide groups of Leu1 and Gln2 at the N-terminus of the helix are positioned near the free carbonyl groups of Ser6 and Leu7,

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D. Sinnaeve, M-ADelsuc, J.C. Martins and B.Kieffer - submitted



Acknowledgments• IGBMC

• Bruno Kieffer • Matthieu Tanty • Justine Vieville• Lionel Chiron• Christian Koehler

• Strasbourg - NMRTEC S.A.S.• Jean-Philippe Stark• Marie-Aude Coutouly• Marc Vitorino• Olivier Assemat• Redouane Hajjar

• Strasbourg University• Lionel Allouche• Bertrand Villeno

• ChimieParisTech - Paris• François-Xavier Coudert

• Gent University• José Martins• Davy Sinnaeve

• ENS - Lyon• Cyrille Monnereau• Sandrine Denis-Quanquin

• Funding


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