spin hyperpolarization by dissolution dynamic nuclear polarization ( d - dnp ) has become a major area of research in nmr .
this emerging method provides a way of boosting the sensitivity of nmr experiments by enhancing the intrinsically low nuclear spin polarization dictated by boltzmann s law .
thus , c  nmr signals of small molecules have been enhanced by up to four orders of magnitude.1 in a typical d - dnp experiment , the frozen sample is initially polarized at low temperatures and moderate fields , and the signals are subsequently measured in solution in a separate detection apparatus operating at room temperature .
this transfer , sometimes poetically called voyage , can be performed either manually or by means of a pneumatic system . during the voyage , the hyperpolarized molecules experience low magnetic fields ( sometimes as low as the earth s field , or even lower ) , which have detrimental effects on the enhanced polarization .
this is one of the reasons why d - dnp has been most useful for nuclear spins with long t1 , such as the isolated low - gamma quaternary c spin in 1-c pyruvic acid.2 on the other hand , apart from some exotic experiments,3 
 h spins have hardly been exploited by d - dnp , as their short t1 relaxation times mean that the hyperpolarization is driven back rapidly toward boltzmann equilibrium .
however , we have shown recently that h can be polarized very efficiently and rapidly up to pz(h)=91  % with a buildup time constant as short as dnp(h)=150  s at b0=6.7  t and t=1.2  k.4 one possible strategy for taking advantage of this large h hyperpolarization consists in storing the magnetization in the form of long - lived states ( lls)5 with extended lifetimes . in recent years , several successful studies combining d - dnp with lls6 have shown that hyperpolarized magnetization can be converted into lls with extended lifetimes tllst1 . in a pair of equivalent spins 1/2 , the singlet state s0=(|-|)/2 is largely disconnected from the triplet states t+1=| , t0=(|+|)/2 and t1=| because relaxation mechanisms that are symmetric with respect to spin exchange ( such as the dipole 
triplet transitions.7 therefore , if a triplet  singlet population imbalance ( tsi ) is prepared by any means , it is likely to be long - lived .
we use the expression tsi in analogy to the a / e imbalance ( aei ) recently described for methyl groups by benno meier et  al.8 both tsi and aei refer to a difference between the average populations of spin states belonging to different irreducible representations of the spin permutation group , that is , a and e in methyl groups and g and u ( or triplet and singlet states ) in pairs of equivalent spins .
the excitation and detection of an lls involving a pair of equivalent spins is challenging because the magnetic equivalence needs to be lifted during both excitation and detection but preserved during storage . in this context , two possible scenarios are : 1 )  in most experiments described so far , the symmetry is imposed on an otherwise inequivalent two - spin system during the storage period only , or 2 )  in this work , the symmetry of an inherently equivalent two - spin system is broken during both excitation and detection .
para - hydrogen9 offers the best example of nuclear singlet order in a molecule with two equivalent spins .
the singlet state of h2 can be produced at low temperatures ( typically 40  k ) in the presence of a paramagnetic catalyst , which allows singlet  triplet interconversion by lifting the symmetry of h2 near the catalytic surface .
the singlet spin state of h2 has the lowest energy , primarily determined by the quantization of its rotational state , and therefore , is predominantly populated at low temperatures .
this leads to the creation of a large tsi compared to h2 in boltzmann equilibrium at room temperature .
para - h2 is not magnetically active , and therefore can not be observed directly by nmr , but it can be converted into observable signals through an asymmetric hydrogenation reaction by which the two protons stemming from para - h2 become inequivalent . on the other hand ,
a symmetric hydrogenation process can generate a molecule in which the equivalence of the two protons is preserved .
this is the case , for example , for the hydrogenation of acetylene to form ethylene,10 or of dimethyl acetylene dicarboxylate to produce dimethyl maleate.11 the preserved para state can subsequently be rendered accessible to nmr by another chemical reaction that lifts the symmetry of the molecule .
if one starts with an inequivalent two - spin system , a precursor state , that is , a state that acquires a long - lived property as soon as the two spins are made equivalent during the storage interval , can be prepared by using suitable rf pulse sequences,12 by adiabatic transport to low fields,13 or by chemical reactions.6b alternatively , a compromise can be found by using systems containing nearly equivalent spins14 in which the singlet and triplet states are only weakly mixed , but with an admixture that can be augmented by suitable pulse sequences to induce a singlet - to - magnetization ( s2 m ) conversion .
most experiments in which d - dnp is combined with lls6a  e rely on rf pulse sequences to prepare the lls , usually after the transfer of the hyperpolarized sample to the detection magnet . as a result ,
however , tayler and co - workers6f have shown that lls order can be populated directly before the transfer by d - dnp for the two inequivalent c spins in 1,2-c2-pyruvic acid .
they pointed out that the polarization of the singlet state ps ( = ptsi , vide  supra ) is proportional to the square of the spin zeeman polarization pz ( i.e. , ptsi = ps=1/3pz ) . therefore , provided a high spin polarization can be reached by d - dnp , say pz=50  % , a significant amount of singlet order , in this example ptsi=8.33  % , can be created directly without any rf pulses . in the case where pz=91  % can be attained , one obtains ptsi=28  % .
such high levels of polarization can indeed be prepared directly by dnp for h at b0=6.7  t and t=1.2  k and indirectly for c or other nuclei through cross polarization from protons.4 in this work , we demonstrate that a tsi can be efficiently populated by d - dnp for the pair of magnetically equivalent h spins in fumarate , and that this is preserved in the liquid state after dissolution for a long time ttsi , which was estimated to be of the order of 50  s. we refer to this type of lls as hyperpolarized equivalent long - lived states ( hells ) .
we show how hells can be readily  revealed  by allowing fumarate to undergo a biologically relevant enzymatic conversion into malate .
for efficient d - dnp , the samples usually consist of frozen glassy solids containing typically 1050  mm polarizing agents such as tempol in addition to the molecules of interest . in our experiment ,
the molecule of interest shall possess two spins i and s that are magnetically equivalent in the liquid phase , but inequivalent in the frozen state and in moderate magnetic fields because they are exposed to slightly different environments and therefore experience different chemical shifts because of chemical shift anisotropies ( csas ) and different internuclear and electron  nuclear dipolar couplings . given that freezing to low temperatures lifts the equivalence ,
the energy levels are better expressed in the product basis ( pb ) . at t=1.2  k and b0=6.7  t ,
therefore , the deviations of diagonal elements from the demagnetized state =e will be ( n , n , n , n)=1/4(2pz+pz , pz , pz , 2pz+pz)=(0.003 , 0 , 0 , 0.003 ) . assuming , for simplicity , that dnp could confer a zeeman polarization pz=100  % , only the lowest energy level | would be populated by hyperpolarization , so that ( n , n , n , n)=(0.75 , 0.25 , 0.25 , 0.25 ) ( see figure  1  a : tsi preparation ) .
as soon as the polarized sample is heated and dissolved to the liquid state , csas and dipolar couplings are averaged out , so that the spins i and s become magnetically equivalent .
triplet basis ( stb ) . in our case , as n=n , ( and hence n=n ) , it is easily seen that (pb)=(stb ) [ and hence (pb)=(stb ) ] , with the following diagonal elements : ( n , n , n , n)=(nt+1 , nt0 , ns0 , nt1)=1/4(2pz+pz , pz , pz , 2pz+pz ) . hence , ptsi=ns01/3(nt+1+nt0+nt1)=pz/3 .
the tsi will thus result from the depletion of n and n by hyperpolarization ( figure  1  b ) .
the spins are equivalent , so the tsi can be stored indifferently in a low or high magnetic field ( in a magnetic path for example ) . during the storage period
, the populations of the three triplet states will equilibrate , that is , the deviations of the population of the three triplet levels will average out to give ( nt+1)=(nt0)=(nt1)=1/3(nt+1+nt0+nt1)=1/4pz/3 .
the system of two equivalent spins can then be transformed ( chemically or enzymatically ) into a system of two inequivalent spins , so that the  sealed  hyperpolarization can be  revealed  by conversion into observable magnetization .
if the reaction is fast and goes to completion , one can convert  from the stb back to the pb by using a suitable base transformation ( see ref . 
(pb ) resulting from this transformation can be expressed as a superposition of longitudinal two - spin order and zero - quantum coherence since (pb)=pz/6  ( 2izsz+2zqx ) .
schematic deviations of the populations from the fully saturated state =e among the energy levels of the two protons of fumarate a )  in the polarizer at 6.7  t and 1.2  k without dnp at boltzmann equilibrium ( pz(h)=0.57  % ) and after dnp polarization to the theoretical limit pz(h)=100  % , b )  during the transfer , which may go through low magnetic fields or through a magnetic tunnel to sustain a higher field , and c )  in the detection magnet , typically at 7  t and 300  k , where the spins are made inequivalent by an enzymatic conversion . in each scheme , the deviations of the diagonal elements from the demagnetized state =e are given as a function of the polarization pz . in ( c ) , the full density matrix is given to show the off - diagonal elements .
enzymatic reactions are not instantaneous , and do not necessarily lead to complete conversion into the product .
figure  2 shows an example of the conversion of fumarate into malate by fumarase under conditions that can be combined with d - dnp .
in fact , a highly polarized state =2izsz+2zqx is indeed produced instantaneously in malate whenever fumarate molecules carrying a tsi undergo an enzymatic conversion , but the zqx term immediately starts evolving under the difference of chemical shifts , and therefore rapidly dephases and averages to zero as the reaction proceeds .
furthermore , the hyperpolarized tsi of fumarate , once it is transferred to malate , will tend to relax to thermal boltzmann equilibrium .
enzymatic conversion of fumarate into malate by fumarase at 300  k monitored by integration of the conventional h  nmr signals of the two species .
the nuclear polarizations are in thermal boltzmann equilibrium , without resorting to dnp . a solution of fumarase ( 4  l , 5.8  mg  ml , i.e. , 10  units ) was injected into a fumarate solution ( 500  l , 50  mm ) at ph  8 in a buffer of 25  mm tris and 200  mm nacl .
it is , however , possible to  sustain  the lls of malate by so - called  high - field 
methods,7c ,  12 ,  15b for example , by applying an rf irradiation halfway between the two chemical shifts ( either continuous - wave ( cw ) , or , if desired , by applying a waltz-16 pulse train),16 thus preserving the full =2izsz+2zqx state .
this strategy allows one to slow down relaxation of 2izsz and prevent dephasing of zqx .
for the two inequivalent protons in malate , we thus determined tlls=6  s at b0=7  t and t=298  k. moreover , the use of waltz-16 pulse trains has the advantage of wiping out any single - quantum magnetization that would not arise from hells . a conventional lls detection sequence , for example , the second half of the 
sarkar sequence15b(figure  3 ) , can then be used to transform =2izsz+2zqx into observable magnetization .
after dissolution , the hyperpolarized solution containing fumarate that carries the tsi is transferred to a holding chamber just above the nmr tube to determine its lifetime ttsi during a variable preinjection delay tsi .
the fumarate solution is then injected into a solution containing fumarase to start the conversion of fumarate into malate , accompanied by a conversion of the tsi on fumarate into an lls on malate .
a waltz-16 pulse train is applied during the delay lls with the carrier halfway between the chemical shifts of the two protons of malate to make these two protons effectively equivalent .
sarkar sequence.15b the conversion of the lls into observable magnetization is most efficient when 1=1/(4  jis)and 2=1/(2is)(jis=10.4  hz and is=960  hz at 300  mhz ) .
the detection scheme can be repeated n times , bearing in mind that the lls on malate is replenished during each sustaining interval lls by enzymatic conversion of fumarate that carries a slowly relaxing tsi .
the lifetime of the lls of malate ( tlls=6  s at 300  mhz if the rf amplitude of the cw field is 1=3  khz ) is short compared to the enzymatic transformation , so the time lls ( see figure  3 ) allocated for the lls to accumulate in malate before it is converted into observable signals needs to be optimized carefully .
the concentrations [ f ] and [ m ] of fumarate and malate can be described by pseudo first - order kinetics as shown in equation  ( 1 ) , in which [ f](t ) and [ m](t ) are the concentrations of fumarate and malate , kfm and kmf are the apparent kinetic constants of the overall enzymatic conversion of fumarate into malate and vice  versa , without considering the details of the michaelis 
menten mechanism.(1 ) 
 1 the temporal evolution of the expectation value plls in malate arising from the conversion of fumarate can be obtained by solving numerically the rate equations [ eq . 
( 2 ) ] , in which ptsi and plls are the expectation values of the tsi in fumarate and of the lls in malate , and rtsi and rlls are their relaxation rates.(2 ) 
 2 the  apparent  rate constants kfm and kmf can be obtained by fitting the signal amplitudes in figure  2 to the rate equations in equation  ( 1 ) .
one can then calculate the temporal evolution of ptsi in fumarate in the presence of ten units of enzyme , as well as plls of malate obtained by the conversion of the tsi of fumarate into an lls of malate that relaxes with tlls ( figure  4 ) .
these curves were obtained by assuming that ttsi=60  s for fumarate ( on the basis of preliminary observations as discussed below ) , and using the experimentally determined time constant tlls=6  s for malate . according to figure  4 , the optimal delay to maximize the conversion of the tsi of fumarate into the lls of malate is 10  s. thus , one should wait lls=10  s while sustaining the lls by a suitable rf field before attempting to convert the lls of malate into observable magnetization .
the alternation of rf irradiation and signal observation can be repeated n times . during each interval
lls , the lls on malate will be replenished by the enzymatic conversion of the slowly relaxing tsi of fumarate .
the decay of the magnetically silent tsi of fumarate will be reflected indirectly in the decay of the malate signal as n increases .
moreover , it can be seen in figure  4  b that only around 1  % of the hells of fumarate is transferred to malate during each loop n=1 , 2 ,  ,
n. a )  temporal evolution of the ( unobservable ) ptsi of fumarate and b )  signal of malate obtained by numerical solution of equation  ( 2 ) with ttsi=60  s and tlls=6  s , and the apparent forward and backward rate constants kmf=4.510  s and kfm=3.710  s=0.825  kmf optimized by fitting the curves in figure  2 .
the vertical scale was increased 100  times in ( b ) to show the malate signal , which is barely visible as ( -- ) in ( a ) because of the slow rate of the enzymatic conversion .
a sample comprising ten frozen pellets of 10  l each of 0.5  m fumarate with 50  mm tempol was hyperpolarized by microwave irradiation at b0=6.7  t and t=1.2  k for about 20  min .
the sample was then dissolved , together with ten frozen pellets of 10  l each of 3  m sodium ascorbate in d2o,17 with 5  ml d2o at 400  k and 1.0  mpa , and transferred in 4.5  s to a holding chamber just above the magnetic center of a 7  t nmr ( 300  mhz ) spectrometer , where the static field is bhold>6.5  t. after a preinjection delay 1<tsi<60  s , which allows one to assess the lifetime ttsi of the tsi ( ptsi ) of hyperpolarized fumarate in the holding chamber , the solution was injected into a 5  mm nmr tube containing fumarase to start the conversion of fumarate into malate , and to transfer concomitantly the tsi of fumarate into an lls on malate .
the latter was sustained by a waltz-16 pulse train with an rf amplitude 1=3  khz .
the sequence of figure  3 was then used to convert the lls of malate into observable magnetization .
figure  5  d shows four spectra of malate acquired at 7  s intervals ( n=4 loops , each comprising a sustaining interval lls=6  s and an acquisition time of 1  s ) after the injection of hyperpolarized fumarate into the nmr tube containing fumarase . in this case , the preinjection delay tsi=1  s during which the fumarate was kept in the holding chamber was negligible compared with ttsi .
the enzymatic conversion is relatively slow , so the signals in figure  5  d arise from the conversion of a small fraction of fumarate into malate ( 1  % every 7  s , according to figure  4  b ) .
the decay of the malate signal with increasing n reflects 1 )  the decay of the inaccessible tsi of fumarate with a time constant ttsi owing to its relaxation ( believed to be very slow ) , 2 )  the consumption of fumarate with a time constant 1/kfm owing to its enzymatic conversion into malate , and 3 )  the decay of the lls of malate with a time constant tlls=6  s ( figure  4  a ) .
however , it is risky to extract a reliable estimate of ttsi from numerical fits of a single decay .
a )  conventional nmr spectrum excited by a 90 pulse 25  min after injection into a solution containing fumarase , when the enzymatic reaction has reached a steady state and the hyperpolarization ( both ptsi in fumarate and plls in malate ) has decayed to thermal equilibrium .
the hdo peak was attenuated by presaturation with a selective pulse with an rf amplitude of 75  hz and a duration of 5  s. b )  spectrum of malate ( without significant stopover in the holding chamber since tsi=1  sttsi ) recorded with the sequence of figure  3 , shortly after injection ( n=1 ) into a solution containing fumarase in the 7  t nmr system .
c )  spectrum of malate recorded after keeping the hyperpolarized fumarate for tsi=60  s in the holding chamber at b0>6.5  t prior to injection into the fumarase solution .
d )  the first four spectra of malate acquired with n=1 , 2 , 3 , and 4 at intervals of 7  s using the sequence in figure  3 ( tsi=1  s , lls=6  s , acquisition time 1  s ) showing that plls is replenished through the enzymatic reaction .
the lifetime ttsi can be estimated more accurately by repeating the entire experiment such that the fumarate that carries the hyperpolarized tsi is kept in the holding chamber during a longer preinjection delay tsi=60  s. although it is challenging to reproduce the experiment under identical conditions , we observed that the remaining signal of malate after tsi=60  s was reduced by a factor of approximately 3.5 ( figure  5  b , c ) , implying that ttsi50  s. this is somewhat shorter than the lifetime ttsi=270 
s reported by zhang et  al.11 for deuterated dimethyl maleate produced by the addition of para - h2 to deuterated dimethyl acetylene dicarboxylate .
this discrepancy may be caused by the presence of dissolved paramagnetic triplet oxygen in the superheated water used in our dissolution experiments , or to the presence of some residual tempol radicals , as the reduction by ascorbate may not be quantitative . because the waltz-16 pulse train destroys magnetization arising from any sources other than hells , single - quantum terms arising either from d - dnp or from a partial return to thermal boltzmann equilibrium are wiped out ( compare figure  5  b , c with figure  5  a ) .
the detected signals can therefore unambiguously be traced back to the tsi of fumarate prepared by d - dnp , stored in the holding chamber for a time tsi , and converted into lls on malate by the enzyme .
the remaining peaks of fumarate and hdo in the spectrum of figure  5  b probably stem from hyperpolarized single - quantum magnetization that was not fully saturated by the waltz-16 pulse train and was brought into the active volume of the rf coil by convection .
we have shown that a pure tsi can be created readily by d - dnp in a system that contains two magnetically equivalent spins in solution .
once dissolved , this imbalance displays a lifetime ttsi that is much longer than the longitudinal relaxation time t1 .
we believe this to be the first proof of principle of the creation of hyperpolarized long - lived states for equivalent spins ( hells ) by d - dnp .
such a long - lived spin order can be used readily to monitor a slow enzymatic process of biochemical relevance , but may find applications in other areas of magnetic resonance such as imaging ( mri ) , for which hyperpolarization by d - dnp has become a technique of choice to enable metabolic imaging , and in which short lifetimes of hyperpolarized molecules are usually a major limitation .
the hells methodology will be applied to more challenging molecules containing magnetically equivalent pairs of spins , such as ch2rr , ch2cl2 , and possibly h2o .
we are currently investigating molecules with interesting lifetimes and interesting chemical or biochemical properties that can be addressed by hells .
as fumarate plays a crucial role in the krebs cycle , it may be of interest for in  vivo studies as it has been demonstrated to be a probe for cellular necrosis.18
solutions of 0.5  m dibasic sodium fumarate ( sigma  aldrich ) in the glass - forming mixture d2o:[d6]ethanol ( 60:40 v / v ) were doped with 50  mm tempol ( sigma  aldrich ) .
ten frozen pellets of 10  l each of this mixture were inserted in the polarizer , along with ten frozen pellets of 10  l each containing 3  m ascorbate ( sigma  aldrich ) in d2o to scavenge the radicals after dissolution.17 dnp was performed at 1.2  k and 6.7  t in a home - built polarizer by applying frequency - modulated microwave irradiation19 at fw=188.3  ghz and pw=100  mw , with a modulation frequency of 10  khz and modulation amplitude of 50  mhz .
the polarized pellets were dissolved in 0.7  s with 5  ml d2o , preheated to t=400  k at p=1.0  mpa , and transferred in 4.5  s to a 7  t ( 300  mhz ) magnet by pushing with helium gas at 0.6  mpa through a ptfe tube ( 1.5  mm inner diameter ) running through a magnetic tunnel ( 3  m length ) .
the hyperpolarized solution was kept at b0>6.5  t in a holding chamber just above the nmr sample tube for a variable delay tsi to monitor the relaxation of the tsi of fumarate .
the sample was then injected in 2  s into an nmr tube containing d2o ( 200  l ) for field - frequency locking , nacl ( 200  mm ) and tris buffer ( 25  mm ) , and fumarase ( 5  l , 5.8  mg  ml , 12.5  units ) from porcine heart ( sigma  aldrich ) .
finally , the lls detection sequence described in figure  3 was applied with n sustaining delays of lls=6  s each with waltz-16 irradiation .
solutions of 0.5  m dibasic sodium fumarate ( sigma  aldrich ) in the glass - forming mixture d2o:[d6]ethanol ( 60:40 v / v ) were doped with 50  mm tempol ( sigma  aldrich ) .
ten frozen pellets of 10  l each of this mixture were inserted in the polarizer , along with ten frozen pellets of 10  l each containing 3  m ascorbate ( sigma  aldrich ) in d2o to scavenge the radicals after dissolution.17
dnp was performed at 1.2  k and 6.7  t in a home - built polarizer by applying frequency - modulated microwave irradiation19 at fw=188.3  ghz and pw=100  mw , with a modulation frequency of 10  khz and modulation amplitude of 50  mhz .
the polarized pellets were dissolved in 0.7  s with 5  ml d2o , preheated to t=400  k at p=1.0  mpa , and transferred in 4.5  s to a 7  t ( 300  mhz ) magnet by pushing with helium gas at 0.6  mpa through a ptfe tube ( 1.5  mm inner diameter ) running through a magnetic tunnel ( 3  m length ) .
the hyperpolarized solution was kept at b0>6.5  t in a holding chamber just above the nmr sample tube for a variable delay tsi to monitor the relaxation of the tsi of fumarate .
the sample was then injected in 2  s into an nmr tube containing d2o ( 200  l ) for field - frequency locking , nacl ( 200  mm ) and tris buffer ( 25  mm ) , and fumarase ( 5  l , 5.8  mg  ml , 12.5  units ) from porcine heart ( sigma  aldrich ) .
finally , the lls detection sequence described in figure  3 was applied with n sustaining delays of lls=6  s each with waltz-16 irradiation .
 hyperpolarization by dissolution dynamic nuclear polarization ( d - dnp ) offers a way of enhancing nmr signals by up to five orders of magnitude in metabolites and other small molecules . nevertheless , the lifetime of hyperpolarization is inexorably limited , as it decays toward thermal equilibrium with the nuclear spin - lattice relaxation time . 
 this lifetime can be extended by storing the hyperpolarization in the form of long - lived states ( lls ) that are immune to most dominant relaxation mechanisms . 
 levitt and co - workers have shown how lls can be prepared for a pair of inequivalent spins by d - dnp . here , we demonstrate that this approach can also be applied to magnetically equivalent pairs of spins such as the two protons of fumarate , which can have very long lls lifetimes . as in the case of para - hydrogen , these hyperpolarized equivalent lls ( hells ) 
 are not magnetically active . however , a chemical reaction such as the enzymatic conversion of fumarate into malate can break the magnetic equivalence and reveal intense nmr signals . 
Introduction
Experiments
Results
Conclusion
Experimental Section
DNP samples
DNP polarization and dissolution
Enzymatic detection