Patent Application: US-66272410-A

Abstract:
a method for nuclear magnetic resonance spectroscopy of a sample comprises preparation of the sample and carrying out an nmr spectroscopy measurement . preparation includes excitation of long lived coherences between the singlet state s 0 and the central triplet state t 0 of nuclei of the sample . the thermal equilibrium boltzmann distribution is thereby transformed into a difference , which is flipped to the transverse plane , and irradiation of the sample with an rf - field is initiated . the llc is sustained by maintaining the rf - irradiation during an interval t 1 and the llc is converted into observable magnetisation by interrupting the rf - irradiation . the method allows nuclear magnetic resonance spectroscopy measurements with improved spectral resolution .

Description:
the present invention focuses on elements , in particular off - diagonal elements , of the liouvillian matrix that describes the evolution of a suitably prepared two spin - ½ system subjected to a preferably continuous rf field 9 - 12 . a coherent superposition between the singlet and central triplet states can be readily defined in the singlet - triplet base 3 : these will henceforth be called long - lived coherences ( llc ). in terms of products of cartesian operators in the product base , these may also be written : the imaginary part leads to oscillations that are determined by the scalar coupling j is , while the decay of the coherence is governed by r llc . a counterpart with an opposite oscillation frequency − j is will be discussed elsewhere . as shown below , the lifetime t llc = 1 / r llc is usually significantly longer than the transverse relaxation times t 2 of the single - quantum coherences , i . e ., t llc & gt ;& gt ; t 2 . the coherent and relaxation properties of llc can be utilised to record very high - resolution 2d spectra , notably in order to measure j - couplings with high precision or to resolve nearly - degenerate signals . in order to excite llc , one can transform the thermal equilibrium boltzmann distribution ( i z + s z ) into a difference ( i z − s z ). an example for a simple pulse sequence is shown in fig1 b , where one of the two doublets in the spectrum is inverted by a semi - selective π pulse . next , a ( π / 2 ) y pulse is applied to excite ( i x − s x ), followed by continuous - wave ( cw ) rf irradiation along the x - axis . this perturbation in effect suppresses the chemical shifts , so that the system is best described in the singlet - triplet basis . in the process , the difference ( i x − s x ) is converted into q llc . the quantum yield of this conversion is 100 %. the llc is sustained by rf irradiation and the real component of the complex coherence is measured by switching the rf field off after a variable evolution time t 1 in the manner of two - dimensional spectroscopy . if only the effect of the dipolar interaction between two protons i and s is considered , the transverse relaxation rate of the single - quantum coherences in a weakly - coupled two - spin systems is described by r 2 = ( b is 2 20 ) ⁡ [ 9 ⁢ j ⁡ ( 0 ) + 15 ⁢ j ⁡ ( ω ) + 6 ⁢ ( 2 ⁢ ω ) ] ( 4 ) j ⁡ ( ω ) = τ c 1 + ω 2 ⁢ τ c 2 , b is = - μ 0 4 ⁢ π ⁢ γ 2 ⁢ ℏ r is 3 is the strength of the homonuclear dipolar coupling between two spins i and s , r is is the distance between them , τ c is the rotational correlation time of the molecule , and the other quantities have their usual meaning . on the other hand , it can be shown 13 , 14 that the llc decay rate is given by : hence , the llc is predicted to have longer lifetimes than single - quantum coherences in all motional regimes , i . e ., for arbitrary molecular tumbling rates , as long as the dipolar coupling between the spins is the predominant interaction . the ratio is r llc / r 2 = ⅓ in the fast - tumbling limit τ c & lt ;& lt ; 1 / ω 0 ), when the spectral densities are equal at all frequencies , and r llc / r 2 = 1 / 9 in the spin diffusion limit ( slow tumbling , τ c & gt ;& gt ; 1 / ω 0 ), when only the spectral densities at zero frequency remain significant . in terms of lifetimes , this implies that the ratio varies in the range 3 & lt ; t llc / t 2 & lt ; 9 . extraneous relaxation mechanisms such as the dipolar interaction with spins outside the pair on which llc is excited will tend to reduce the advantage . the modulation of the chemical shift anisotropy ( csa ) of the spins will also have a deleterious effect on the relaxation time constants of the llc , except in favourable cases , when it has the same spin - exchange symmetry as the dipole - dipole interaction between the two coupled spins 14 . the decay rates of llc have been experimentally determined and compared with the decay rates of the single - quantum coherences associated with the two diastereotopic protons h 1 α and h 2 α of gly - 76 in the mobile c - terminal part of the protein ubiquitin . numerical simulations assuming pure dipolar relaxation predict a relaxation rate r llc = 2 . 3 s − 1 . the relaxation rate constants measured in the experiments shown in fig1 c and d are r llc = 2 . 5 ± 0 . 7 s − 1 and r 1ρ ≈ r 2 = 5 . 6 ± 0 . 1 s − 1 , so that the experimental ratio is r llc / r 2 = 0 . 46 or t llc / t 2 = 2 . 17 . the fourier transform of the oscillations yields the magnitude of the j is coupling with very high accuracy , since the linewidth is determined by the relaxation rate r llc . to this effect , 2d experiments were performed with the pulse sequence of fig1 b . in fig2 , a 2d spectrum is shown where the chemical shifts are seen in the direct ω 2 dimension , whereas only one frequency , which corresponds to the j is coupling constant , is detected in the ω 1 dimension . by increasing the time increment δt 1 , one can adequately sample the oscillations up to a long t 1 max to catch the signal until it has decayed completely . undersampling leads to spectral aliasing , but since there is only one peak in the indirect dimension , it is easy to correct for this effect . the 2d spectrum in fig2 b was recorded by undersampling in the ω 1 dimension , recording 220 points with increments δt 1 = 50 ms , so that the spectral width in the ω 1 dimension was 10 hz and t 1 max = 11 s . the full linewidth at half - height of the signal was found to be δv 1 / 2 = 0 . 6 hz in the ω 1 dimension . since the coupling constant j is between the two geminal protons h 1α and h 2 α of glycine is known to be in the vicinity of 17 hz , it is clear that the signal appearing at 2 . 17 hz in the spectrum in fig2 a must be folded three times , so that the true value is j is =− 17 . 17 hz . in conclusion , long - lived coherences offer a means of reducing linewidths much below the usual limits of nmr spectroscopy . this opens the way for 2d spectroscopy with very well - resolved peaks in the indirect dimension and improved sensitivity . the method can be used for spectral editing and assignment . as for lls 10 , 15 , 16 , it may turn out to be possible to excite and sustain llc in groups involving more than two coupled spins . the numerical simulations have been performed using the package gamma 17 by subjecting an initial state defined by an operator ( i x − s x ) to a liouvillian including continuous rf irradiation and dipolar relaxation and describing the evolution by means of the liouville - von neumann equation . a spin system consisting of four spins was considered ( two aliphatic protons in each of the two residues gly - 75 and gly - 76 in the relatively mobile c - terminal loop of ubiquitin ), with spin interactions modulated at an effective correlation time τ c = 2 ns . ubiquitin with a natural isotopic distribution was dissolved in d 2 o to a concentration of 2 mm . the 2d spectra were acquired at t = 300 k and b 0 = 4 . 9 t ( 400 mhz ), using time - proportional phase increments 18 ( tppi ) in the indirect dimension . the amplitude of the continuous - wave rf irradiation was v 1 = 1 . 9 khz . each 2d experiment used 128 transients and a relaxation delay of 2 s . a semi - selective gaussian π pulse of 30 ms duration was used to invert the doublet of one of the two spins . m . carravetta , o . g . johannessen & amp ; 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