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Utilizing the Scalar Order of Parahydrogen

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He and his colleagues at HMRI have been instrumental in all aspects of the experimental work. Nuclear magnetic resonance (NMR) pulse sequences are designed to perform efficient spin order transfer through the scalar spin couplings between the two nascent protons and a heteronuclear spin label target.

History and Introduction

These and other discoveries formed the basis for making the nucleus a sensitive probe of the local molecular environment. Although NMR is powerful as a sensitive probe of molecular structure and dynamics, it is also very insensitive.

Figure 1.  The separation of energy levels between states of protons with their magnetic moment  aligned  with  the  field  and  against  the  field  is  dependent  upon  the  magnitude  of  the  field.   This  energy 
Figure 1.  The separation of energy levels between states of protons with their magnetic moment  aligned  with  the  field  and  against  the  field  is  dependent  upon  the  magnitude  of  the  field.   This  energy 

Increasing polarization

Although these techniques increase the polarization available for detection of these heteronuclei, it is by factors on the order of the ratio of the gyromagnetic ratios. Although these are important improvements over the equilibrium values, the actual population difference remains the same order of magnitude as for protons at equilibrium.

Hyperpolarization

The possible signal amplification from the technique depends on the purity of the spin state of the reactant hydrogen. The value of θ depends on the scalar coupling constants of the system as defined in Eq.

Figure 2.  Simulated  PASADENA  spectrum 10 ms after reaction for a) the  reaction of 1‐bromo‐2‐
Figure 2.  Simulated  PASADENA  spectrum 10 ms after reaction for a) the  reaction of 1‐bromo‐2‐

Recent advances

When the injected molecule reacts to form daughter molecules that are also hyperpolarized, those new molecules are initially at much lower concentration than the initial molecule, and thus have much lower signal. Also, the signal from the initial molecule can overwhelm the signal from the lower concentration products.

Overview of thesis sections

Background

Parahydrogen

The rotational part of the wave function is characterized by the eigenfunctions of a rigid rotor. The lowest energy state of a system is that where the system is in a spin singlet state.

PASADENA

In practice, a catalyst is needed that allows sufficient mixing of the spin states to bring the pattern into equilibrium in a reasonable time. This is accomplished by chemically synthesizing the molecule of interest by adding a parahydrogen molecule across a double or triple bond in a way that preserves the spin state of both protons.

Order Preservation

For the case of two spins (23), this "time suspension" of the spins while the chemical reaction product accumulates increases the achievable polarization by a factor of two, allowing P P= f ideally. Thus, decoupling allows all the order from the parahydrogen to be available to the experimenter within a new molecule.

Three Spin System

Pulse sequence algorithms

The effective strategy turns out to depend non-trivially on the coupling ratio through the parameter θ (Eq. To better address these cases, new algorithms have been introduced that use pulses in the system to effectively change the mean of the Hamiltonian by turning off parts of the Hamiltonian in Eq. 16) during one or more evolution periods develop.

Medium range pulse sequence algorithm

  • Algorithm for θ π = 4
  • Modifications for a larger range
  • Operation in real systems
  • Behavior under experimental error

The pulse sequences derived from the medium θ algorithm are specific to the coupling constants of the given molecule. Contour plot of the percent polarization on the target 31P core generated by the pulse sequence derived for 1-phenylethylphenylphosphinic acid over a wide range of similar scalar coupling constants.

Figure  6.    Schematic  of  the  medium  θ  pulse  sequence  algorithm.    The  main  pulses  of  the  algorithm  are shown  in black and  recommended  echo  pulses  are  shown  in grey.  Solid pulses are  π  and  open pulses are  π 2 .  The echo pulses o
Figure  6.    Schematic  of  the  medium  θ  pulse  sequence  algorithm.    The  main  pulses  of  the  algorithm  are shown  in black and  recommended  echo  pulses  are  shown  in grey.  Solid pulses are  π  and  open pulses are  π 2 .  The echo pulses o

Small range pulse sequence algorithm

Algorithm for the limit θ → 0

At the large end of the range, an example is the molecule ethylphosphonyl dichloride, where the target is 31P. An example of a molecule representing the lower part of the small θ region is diethylmercury, where 199Hg is the target nucleus.

Figure 18.  Schematic of the small  θ  range pulse sequence.  The main pulses of the algorithm are  dark  and  recommended  echo pulses are light.  Solid  pulses are  π ,  open pulses are  π 2 ,  and decoupling  uses a typical cyclic method that returns th
Figure 18.  Schematic of the small  θ  range pulse sequence.  The main pulses of the algorithm are  dark  and  recommended  echo pulses are light.  Solid  pulses are  π ,  open pulses are  π 2 ,  and decoupling  uses a typical cyclic method that returns th

Large range pulse sequence algorithm

Fixed pulses are π, open pulses are π 2, and decoupling uses a cyclic method that returns the polarization to the starting point, such as MLEV‐16. Therefore, the value of τ1l =τ3l must be forced to the integer or half-integer multiple of τres that is closest to the prescribed time given by Eq.

Figure  22.    Schematic  of  the  large  θ  range  pulse  sequence.    The  number  of  pulses  in  the  J‐
Figure  22.    Schematic  of  the  large  θ  range  pulse  sequence.    The  number  of  pulses  in  the  J‐

Modifications for more consistent polarization

A means of redirecting the chemical shift of the target and mitigating the effects of tracer isotopes is also required. Expected efficiency of the pulse sequence obtained for 15N-choline if the scalar coupling values ​​differ from those in the literature.

Figure  23.  The  wait  times  required  by  the  large θ  sequence  algorithm  generally  need  to  be  optimized  in  order  to  achieve  unity  polarization.    The  total  time  for  the  sequence  as  calculated (line)  is  compared to the total  of 
Figure  23.  The  wait  times  required  by  the  large θ  sequence  algorithm  generally  need  to  be  optimized  in  order  to  achieve  unity  polarization.    The  total  time  for  the  sequence  as  calculated (line)  is  compared to the total  of 

Comparison of sequence algorithms

Second, when 0.3532< ≤θ arctan 1 2( ), both algorithms generate sequences that perform similarly, with only a small time advantage found when using the small-range sequence. The time performance of the small (solid) and medium (dotted) range pulse sequences over the range in which one or both generate unit polarization.

A large θ pulse train algorithm will always provide a fully polarized target core when relaxation is neglected. Time performance of the optimized large-pulse sequence algorithm compared to different variants of the medium-pulse sequence algorithm that can provide 50% polarization to the target nucleus.

Figure 28.  The time performance of the optimized large pulse sequence algorithm, compared to  that  of  various  versions  of  the  medium  pulse  sequence  algorithm  which  are  able  to  deliver  99%,  90%,  75%, or  50%  polarization  to  the  target 
Figure 28.  The time performance of the optimized large pulse sequence algorithm, compared to  that  of  various  versions  of  the  medium  pulse  sequence  algorithm  which  are  able  to  deliver  99%,  90%,  75%, or  50%  polarization  to  the  target 

Instrumentation and execution

Instrument hardware

The reactor is surrounded by a solenoid electromagnet that provides a stable magnetic field Bo in the z direction along the axis of the reactor. The board also has analog outputs, one of which is the input to the amplifier that powers the B1 saddle coil to generate the pulses used to provide the pulse sequence for hyperpolarization of the product molecules in the reactor.

Figure  29.  Schematic  of  the  reactor system.   The  aqueous  mixture  of precursor and  catalyst  is 
Figure  29.  Schematic  of  the  reactor system.   The  aqueous  mixture  of precursor and  catalyst  is 

Computer program

Only one type of "pulse" step can be used during a particular run of a pulse program. This variable contains the type of isotope, the carrier frequency of the isotope at the given static field, the amplitude (which must be set from calibration), and the π 2 times for different pulse types.

Figure  32.    Flow  chart  of  the  pulse  program  described  in  the  text  including  manual  and 
Figure  32.    Flow  chart  of  the  pulse  program  described  in  the  text  including  manual  and 

Field calibration

The test pulse is activated, then the sample is moved back to the high-field instrument. A π 2 pulse is applied to the sample in the high-field spectrometer, and the amplitude of the signal indicates the magnitude of the longitudinal polarization after the test pulse.

Figure 33.  Experimental data points showing an example of a  calibration curve for determining  the static field using a  13 C pulse applied to deuterated and 1‐ 13 C labeled acetate.  The line is intended only  as an aid for the eye. 
Figure 33.  Experimental data points showing an example of a  calibration curve for determining  the static field using a  13 C pulse applied to deuterated and 1‐ 13 C labeled acetate.  The line is intended only  as an aid for the eye. 

Pulse calibration

Polarization

Of the four terms in the Hamiltonian, only the first two lead to important evolution. An example of the sequence of the steps of the experiment is illustrated in Fig. The line is the least squares fit of the experimental data points to the functional.

In some cases, the transport of the sample to the high-field instrument was carried out pneumatically.

Polarization verification

This technique is complicated by the extra scalar couplings in the case of the three-spin system required for heteronuclear PASADENA. When a nucleus connects to two coupled protons, the polarization of that nucleus is visible in the peak pattern of the protons.

Figure  35.  When a nucleus  couples  to  a  proton,  the  polarization  of  that  nucleus is apparent  in 
Figure  35.  When a nucleus  couples  to  a  proton,  the  polarization  of  that  nucleus is apparent  in 

Molecule selection and characterization

  • Measurement of T 1
  • Measurement of coupling constants
  • Molecular variations
  • Low field effects

When possible, this strategy can also be used to quickly measure relaxation time. To do this, the relaxation of the inversion of the enhanced state to equilibrium is subtracted from the relaxation of the enhanced state to equilibrium, resulting in decay to zero.

Lab frame introduction

In the rotating frame, the deviations from the path of the magnetization from a smooth arc are clearly visible, while in the laboratory frame these deviations are hidden by the larger effect of precession. In this case, those parts of the Hamiltonian that depend on the relative frequency between the nuclei are neglected.

Figure 37.  Comparison of the lab frame and rotating frame.  The two plots follow the rotation of  a unit vector of magnetization  acted on by a  four  cycle linear square inversion pulse in (a)  the lab frame  and (b) the rotating frame.  In the rotating 
Figure 37.  Comparison of the lab frame and rotating frame.  The two plots follow the rotation of  a unit vector of magnetization  acted on by a  four  cycle linear square inversion pulse in (a)  the lab frame  and (b) the rotating frame.  In the rotating 

Using GAMMA for lab frame calculations

As such, it provides a useful framework for modeling NMR experiments in the usual spin multiplication frame and in the laboratory frame for comparison. Shaped pulses in the multiple rotating frame version of GAMMA are defined as a similar series of piecewise constant segments in the rotating frame appropriate for the Larmor frequencies of each kernel.

Pulse length at low field

In the laboratory setting, the circularly polarized pulse (dotted) shows uniform Rabi frequency, but the linear pulse (solid) does not and requires careful selection of. The choice of the total length of the pulse among the allowed lengths is much more complicated.

Figure 38.  The optimal static field and pulse strength to give near perfect inversion with  square  pulses that are near four cycles of the carrier frequency long at a few example wavelet phases as shown in  the legend. 
Figure 38.  The optimal static field and pulse strength to give near perfect inversion with  square  pulses that are near four cycles of the carrier frequency long at a few example wavelet phases as shown in  the legend. 

Unintended nutation of other isotopes

These are square pulses that are six periods of the carrier wave of the target nucleus. This is due to the relative sensitivity of the nuclei and the consequences of this sensitivity.

Figure  40.    Pulses  intended  for  one  isotope  have  significant  affect  on  other  isotopes  in  the 
Figure  40.    Pulses  intended  for  one  isotope  have  significant  affect  on  other  isotopes  in  the 

Bloch‐Siegert effects

Therefore, it would be reasonable to construct an instrument capable of emitting a circularly polarized pulse in order to overcome some of the problems associated with the use of a low field. However, circular polarization only helps with an on-resonant isotope; the effects of each pulse on other isotopes continue to be a problem, and the selectivity of this problem is even increased in some cases.

Wavelet phase dependence

Solutions for wavelet phase dependence

The key to performing a successful low-field pulsing experiment is to find a method that reduces these effects to an acceptable level without causing other problems that are unacceptable for the particular experiment.

Increase pulse time

Only allow certain wavelet phases

Composite pulses

The alternative composite (π 2 ) (x π 2 ) (y π 2 ) x (solid line) shows very little dependence on wave phase at the price of incomplete inversion for all. are proton pulses with a square envelope. The carrier frequency and γHB0 are set to 75 kHz and γHB1 is set so that perfect inversion is possible in one wave phase for the first pulse and set to give the best overall inversion for the second pulse.

Figure  46.    A  well  constructed  composite  pulse  can  reduce  the  wavelet  phase  dependence  or  simply  change  it.    The  well  known  ( π 2 ) x π πy( 2 ) x  pulse  (dotted  line)  shows  as  much  variation  in  the 
Figure  46.    A  well  constructed  composite  pulse  can  reduce  the  wavelet  phase  dependence  or  simply  change  it.    The  well  known  ( π 2 ) x π πy( 2 ) x  pulse  (dotted  line)  shows  as  much  variation  in  the 

Shaped pulses

Further Considerations

Although the well-known Zeeman polarization is generally the spin order of choice in an NMR experiment, other types of spin order have been used. Using the spin order transfer algorithms described in reverse would allow singlet spin order to be generated starting from Zeeman order.

Refocused INEPT

In any application, the magnitude of the gradient is limited by the physical constraints of the system. In cases where the chemical shift of the protons is sufficient, selective pulses can be used to confine the transferred Zeeman spin order to one of the protons when the.

Figure  51.    Expected  average  polarization  on  the  two  protons  of  succinate  from  molecular  addition of hydrogen to a deuterated precursor in base as a percentage of the starting polarization on the  heteronucleus  for  guiding  the  choice  of 
Figure  51.    Expected  average  polarization  on  the  two  protons  of  succinate  from  molecular  addition of hydrogen to a deuterated precursor in base as a percentage of the starting polarization on the  heteronucleus  for  guiding  the  choice  of 

Generation of singlet order

For TFPP, which was demonstrated with an unselective refocused INEPT sequence (48), any of the three distinct protonated sites to which polarization transfer was observed could be chosen for selective transfer, since they are all separated by more than 1 PPM. Selective polarization transfer was demonstrated to the nine equivalent methyl protons by including a single selective π pulse within the refocused INEPT sequence ( 49 ).

Conclusions

Solution conformation of proteinase inhibitor-IIA from bull seminal plasma by 1H nuclear magnetic resonance and distance geometry.

Gambar

Figure 2.  Simulated  PASADENA  spectrum 10 ms after reaction for a) the  reaction of 1‐bromo‐2‐
Figure 4.  The mole fraction of parahydrogen in a hydrogen sample as a function of temperature. 
Figure  7.    Coordinates  for  graphically  describing  the  evolution  of  K x  under  the  intrinsic  Hamiltonian. 
Figure  8.   Evolution  of the system  during the first  two  wait  times.   In the space  defined  by  the 
+7

Referensi

Unduh sekarang ( PDF - 150 Halaman - 1.59 MB )

Garis besar

Operation in real systems Behavior under experimental error Algorithm for the limit θ → 0 Instrument hardware Computer program Shaped pulses Refocused INEPT

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