Patent Application: US-201213466155-A

Abstract:
a method for nuclear magnetic resonance spectroscopy of a sample involves excitation of long lived coherences between the singlet state s 0 and the central triplet state t 0 of nuclei of the sample by initiating irradiation of the sample with an rf - field with carrier frequency ω rf ; sustaining of the llc by maintaining the rf - irradiation during an interval τ 2 ; converting the llc temporarily into observable magnetisation by interrupting the rf - irradiation during an observation interval τ 3 ; detecting nmr - signals during the observation interval τ 3 and reconversion of the observable magnetisation back into llc after the observation interval τ 3 . these steps are repeated n times , wherein n is a positive integer . the method allows ultra high - resolution spectra of long - lived coherences to be obtained .

Description:
in an experiment according to the invention , the signals are observed during brief interruptions ( observation interval τ 3 ) of a sustaining rf field ( scheme b1 in fig1 ). this leads to a temporary conversion of llc &# 39 ; s into observable magnetization , e . g . i x − s x . in the simplest version of the inventive method , the observation intervals τ 3 are kept below 0 . 1 ms , so that the evolution of i x − s x under chemical shifts , couplings and transverse relaxation can be neglected ( fig1 b1 ). in a more sophisticated variant of the inventive method , the sensitivity can be improved by increasing the duration of the observation intervals τ 3 beyond 0 . 1 ms , and by inserting π refocusing pulses in the centre of the observation intervals τ 3 ( one refocusing pulse in each observation interval τ 3 ) to refocus chemical shifts ( scheme b2 in fig1 ). in the example shown in fig1 the initial populations , described by the density operator σ = i z + s z ( which may be enhanced by dnp ), is transformed into σ = i x − s x . scheme a1 of fig1 starts with a non - selective ( π / 2 ) x pulse to excite the state σ =− i y − s y followed by a delay τ 1 = 1 /( 2 | δω is |), where δω is = ω i − ω s . since the rf carrier frequency is normally positioned half - way between the two chemical shifts at ω rf =( ω 1 + ω s )/ 2 , σ =− i y − s y is transformed into σ = i x − s x during the delay τ 1 . the precession under j is in the interval τ 1 can usually be neglected in weakly coupled systems where 2πj is & lt ;& lt ; δω is . in scheme a2 , a semi - selective ic pulse applied to either spins i or s to invert the populations across either of the two doublets is immediately followed by a non - selective ( π / 2 ) y pulse to excite σ = i x − s x . 8 - 9 in aqueous solutions , it may be necessary to suppress the intense hdo peak . scheme a3 uses an echo sequence ( π / 2 ) x − τ −( π ) x ( i , s ) − τ − with a band - selective refocusing pulse that acts on spins i and s but is too weak to refocus the solvent resonance . the two pulsed field gradients ( pfg &# 39 ; s ) g 1 lead to dephasing of all magnetization components with offsets that lie outside the range of the band - selective refocusing pulse . like in scheme a1 , σ = i x − s x is created after a delay , in scheme a3 the delay is 2τ + τ 1 = 2τ + 1 /( 2 | δω is |). finally , scheme a4 uses a ‘ long - lived state filter ’ as explained elsewhere 15 . the latter two schemes also have the advantage of avoiding possible radiation damping induced by large hdo signals , especially when enhanced by dnp . both schemes b1 and b2 in fig1 rely on a continuous - wave ( cw ) rf field for ‘ sustaining ’ or ‘ locking ’ the llc , to suppress the chemical shifts of spins i and s , with a carrier ω rf =( ω i + ω s )/ 2 and an rf amplitude that is usually chosen to be larger than the offset ω 1 & gt ;| ω i − ω s |/ 2 . more sophisticated methods may also be used to sustain llc &# 39 ; s over greater bandwidths as described elsewhere . 24 during rf irradiation , the eigenstates of the hamiltonian are converted from the product base into the singlet - triplet base . 9 in the process , the density operator τ = i x — s x is converted into σ =(| s 0 t 0 |+| t 0 s 0 |), i . e ., into a zero - quantum coherence spanning the central triplet state t 0 = n (| αβ + βα ) and the singlet state s 0 = n (| αβ −| βα ) where n = 2 − 1 / 2 . in the windows τ 3 or τ 3 / 2 , where the rf field is switched off , the density operator is briefly converted back into single - quantum coherences σ = i x − s x , so that signals can be observed . in both schemes b1 and b2 in fig1 , the llc &# 39 ; s are sustained during the intervals τ2 , while the signals are detected in the windows τ3 or τ 3 / 2 . the sustain - observe cycles are repeated n times , resulting in ‘ sustained induction decays ’ ( sid &# 39 ; s ) with a total length t max = nδt digitised at intervals δt . these δt intervals are equivalent to the ‘ dwell times ’ of ordinary free induction decays . the signals can be fourier transformed , giving a frequency domain spectrum with a digital resolution that is determined by 1 / t max and a spectral width 1 / δt that should be larger than the total coupling 2t = 2j + 4d if one wishes to avoid aliasing . ‘ windowed acquisition ’ has been used previously in solid - state nmr methods such as wahuha , mrev and their numerous variants 25 - 26 and for homonuclear dipolar decoupling with shaped rf pulses in the manner of dumbo . 27 if the observation windows are too short , the signals can be perturbed by transient effects due to transmitter break - through , bearing in mind that the preamplifier must be protected during rf irradiation , and that this protection must be removed in the windows . on the other hand , if the observation windows are too long , the single - quantum coherences σ = i x − s x will decay through transverse t 2 relaxation , dephase in the inhomogeneous static field , and evolve under the chemical shifts and scalar couplings . with an analogue - to - digital converter ( adc ) running at 500 khz , one can acquire a sample point every 2 μs , and take averages over all points recorded in each observation interval τ 3 of scheme b1 or in the first and / or second τ 3 / 2 interval of scheme b2 . reducing the number of sampling points leads to a loss in signal - to - noise ratio . in practice , the dead time between the point where the cw rf field is switched off and where the signal can be observed is typically 3 μs , so that 8 sampling points can be taken in each window if τ 3 = 20 μs , or 498 points in each window if τ 3 = 1000 μs . if the sustaining intervals in scheme b1 of fig1 are adjusted to keep a constant dwell time δt = τ 2 + τ 3 = 50 ms so that a spectral width is 1 / δt = 20 hz or ± 10 hz , windows τ 3 = 20 μs or 1000 μs , lead to rf duty cycles of 99 . 96 or 98 % respectively . during the irradiation intervals τ 2 , the coherence q llc =(| s 0 t 0 |+| t 0 s 0 |) evolves under the effect of the total coupling 2t is = 2j is + 4d is and decays with the relaxation rate r llc = r llc = 1 / t llc in terms of the usual cartesian product operators , this leads to : σ 2 [( i x − s x ) cos ( 2 πt is τ2 )+( 2 i y s z − 2 i z s y ) sin ( 2 πt is τ 2 )]· exp (− τ 2 · r llc ) ( 2 ) this is consistent with recent work 9 , but our initial papers underestimated the effect of the couplings by a factor 2 . during each observation window τ 3 in the scheme b1 of fig1 , the density operator evolves under the chemical shifts and again under the total coupling constant t is , albeit reduced by a factor 2 , and decays with the single - quantum relaxation rate r 2 = 1 / t 2 . the overall effect for each sustain - and - observe cycle δt = τ 2 + τ 3 in scheme b1 can be written : τ 3 = cos ( δω is / 2 · τ 3 )[( i x − s x ) cos ( 2 πt is δt ′)+( 2 i y s z − 2 i z s y ) sin ( 2 πt is δt ′)]· exp (−& lt ; r & gt ; δt )+ sin ( δω is / 2 · τ 3 )[( i x s x ) cos ( 2 πt is δt ′)+( 2 i y s z + 2 i z s y ) sin ( 2 πt is δt ′)]· exp (−& lt ; r & gt ; δt ) ( 3 ) where δt ′= τ 2 + τ 3 / 2 = δt − τ 3 / 2 , reflecting the scaling of the total coupling constant when the rf field is switched off . we can define and apparent total coupling constant : using the notation r 2 = r sqc = κr llc with κ ≦ 9 , the average decay rate & lt ; r & gt ; in eq . ( 3 ) is for κ = 3 , τ 2 = 49 . 98 ms and τ 3 = 20 μs , this amounts to a mere 0 . 08 % increase in the average relaxation rate and hence to a negligible contribution to the line - width . when the cw rf field along the x - axis is switched on again , the differences i x − s x and 2i y s z − 2i z s y resume their identity as llc &# 39 ; s , while the sum i x + s x is spin - locked and decays , and the sum 2i y s z + 2i z s y is dephased under the effect of the rf field inhomogeneity . with a chemical shift difference δω is /( 2π )= 300 hz , we have cos ( δω is τ 3 )= 0 . 9993 ˜ 1 . this infinitesimal ‘ leakage ’ of the llc may seem negligible , but it is amplified as the sustain - observe sequence is repeated n times with cos ( δω is τ 3 ) n so that cos ( δω is τ 3 ) 100 = 0 . 936 , thus affecting the decay of the llc . the resulting time domain signals sampled at intervals δt are in order to suppress contributions from i x + s x and 2i y s z + 2i z s y , scheme b2 uses a π pulse in the middle of each observation window to refocus the chemical shifts . as a result , the density operator at the end of each window τ 3 in scheme b2 is : σ 7 =[( i x − s x ) cos ( 2 πt is δt ′)+( 2 i y s z − 2 i z s y ) sin ( 2 πt is δt ′)]· exp (−& lt ; r & gt ; δt ) ( 7 ) fig2 e shows a ‘ sustained induction decay ’ ( sid ) that can be compared with the fid presented in fig2 a and with the modulated echo decay of fig2 c . the three signals stem from the two protons in an isotropic solution ( where t is = j is ) of 2 , 3 - dibromothiophene ( 20 mm in dmso - d 6 with 30 mm ascorbic acid 28 to scavenge paramagnetic oxygen ), recorded with a simple π / 2 pulse ( fig2 a ), observed in a j - resolved 2d manner 29 ( fig2 c ), and recorded ‘ on the fly ’ llc &# 39 ; s in windows τ 3 / 2 = 100 is according to the invention with scheme b2 ( fig2 e ). their fourier transforms are presented in fig2 b , 2 d and 2 f respectively . the llc &# 39 ; s ‘ sid ’ signal is described by eq . ( 8 ) and slowly decays with a time - constant & lt ; t & gt ;= 1 /& lt ; r & gt ;= 19 . 9 s . its fourier transforms ( fig2 f and 2 g ) show two lines at v =± j is separated by 2j is with line - widths & lt ; δν & gt ;= 1 /( π & lt ; t & gt ;)= 16 . 4 mhz ( resolution enhanced by a factor ε δ = v /& lt ; δν & gt ;˜ 180 and 8 . 5 with respect to conventional fid and echo modulation respectively ). the fact that the couplings are twice as effective in the rotating frame than in the laboratory frame is reminiscent of total correlation spectroscopy (&# 39 ; tocsy &# 39 ;) 30 . note that the antiphase terms 2i y s z − 2i z s y cannot induce any signals in the orthogonal channel , so that we have a case of pure amplitude ( rather than phase ) modulation . the ‘ on the fly ’ llc spectrum according to the invention of the two diastereotopic protons of glycine in l - ala - gly is shown in fig2 h . fig3 a shows how the insertion of refocusing pulses in the middle of the observation windows allows one to eliminate the effects of chemical shifts . for longer windows 100 is & lt ; τ 3 & lt ; 2 ms , scheme b2 provides longer decays and hence narrower line - widths . note that the narrowest lines are obtained , albeit at the expense of sensitivity , with scheme b1 with very short observation windows ( typically τ 3 = 20 μs ). fig3 b shows how refocusing pulse allow one to obtain an accurate measurement of scalar couplings j is ( or total couplings t is in anisotropic media ) even for long observation windows τ 3 . ( the slight decrease in j is app for long τ 3 is described by eq . ( 4 )). finally , fig3 c shows how longer observation windows τ 3 , which allow one to average over a larger number of data points in each window , result in improved signal - to - noise ratios , which are proportional to τ 3 1 / 2 . in principle , the evolution of llc &# 39 ; s is immune to the inhomogeneity of the magnetic field if one uses the scheme b2 of fig1 . we should remember however that all excitation schemes a1 - a4 of fig1 require one to distinguish the chemical shifts of the two spins i and s , although it is not necessary to resolve their mutual coupling constant . the methods can thus tolerate a moderate inhomogeneity of the static field , as long as the line - widths fulfil the condition δν *= 1 /( πt 2 )*& lt ; δω is . fig4 shows how a deliberate missetting of the shim currents ( z 1 , z 2 , z 3 , x , y , z 0 x , and z 0 y ) to broaden the line - widths in the conventional ( single - quantum ) spectrum to about δν *= 20 hz has little effect on the averaged line - widths & lt ; δν & gt ; of the llc &# 39 ; s and the apparent scalar couplings j is app (+ 5 . 3 and + 3 mhz , respectively ). ex - situ nmr 4 - 5 and mri in moderately inhomogeneous fields ( e . g ., in the vicinity of discontinuities of the magnetic susceptibility ) may benefit from this property . very weak molecular alignments , yielding minute residual dipolar couplings ( rdc &# 39 ; s ) in the mhz range , can be readily determined with the inventive method . fig5 shows the ‘ on the fly ’ llc spectra according to the invention of two solutions of 3 - bromothiophene - 2 - carboxylic acid in ( 1 : 1 ) d 2 o / dmso - d 6 , with and without addition of a 0 . 25 % pentaethylene glycol monododecyl ether ( c 12 e 5 ). the very weak alignement of the solute gives rise to a net rdc with 2 - d is app =− 10 . 7 ± 0 . 4 mhz . the order parameter of the r hh vector that connects the two protons in 3 - bromothiophene - 2 - carboxylic acid can be estimated to be as small as s ≦( 2 . 52 ± 0 . 10 )· 10 − 6 ( assuming that the internuclear distance is r hh = 2 . 662 å like in thiophene 31 , and assuming that the average r hh vector is oriented along b 0 , i . e ., θ = 0 ). since llc spectra can be recorded in a single scan , they can be boosted by ‘ dissolution ’ dnp . spectra of a 20 μl solution of 50 mm 2 , 3 - dibromothiophene dissolved in a 3 : 2 dmso - d 6 / d 2 o ( v / v ) mixture doped with 30 mm tempol are compared in fig6 with and without hyperpolarization by ‘ dissolution ’ dnp ( see methods section below ). the dissolution , transfer and injection required 3 . 2 s . after an additional 3 s of settling time in the nmr tube , some bubbles and convection currents cannot be ruled out . these tend to broaden ordinary ( single - quantum ) line - widths , but have little effect on llc spectra . the llc &# 39 ; s were excited , sustained , and observed with sequences a3 and b2 of fig1 . the enhancement was ε dnp ≈ 300 . it may be possible to improve this performance by preventing losses of the proton polarization due to relaxation in low fields during the voyage between the dnp polariser and the nmr magnet . 32 a 20 μl solution of 50 mm 3 - bromothiophene - 2 - carboxylic acid ( 97 %, aldrich ) dissolved in a 3 : 2 mixture of dmso - d 6 / d 2 o ( v / v ) ( 99 . 98 %, aldrich ) doped with 30 mm 4 - hydroxy - 2 , 2 , 6 , 6 - tetramethylpiperidine 1 - oxyl ( tempol ) ( purum , ≧ 97 . 0 %, fluka ). the freshly prepared mixture was rapidly frozen in liquid nitrogen to form 104 beads . a 3 m d 2 o solution of sodium l - ascorbate (≧ 99 %, aldrich ) was prepared and rapidly frozen in liquid nitrogen ( 104 beads ). a 20 mm isotropic solution of 2 , 3 - dibromothiophene ( 98 % aldrich ) in dmso - d 6 with addition of 30 mm l - ascorbic acid ( bioxtra , ≧ 99 . 0 %, sigma ) for scavenging paramagnetic oxygen was prepared and sealed in a 5 mm nmr tube . two 50 mm solution of 3 - bromothiophene - 2 - carboxylic acid in a ( 1 : 1 ) d 2 o / dmso - d 6 mixture with addition of 30 mm l - ascorbic acid for scavenging paramagnetic oxygen were prepared , one with and the other without addition of 0 . 25 % of pentaethylene glycol monododecyl ether ( c 12 e 5 , sigma ≧ 98 %) for partial alignment , and sealed in 5 mm nmr tubes . a 0 . 5 m solution of l - ala - gly ( sigma ) in d 2 o with addition of 30 mm sodium l - ascorbate (≧ 99 %, aldrich ) was prepared and sealed in a 5 mm nmr tube . all chemicals were used without further purification . dnp was performed by thermal mixing at 1 . 2 k and 3 . 35 t in a home - built ‘ dissolution ’ dnp polarizer 33 - 35 by applying a cw microwave irradiation at f μw = 93 . 89 ghz and p μw = 30 mw for 5 minutes . the dnp build - up of 1 h magnetization is fast ( τ dnp ˜ 120 s ) and yields high proton spin polarization p ( 1 h )˜ 20 - 40 % depending on sample composition . 36 about 20 μl of frozen beads of the polarized sample , together with 90 μl of frozen beads of a 3 m d 2 o solution of sodium ascorbate , were rapidly dissolved with 3 ml of preheated d 2 o ( t = 440 k and p = 1 . 2 mpa ) and intimately mixed within 700 ms , transferred in 1 . 5 s to a 11 . 7 t nmr magnet through a 1 mm inner diameter ptfe tube pressurized with helium gas at 0 . 6 mpa , and allowed to settle for 0 . 5 s , prior to injection into a pre - locked nmr tube , which required another 0 . 5 s . after a further 3 s settling time in the nmr tube to allow turbulences to slow down , the llc was excited , sustained , and observed with the sequences a3 and b2 of fig1 . nmr measurements were performed on a 500 mhz spectrometer equipped with an inverse 5 mm bruker cryoprobe ™. the ‘ on the fly ’ llc pulse program and excitation / acquisition sequences were designed and performed with topspin 2 . 1 . in conclusion , the present invention describes an ‘ on - the - fly ’ method where the radio - frequency ( rf ) irradiation required to sustain the llc &# 39 ; s in high magnetic field is briefly interrupted , normally at regular intervals , so that the llc &# 39 ; s are temporarily converted into single - quantum coherences ( sqc &# 39 ; s ) that can be observed . the method according to the invention allows one to obtain ultra high - resolution spectra of long - lived coherences ( llc &# 39 ; s ) ‘ on the fly ’ in one - dimensional fashion by time - shared ‘ windowed acquisition ’. this allows one to determine very accurate total couplings t = j + 2d . the method can be applied to either isotropic or anisotropic phases , providing ultra - high resolution even in moderately inhomogeneous magnetic fields . the signals can be enhanced by “ dissolution ” dnp 10 . the technique has been applied to pairs of spins in this study , but it is intended to extend the scope of application of ‘ on the fly ’ llc &# 39 ; s in the near future to multiple spin systems ( n & gt ; 2 ) with broad - band excitation and detection ( replacing cw by composite pulses ) of several llc &# 39 ; s in the same molecule or in mixtures . since inhomogeneous fields are not detrimental to llc &# 39 ; s , ex - situ or in - cell studies should be readily feasible with unprecedented linewidths , and since the long lifetimes of llc &# 39 ; s are exquisitely sensitive to the presence of paramagnetic species 28 , we believe they should be sensitive probes for the detection paramagnetic species such as oxygen . 1 . ernst , r . r . & amp ; anderson , w . a . application of fourier transform spectroscopy to magnetic resonance . rev . sci . instrum . 37 , 93 ( 1966 ). 2 . allerhand , a ., addleman , r . e . & amp ; osman , d . ultrahigh resolution nmr . 1 . general considerations and preliminary results for c - 13 nmr . j . am . chem . soc . 107 , 5809 - 5810 ( 1985 ). 3 . balbach , j . j ., conradi , m . s ., cistola , d . p ., tang , c . g ., garbow , j . r . & amp ; hutton , w . c . high - resolution nmr in inhomogeneous fields . chem . phys . lett . 277 , 367 - 374 ( 1997 ). 4 . appelt , s ., kuhn , h ., hasing , f . w . & amp ; 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