Brownian Motion. S(f) Carr-Purcell Spin Echo Pulse Sequence. Advanced NMR Methods. Spin Echo Pulse Sequence: phase history Δ/2 Δ/2

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1 Slide copies: Lecture 5: NMR and Diffusion Cuvier, Charcot et la Fée Verte Advanced NMR Methods 5 Carr-Purcell Spin Echo Pulse Sequence 90 x τ 180 y τ Z 90 x Z Pulsed field gradients and spin echoes diffusion coefficient and molecular size diffusion-ordered spectroscopy (DOSY) and mixture analysis measurement of molecular association new techniques Consider the behaviour of two nuclear magnetizations, one with a high Larmor frequency and one with a low X Z Y τ 180 y τ X Z Y Larmor frequency X Y X Y Spin Echo Pulse Sequence: phase history Brownian Motion 90 x 180 y RF Δ/2 Δ/2 φ S(f) t! Refocussing condition: G*!dt = 0! " # 0 Molecules in solution move at random because of collisions. How far they move on average in a given length of time t depends on the diffusion coefficient D: the root-mean-square displacement for diffusion in three dimensions is 6Dt 1

2 The Diffusion Coefficient Brownian Motion During a Spin Echo For a solute molecule diffusing through a continuum solvent (i.e. where the solvent molecules are much smaller than the solute), the diffusion coefficient D depends on the solvent viscosity η and the solute hydrodynamic radius a according to the Stokes-Einstein equation: D = kt 6!"a The hydrodynamic radius a is the effective average radius of the solvated solute molecules, and will depend on the molar mass MW. Assuming similar chemistries (i.e. constant density), Field gradient Higher Larmor frequency for a spherical molecule such as a globular protein, for a random coil polymer or a flat disk, D! ( MW ) "1/3 D! ( MW ) "1/2 Lower Larmor frequency for a rigid linear molecule D! ( MW ) "1 In practice D will also depend on molecular shape, interactions etc. In the presence of a field gradient, diffusion during Δ causes spins to lose phase coherence, attenuating the spin echo at a rate that depends on gradient strength G and diffusion coefficient D Measuring Diffusion with NMR: the pulsed field gradient spin echo (PFGSE) Spin echo sequence: effect of diffusion RF Δ/2 Δ/2 φ S(f) spin phases scrambled phases unscrambled if spins haven t moved Different spins follow different random paths through the sample, building up different phase histories and leading to reduced net magnetization at time Δ 2

3 Measuring Diffusion with NMR: the pulsed field gradient stimulated echo (PFGSTE) Motion in NMR Experiments: the Bloch-Torrey equation RF G The Bloch-Torrey equation describes the evolution of transverse magnetization M + = M y - im x as a function of position r and time t in the presence of a field gradient g and of diffusion with coefficient D and/or flow with velocity v: dm + (r,t) dt =!i" r.gm +! M + / T 2 + D# 2 M +! #.vm + free precession spin phases scrambled phases unscrambled if spins haven t moved relaxation diffusion flow Splitting the 180 pulse of a spin echo into two 90 pulses stores the magnetization as M z for most of the delay Δ, reducing losses and allowing longer diffusion times Measuring Diffusion with NMR: the Stejskal-Tanner equation Constructing a DOSY Spectrum 400 MHz 1 H DOSY spectrum of choline, acetone and DSS in D 2 O Random diffusion between the two field gradient pulses leads to a Gaussian distribution of solute molecule displacements, a Gaussian distribution of NMR signal phase changes, and hence a Gaussian dependence of NMR spin echo signal on gradient strength G: G Field gradient! A(g) = S(g) $ " # S(0) % & = exp '( 2 g 2 ) 2 D*' ( ) where γ is the magnetogyric ratio, g is the gradient pulse amplitude, and δ is the gradient pulse width. Δ is the effective diffusion time, which is Δ less a small correction for diffusion during the gradient pulses:!' =! " # / 3 TSP Choline Acetone HDO measure PFGSTE spectra as a function of G fit peak heights to get diffusion coefficients D extend 1D peaks into a second dimension, with Gaussian shapes centred on the D s widths determined by the standard errors σ D Despite the name, DOSY is not like COSY/NOESY/TOCSY: spectra are statistical constructs from, not transforms of, experimental data 3

4 Choosing a DOSY Pulse Sequence DOSY Processing Methods Stimulated (STE) or spin (SE) echo? SE can suffer from J modulation and is more vulnerable to B 0 disturbances, but if T 2 T 1 retains maximum S/N STE loses half S/N, but is generally preferred Bipolar or unipolar? Bipolar pulse sequences cut B 0 disturbances and refocus chemical shifts, but can need longer phase cycles High resolution or low resolution? If most signals are resolved in NMR spectrum, use 2 parameter monoexponential fitting (HRDOSY) with careful baseline correction: good (few %) resolution in D, but one (compromise) D per peak If most signals overlap in NMR spectrum, use multiexponential fitting (CONTIN or alternatives): poor resolution in D, but can separate degenerate signals with different D s LED? Adding a z filter to the end of the sequence fixes phases and allows time for eddy currents to fade, but can hide problems and needs long phase cycle. Very useful if system has poor gradient recovery. DOSY Acquisition Conditions 500 MHz 1 H spectrum of Port Wine VT regulation? Temperature gradients cause convection: keep sample close to quiescent temperature if possible (i.e. no VT). If VT is needed, check carefully for convection and use compensated sequence if necessary Gradient pulse shape? Half-sine shapes can reduce lineshape errors; like LED, useful if gradient recovery is poor What range of gradient strengths? G, δ and Δ control attenuation for given D. Keep δ to a few ms; keep Δ < T 1 ; avoid very low G s; choose range of G to sample attenuation evenly down to < 30% for slowest signal ppm ppm (with triple presaturation of water and ethanol) J. Agric. Food Chem. 52, 3736 (2004) 4

5 500 MHz 1 H 2D DOSY Spectrum of Port Wine α-glucose 13 C α-glucose α-glucose 13 C Anomeric region, showing C 1 signals of sugars of different sizes GLC Cuvier, Le Règne animal distribué d'après son organisation (1817) 500 MHz 1 H DOSY of Gerbil Brain PCA Extract Motor Neurone Disease/ALS/Maladie de Charcot GPC m- ino glu NAA cr cr GABA succ GABA lac cre ala lac tau cho etn ac J. Magn. Reson. B 108, (1995) 5

6 600 MHz 1H DOSY of Human Brain Aqueous Extract missing in MND Aqueous extract of normal motor cortex (TN Huckerby, Lancaster University) 29Si DOSY Spectrum of Aqueous Tetramethylammonium Silicate O = 29Si 2D DOSY of Cyclic Siloxane Oligomers - Si O - - OO n 16 n n=4 Silica dissolves in strong alkali to give a wide variety of silicate oligomers, the precursors of cage structures such as zeolites Chem. Commun., 2001, INEPT-IDOSY spectrum of a mixture of cyclic siloxane oligomers in benzene-d6 Phys. Chem. Chem. Phys. 6, 3221 (2004) 6

7 Diffusion Coefficients of Cyclic Siloxane Oligomers 500 MHz 1 H Spectrum of Port Wine slope = ppm Diffusion coefficients of a mixture of cyclic siloxane oligomers in benzened 6, measured using 29 Si Oneshot, 29 Si INEPT-IDOSY and 1 H Oneshot pulse sequences at three different concentrations ppm (with triple presaturation of water and ethanol) J. Agric. Food Chem. 52, 3736 (2004) 3D 2DJ-iDOSY Pulse Sequence 2D Planes from 3D 2DJ-iDOSY Spectrum of Port Wine A diffusion domain can easily be added to a 2D experiment to give a 3D DOSY experiment. Incrementing diffusion-encoding gradients and evolution time separately gives a 3D 2DJ-DOSY spectrum. CH 3 CH 2 CH(CH 3 )CH 2 OH CH 3 CH(CH 3 )CH 2 CH 2 OH CH 3 CH 2 CH(CH 3 )OH CH 3 CH 2 CH 2 OH needs only 1 transient per increment; minimum time < 5 min Anal. Chem. 76, 5418 (2004) 2D plane excerpts from a 2DJ-iDOSY 3D spectrum of 90% ruby port / 10% D 2 O, showing subspectra for three different diffusion coefficients corresponding to propanol, butanol and pentanols. 7

8 3D DOSY-HMQC Pulse Sequence DOSY-HMQC spectrum of Quinine, Geraniol and Camphene H!! D! t 1 2! C WURST " G z # J. Magn. Reson., 131, (1998) 2D planes from 3D DOSY-HMQC spectrum Advanced NMR Methods quinine geraniol camphene Lecture 5: NMR and Diffusion Cuvier, Charcot et la Fée Verte Pulsed field gradients and spin echoes diffusion coefficient and molecular size diffusion-ordered spectroscopy (DOSY) and mixture analysis measurement of molecular association new techniques 8

9 Studying Binding: 400 MHz 1 H DOSY Spectrum of a Model Mixture Studying Binding: 400 MHz 1 H DOSY Spectrum of Mixture + Polymer quinine, hydroquinine, methyl nicotinate, chlorobenzoyl quinine, estrone, N-methyl nicotinamide, progesterone, citronellal, citronellol, o-vanillin, 1,6-dehydropregnenolone acetate, cholest-5-en-3-one, pinene Chem. Commun. 2001, quinine, hydroquinine, methyl nicotinate, chlorobenzoyl quinine, estrone, N-methyl nicotinamide, progesterone, citronellal, citronellol, o-vanillin, 1,6-dehydropregnenolone acetate, cholest-5-en-3-one, pinene Artemisinin Solubilisation by Octanoascorbate Artemisia annua, L. artemisinin, qinghaosu J. Pharm. Sci. 91, (2002) 9

10 Artemisinin Solubilisation by Octanoascorbate (i) Artemisinin Solubilisation by Octanoascorbate (ii) 4 mm octanoascorbate 20 mm octanoascorbate Artemisinin Solubilisation by Octanoascorbate (iii) Artemisinin Solubilisation by Octanoascorbate (iv) n S S n effect of micellisation of octanoascorbate on its diffusion dependence of artemisinin solubility on [octanoascorbate] 10

11 Artemisinin Solubilisation by Octanoascorbate (v) Matrix-Assisted DOSY Adding a co-solute to a mixture can exploit differential binding to allow resolution of mixture spectra even where species have the same MW, e.g. isomers Back-calculation of D([ASC8]) from association constant shows good agreement; ca. 1 artemisinin molecule per micelle 400 MHz 1 H DOSY spectra of an equimolar mixture of 48 mm ortho-, meta- and paramethoxyphenol, with TSP reference, in D 2 O, without (a) and with (b) addition of 36 mm sodium dodecyl sulfate (SDS). Different degrees of binding to SDS micelles cause the average diffusion coefficients for the three isomers to differ significantly, allowing separation of their signals. Advanced NMR Methods Effect of Signal Overlap on DOSY Processing Lecture 5: NMR and Diffusion Cuvier, Charcot et la Fée Verte Pulsed field gradients and spin echoes diffusion coefficient and molecular size diffusion-ordered spectroscopy (DOSY) and mixture analysis measurement of molecular association new techniques monoexponential fit Univariate biexponential fit Multivariate 11

12 A Model Mixture Model Mixture: monoexponential fitting Sucrose Propanol HOD Sucrose Propanol 3.4 x m 2 s x m 2 s -1 HOD 15.3 x m 2 s -1 Sucrose, propanol and HOD (in D 2 O) at 25 C; overlapped at 3.5 ppm 15 gradient levels, 64 transients: 1 h 40 min S/N: 25000:1 Baseline corrected and reference deconvoluted Overlapping peaks give compromise diffusion coefficient Model Mixture: biexponential fitting Model Mixture: (S)CORE, Component-Resolved NMR Sucrose Propanol HOD DOSY dataset for a mixture of sucrose and propan-1-ol in D 2 O SCORE 3.4 x m 2 s x m 2 s x m 2 s -1 S = 0 A D A and D B must differ by at least 30% Very dependent on the quality and S/N of data Lineshapes corrected with reference deconvolution Effects of non-uniform field gradients corrected S e + S # DA % $ g!" # DB% $ g!" 0B e Anal. Chem. 78, (2006) M i Least squares fit to sum of N decaying spectra S( f ) = S 0( f )e!d i " 2 # 2 g 2 % $ & Requires known number of components i =1 Fitting time <10 s for SCORE P. Stilbs and K. Paulsen, Rev. Sci. Instrum. 67, 4380 (1996) Anal. Chem. 80, 3777 (2008) J. Magn. Reson. 198, 121 (2009) 12

13 Oneshot DOSY Spectrum at Room Temperature Oneshot DOSY Spectrum at 25 C Polydimethylsiloxane, mesitylene, trimethoxybenzene, sucrose octaacetate and quinine in CDCl 3 (total acquisition time 30 s) Polydimethylsiloxane, mesitylene, trimethoxybenzene, sucrose octaacetate and quinine in CDCl 3 (total acquisition time 30 s) Oneshot DOSY Spectrum at 50 C Effects of Nuclear Motion on Spin Echo Amplitude e 2 τ /T2 relaxation e 2γ2 G 2 Dτ 3 /3 diffusion iγ Gvτ2 e flow 2sin(γGv maxτ 2 ) γgτ 2 with velocity v convection with rectangular velocity spectrum Convection in CDCl 3 at 50 C is so fast that almost all signal is lost 13

14 % & $ % Spin Echo Sequence: Effect of Flow Double Spin Echo Sequence: Effect of Flow RF RF φ φ S(f) S(f) t! Extra refocussing condition: G*!dt = 0! " # t 0 Convection Compensated Double STE DOSY Sequence Convection Compensated DOSY at 50 C RF!/2!/2 G z " & % A(G 2 ) = exp! 2 G 2 " 2 % D(#!!"/3) $ Polydimethylsiloxane, mesitylene, trimethoxybenzene, sucrose octaacetate and quinine in CDCl 3 14

15 Lecture 5: NMR and Diffusion Cuvier, Charcot et la Fée Verte Advanced NMR Methods 5 Pulsed field gradients and spin echoes diffusion coefficient and molecular size diffusion-ordered spectroscopy (DOSY) and mixture analysis measurement of molecular association new techniques 15