# Metabolic Reactions Studied by Zero- and Low-Field Nuclear Magnetic
Resonance

James Eills  Institute for Bioengineering of Catalonia, Barcelona Institute of
Science and Technology, 08028 Barcelona, Spain<EMAIL_ADDRESS>Román
Picazo-Frutos  Helmholtz-Institut Mainz, GSI Helmholtzzentrum für
Schwerionenforschung, 55128 Mainz, Germany  Oksana Bondar  Department of
Molecular Biotechnology and Health Sciences, Center of Molecular Imaging,
University of Turin, 10126 Turin, Italy  Eleonora Cavallari  Department of
Molecular Biotechnology and Health Sciences, Center of Molecular Imaging,
University of Turin, 10126 Turin, Italy  Carla Carrera  Institute of
Biostructures and Bioimaging, National Research Council of Italy, Turin, 10126
Italy  Sylwia J. Barker  School of Chemistry, University of Southampton, SO17
1BJ Southampton, United Kingdom  Marcel Utz  School of Chemistry, University
of Southampton, SO17 1BJ Southampton, United Kingdom  Silvio Aime  Department
of Molecular Biotechnology and Health Sciences, Center of Molecular Imaging,
University of Turin, 10126 Turin, Italy  Francesca Reineri  Department of
Molecular Biotechnology and Health Sciences, Center of Molecular Imaging,
University of Turin, 10126 Turin, Italy  Dmitry Budker  Helmholtz-Institut
Mainz, GSI Helmholtzzentrum für Schwerionenforschung, 55128 Mainz, Germany
John W. Blanchard  Helmholtz-Institut Mainz, GSI Helmholtzzentrum für
Schwerionenforschung, 55128 Mainz, Germany

###### Abstract

State-of-the-art magnetic resonance imaging uses hyperpolarized molecules to
track metabolism in vivo, but large superconducting magnets are required, and
the strong magnetic fields largely preclude measurement in the presence of
conductive materials and magnify problems of magnetic susceptibility
inhomogeneity. Operating at zero and low field circumvents these limitations,
but until now has not been possible due to limited sensitivity. We show that
zero- and low-field nuclear magnetic resonance can be used for probing two
important metabolic reactions: the conversion of hyperpolarized fumarate to
malate and pyruvate to lactate. This work paves the way to a heretofore
unexplored class of biomedical imaging applications.

Helmholtz-Institut Mainz, GSI Helmholtzzentrum für Schwerionenforschung, 55128
Mainz, Germany Institute for Physics, Johannes Gutenberg-Universität Mainz,
55099 Mainz, Germany Institute for Physics, Johannes Gutenberg-Universität
Mainz, 55099 Mainz, Germany Institute for Physics, Johannes Gutenberg-
Universität Mainz, 55099 Mainz, Germany Department of Physics, University of
California at Berkeley, 94720 Berkeley, U.S.A. NVision Imaging Technologies
GmbH, 89081 Ulm, Germany

##  1 Introduction

Nuclear magnetic resonance (NMR) is among the most important spectroscopic
techniques for chemical analysis and biochemical structure elucidation, and
the imaging modality (MRI) is an invaluable diagnostic tool for non-invasive
medical imaging. NMR has the potential to be even more widely applicable if
the nuclear-spin polarization could be boosted beyond its thermal equilibrium
value of $\approx 10^{-5}$ for samples at room temperature in experimentally
achievable magnetic fields. In recent years, nuclear-spin hyperpolarization
techniques – physical and chemical methods to increase NMR signals by 4-5
orders of magnitude 1, 2 – have enabled a new application: hyperpolarized
metabolic imaging.3 Small molecules can be hyperpolarized and injected in
vivo, and tracking their metabolism can yield diagnostic information about
disease progression and treatment response.4, 5 Even with enhanced signals,
conventional high-field magnetic resonance has some drawbacks: (1) high-
resolution spectroscopy is generally only achievable in homogeneous samples;
(2) the high-frequency signals are distorted by and do not readily penetrate
conductive materials, due to the skin effect; (3) MRI scans are not advised
for women in the early stages of pregnancy, or for patients with medical
implants, and; (4) high-field magnets are bulky, heavy, and expensive to
operate - they cannot be deployed in the field which hinders, for example,
point-of-care diagnostics.

Figure 1:  Measurement of hyperpolarized [1–13C]fumarate. (a) Experimental
apparatus. (b) Schematic of the QuSpin OPM placement around the sample,
showing the sensitive axes of the OPMs and the magnetic field lines of a
magnetic sample polarized along the $z$ axis. (c) The hyperpolarization
process for [1–13C]fumarate. The [1–13C]fumarate $J$-couplings are shown in
the inset. (d) Magnetic field ‘pulse’ sequence used for the zero-field
experiments. (e) Zero-field time-domain signal measured along the $x$\- and
$z$-axes of the OPMs generated from a sample of 13C polarized [1–13C]fumarate.
(f) Zero-field spectrum (black) resulting from the Fourier transform of the
z-axis signal. A simulated spectrum is shown beneath in magenta. (g) Magnetic
field ‘pulse’ sequence used for the low-field experiments. (h) Low-field time-
domain signal measured along the $x$\- and $z$-axes of the OPMS generated from
a sample of 13C polarized [1–13C]fumarate. (i) Low-field spectrum (black)
resulting from the Fourier transform of the $z$-axis signal. A simulated
spectrum is shown beneath in magenta.

These disadvantages can be circumvented through the use of an alternative
modality, zero- to ultralow-field (ZULF) NMR, in which measurements are
performed in the absence of a strong magnetic field 6, 7. In this field
regime, chemical shifts are negligible, and the dominant nuclear-spin
interactions are spin-spin ($J$) couplings, which are typically on the order
of Hz to hundreds of Hz. At these low frequencies, conductive materials have a
negligible effect on signals, and because susceptibility-induced magnetic-
field gradients are proportional to the applied field strength, resolution is
unaffected even in complex heterogeneous samples 8, 9. Even though ZULF
spectra do not contain chemical-shift information, individual molecules can
still be identified with high specificity, since the $J$-couplings provide a
means of chemical fingerprinting.10, 11 This is especially simple for
hyperpolarized systems in which only selected chemical species are initially
hyperpolarized, and only these molecules and their downstream products
contribute to the observable signal.

Nevertheless, at such low frequencies of the electromagnetic signals,
inductive detection is inefficient, and ZULF NMR has relied on highly
sensitive superconducting quantum interference devices (SQUIDs), and more
recently on optically pumped magnetometers (OPMs), that are able to detect
magnetic signals with sensitivities on the order of
$\text{fT}/\sqrt{\text{Hz}}$.12, 13 The primary use of OPMs is for
magnetoencephalography (MEG), which is a separate technique for mapping out
brain activity based on the magnetic fields produced by neuronal currents. 14,
15 Despite the exquisite sensitivity offered by OPMs, detection of zero-field
NMR signals is approximately 2 to 3 orders of magnitude less sensitive than
inductive detection at ca. 7 T, assuming the same spin polarization and the
same sample/detector geometry. The lower sensitivity of ZULF NMR has so far
generally precluded applications, particularly in a biomedical context given
the intrinsically low concentrations of biomolecules in biological systems.

In this work we combine recent advances in parahydrogen-based
hyperpolarization methods with state-of-the-art magnetometry to demonstrate
that metabolic transformations can be observed in zero- and low-field NMR
experiments. We investigated two model enzymatic processes: the conversion of
fumarate into malate, which is used in vivo as a marker of cell necrosis 16
and the conversion of pyruvate into lactate, which is by far the most widely-
used metabolic process in hyperpolarization-enhanced imaging.17 Hyperpolarized
13C-labeled metabolites were prepared via parahydrogen-induced polarization
(PHIP)18, 19, which involves chemically reacting a precursor molecule with
molecular hydrogen in the nuclear-spin singlet state (parahydrogen) to yield a
hyperpolarized product molecule. The entangled state of the 1H nuclear-spin
pair can be converted into a magnetic state of the 13C spin via a magnetic
field sweep.20, 21 Preparing the molecules in a 13C-polarized state
facilitates the detection of metabolic transformations, since as long as a
magnetic field of $\gtrapprox$1 $\mu$T is applied to the sample, the 13C
nuclei will remain polarized during chemical transformations. We show that the
combination of PHIP and ZULF NMR enables the study of biological systems using
magnetic resonance in portable devices, without the need for bulky permanent
or superconducting magnets.

Figure 2:  Zero- to low-field NMR spectra of [1–13C]fumarate, measured using
the pulse sequence in Fig. 1(g) (or Fig. 1(d) for the 0 nT spectrum) at
different background magnetic fields. Noise peaks at 27, 50 and 150 Hz have
been partially greyed-out for clarity.

##  2 Results

A schematic of the experimental arrangement is shown in Fig. 1(a). Samples in
5-mm glass NMR tubes were placed in a magnetic shield and measured with two
optically pumped magnetometers.22 A set of three orthogonal Helmholtz coils
was present inside the shield to generate magnetic fields for control of the
spin states and their dynamics. Furthermore, the sample was located within a
long solenoid coil that pierced through the magnetic shield along the $y$
axis, allowing for a magnetic field to be applied to the sample without
significantly affecting the magnetometers.23 The staggered arrangement of the
magnetometers was chosen to reduce common-mode noise while maximizing the
signal from the sample; a gradiometric detection scheme.24 As illustrated in
Fig. 1(b), the magnetic field produced by the nuclear spins in the sample has
opposite sign at the locations of the two sensors. In contrast, many noise
sources which are centered further from the detectors (e.g., Johnson noise
from the magnetic shielding, or vibrations in the room) produce magnetic
fields that are more homogeneous at the positions of the OPMs. By measuring
the difference in the outputs from the two sensors, signals from the sample
are combined constructively, and common-mode noise is cancelled. Because the
sensors have two sensitive axes, it was possible to independently measure
magnetic fields corresponding to magnetization along $x$ and $z$.

Initial experiments to develop and test the pulse sequences were carried out
using the hyperpolarized contrast agent [1-13C]fumarate, since this molecule
comprises a simple three-spin system with the magnetic equivalence of the two
parahydrogen protons lifted by asymmetric $J$-couplings to the 13C spin.25 To
prepare the molecule, a precursor was hydrogenated using para-enriched
hydrogen, and a magnetic field cycle was used to transform the proton singlet
order into 13C magnetization.26 Using this method we produced solutions of
approximately 80 mM [1-13C]fumarate at $\approx$ 30% 13C polarization. The
hyperpolarization process and molecular $J$-couplings are shown in Fig. 1(c),
and further details are provided in the Materials and Methods.

In this work, NMR experiments were performed in two field regimes: zero field,
defined as the regime where the nuclear Larmor frequencies are negligible
compared to the electron-mediated indirect spin-spin ($J$) coupling, and low
field, where the nuclear Larmor frequencies are larger than the $J$-couplings,
but chemical shifts are smaller than the resonance width. The pulse sequence
for the zero-field NMR experiments is shown in Fig. 1(d). The magnetization is
rotated from the $y$ axis to the $z$ axis, after which the applied magnetic
fields are suddenly turned off, resulting in the magnetic signal shown in Fig.
1(e). The spectrum resulting from the Fourier transform of this signal is
shown in Fig. 1(f). The main feature is the peak at 6.9 Hz, split by 100 mHz
due to a 2 nT residual orthogonal field. A simulated spectrum is shown beneath
in magenta. All simulations were performed using the SpinDynamica package for
Mathematica.27

Low-field NMR experiments can be performed by leaving the piercing solenoid on
during signal acquisition. As depicted in Fig. 1(g), the magnetization is kept
along the $y$ axis by a 20 $\mu$T field for sample injection, after which the
field is reduced to a 3.8 $\mu$T detection field and the magnetization is
rotated to the $x$-axis by a DC pulse along $z$, which results in the
precessing magnetic signal shown in Fig. 1(h). The spectrum resulting from the
Fourier transform of this signal is shown in Fig. 1(i). There are two groups
of peaks centered at 40 Hz and 160 Hz, corresponding to signals from the 13C
and 1H nuclei of [1-13C]fumarate, respectively. Simulated spectra are shown in
magenta. The difference in the noise between the magnetic signals in Fig. 1(e)
and (h) is predominantly from the 50 Hz line noise, which is not present in
Fig. 1(e) because a low-pass filter was applied to the data during processing.

The zero- and low-field spectra in Fig. 1(f) and (i) are relatively easy to
interpret since either the Zeeman interaction can be treated as a perturbation
to the $J$-couplings, or vice versa. In Fig. 2, we show spectra of
[1-13C]fumarate measured under different background fields, spanning the range
between the zero- and low-field regimes. The spectra were acquired using the
pulse sequence shown in Fig. 1(g) with the exception of the 0 nT spectrum
which was measured using the pulse sequence in Fig. 1(d). The magnetic field
pulse was set to induce a $\approx 4\pi/6$ rotation of protons and
$\approx\pi/6$ rotation of 13C nuclei, so that both nuclei were excited. The
spectra exhibit increasing complexity as the field increases and the Zeeman
interaction term, which is of the form $B|\gamma_{H}-\gamma_{C}|$, approaches
the magnitude of the $J$-couplings.28 The number of spectral lines decreases
again as the term $B|\gamma_{H}-\gamma_{C}|$ begins to dominate, and the
spectral lines group into frequency bands corresponding to nuclear spin
species. It is for this reason that in this work we carried out experiments in
the two distinct field regimes, and not between the two.

Figure 3:  (a) The enzyme-catalysed interconversion between fumarate and
malate. The addition of H2O breaks the molecular symmetry, and the 1-13C spin
label in fumarate has an equal chance to end up in either the 1- or 4-
position in malate. (b) Zero-field NMR spectra of the reaction solution. The
peaks highlighted with asterisks are carbon satellites from the nat. abun. of
[1,4-13C2]fumarate molecules. (c) Low-field NMR spectra at 3.8$\,\mu$T of the
reaction solution. The amount of fumarase enzyme added to each hyperpolarized
fumarate solution prior to detection is shown in brown. All spectra are shown
with 50 mHz line broadening. Simulations are shown beneath the spectra in pink
and teal for fumarate and malate, respectively. The simulated spectra are
vertically scaled to match the real spectra (see Supporting Information for
further details about the simulated spectra, including all spin coupling
parameters used).

####  2.0.1 Observing fumarate-to-malate conversion

A reaction solution was prepared with 50% 13C labelling in the carboxylate
position of the acetylene dicarboxylate. The same chemical reaction with
parahydrogen was used to produce [1-13C]fumarate, and following the field
cycle to polarize the 13C spin, the solution was mixed with phosphate buffer
solution containing a varied amount of fumarase to catalyze the reaction shown
in Fig. 3(a). The reaction was left to proceed for 10 s at Earth’s field,
after which the solution was measured at zero field using the procedure shown
in Fig. 1(d). The experiment was repeated three times with differing amounts
(0, 21, and 52 U, where U is enzyme units) of the enzyme, fumarase, to
demonstrate how the resulting spectra change as a function of metabolic
activity. This level of fumarase activity is consistent with reported plasma
concentrations following acute kidney injury. 29 Further experimental details
are provided in the Materials and Methods.

The resulting zero-field NMR spectra are shown in Fig. 3(b), and feature peaks
at 6.9, 11.5 and 18.2 Hz corresponding to [1-13C]fumarate and peaks at 3.3,
3.6, 3.9, 6.5 and 10.2 Hz corresponding to [1-13C] and [4-13C]malate. The
malate peaks are visible for molecules that formed prior to zero-field
detection. The enzymatic reaction does not reach equilibrium on the short
timescale of this experiment, and so the malate peaks are largest when 52 U of
enzyme was used, since more malate formed prior to detection. Simulated
spectra for fumarate and malate are shown in pink and teal, respectively, and
are generally in agreement with the experimental data (details of the
simulations are provided in the Supporting Information). The signals are well
resolved, even for the partially overlapping signals at 6.5 and 6.9 Hz.

Low-field NMR experiments were also performed following the same protocol as
above, but using the detection procedure shown in Fig. 1(g). The resulting 13C
spectra are shown in Fig. 3(c). The fumarate yields a characteristic 1:2:1
triplet peak pattern centered at 40 Hz, and malate peaks appear at
approximately 38 and 42 Hz. There are additional malate peaks, visible in the
simulations but not the spectra, but these are of significantly lower
amplitude. If relaxation effects are neglected, the peaks are all of similar
amplitude. To get a better match to the experimental results, dipole-dipole
relaxation between the geminal proton pair in malate was included in the
simulations. The dipole-dipole relaxation assumed a dipolar coupling of 25 kHz
between the protons, and a rotational correlation time of 50 ps. This
relaxation mechanism was introduced for a 10 s period prior to the pulse and
during signal acquisition. Importantly, this relaxation mechanism has a
negligible effect on the peaks at 38 and 42 Hz, but they are much lower in
amplitude than the malate peaks in the zero-field spectra. We hypothesize
there is an additional relaxation mechanism related to hydroxyl proton
exchange that is effective at low fields (see Discussion).

####  2.0.2 Observing pyruvate-to-lactate conversion

The metabolic conversion of pyruvate to lactate (Fig. 4(a)) is by far the
most-studied in hyperpolarization-enhanced MRI experiments,4, 3 with over 25
clinical trials currently recruiting or underway around the world.30 We formed
hyperpolarized [1-13C]pyruvate via the sidearm hydrogenation method:31
propargyl pyruvate was hydrogenated using parahydrogen to produce allyl
pyruvate, and a magnetic field cycle was applied to convert the proton
polarization into 13C polarization. After this, the [1-13C]pyruvate was
chemically cleaved from the allyl sidearm moiety via base-catalyzed aqueous
hydrolysis and then extracted into a phosphate buffer solution to yield a
solution of approximately 80 mM [1-13C]pyruvate at $\approx$ 3.5% 13C
polarization. Further details are given in the Materials and Methods. This
solution was either observed directly, or mixed with a solution containing
lactate dehydrogenase and NADH (nicotinamide adenine dinucleotide) leading to
metabolic conversion of pyruvate to lactate. The concentration of NADH in the
solutions was 150 mM, an excess compared to the 80 mM pyruvate, so complete
conversion to lactate would be expected if the reaction was given sufficient
time to go to completion.

The zero-field results obtained by applying the pulse sequence from Fig. 1(d)
are shown in Fig. 4(b). The bottom spectrum shows hyperpolarized
[1-13C]pyruvate, which is an XA3 spin system (one 13C and three methyl
protons), which exhibits peaks at $J_{\text{AX}}$ and $2J_{\text{AX}}$, where
$J_{\text{AX}}$ is approximately 1.4 Hz. Above is the spectrum for the sample
to which lactate dehydrogenase and an excess of NADH was added, and this shows
a number of additional peaks at frequencies up to 18 Hz. Simulations of the
pyruvate and lactate zero-field spectra are shown beneath in pink and teal,
respectively.

The low-field results obtained by applying the pulse sequence from Fig. 1(g)
are shown in Fig. 4(c). Again, the pyruvate spectrum is relatively easy to
interpret: the 13C lines are centered at 41 Hz due to the 3.83 $\mu$T
background magnetic field, and a 1:3:3:1 quartet is observed due to the 13C
coupling to the three protons. A small line can be observed at 41 Hz, which
corresponds to a small [1-13C]parapyruvate impurity.32 The production of
lactate can also be seen at low field; a multiplet corresponding to lactate
can be resolved in addition to the pyruvate quartet (Fig. 4(c)). Simulations
of the pyruvate and lactate low-field spectra are shown beneath in pink and
teal, respectively.

Figure 4:  (a) The enzyme-catalysed conversion of pyruvate to lactate. (b)
Zero-field NMR spectra of the reaction solution. (c) Low-field NMR spectra of
the reaction solution. For the pyruvate spectra the signal of hyperpolarized
pyruvate was acquired directly. For the spectra that show lactate signals,
lactate dehydrogenase and an excess of NADH was added to the hyperpolarized
pyruvate solution prior to detection. All spectra are shown with 250 mHz line
broadening. Simulations are shown beneath the spectra in pink and teal for
pyruvate and lactate, respectively. The simulated spectra are vertically
scaled to match the real spectra (see Supporting Information for further
details about the simulated spectra, including all spin coupling parameters
used).

####  2.0.3 Microfluidic implementation

To explore the possibilities to extend this spectroscopic technique into
different fields of application, we carried out an experiment with the sample
in a microfluidic lab-on-a-chip device, rather than in a 5 mm NMR tube. The
ZULF apparatus was modified to accommodate a polycarbonate microfluidic chip
inside the magnetic shield, with an OPM directly under the 10 $\mu$L sample
chamber, and a pulse coil to apply magnetic fields to the sample to excite NMR
signals. We carried out the hyperpolarization procedure described above to
produce [1-13C]fumarate, and injected the hyperpolarized solution through a
solenoid guiding field into the shield, and into the microfluidic chip. The
pulse coil was holding a constant 16 $\mu$T magnetic field, and after 5 s this
field was switched off and the resulting zero-field NMR signal was detected. A
schematic of the apparatus is shown in Fig. 5a, and the NMR spectrum obtained
from this experiment is shown in Fig. 5b. Further experimental details are
provided in the Supporting Information.

Figure 5:  Measurement of hyperpolarized [1-13C]fumarate in a microfluidic
chip. (a) The experimental setup, showing the microfluidic chip resting on top
of a 3D-printed former (made transparent for clarity), which supports a coil
and houses the OPM directly beneath the 10 $\mu$L sample chamber. The PTFE
fluid inlet and outlet lines are shown in yellow, and the inlet passes through
a guiding solenoid into the shield. (b) The first 2 s of NMR signal obtained
from a sample of [1-13C]fumarate in the chip (shown by teal circles). A
background time signal was acquired by repeating the experiment without a
hyperpolarized sample and we show the difference between the real and
background signals. A 10 Hz low-pass filter was applied to remove 50 Hz line
noise, and one in five acquired data points is shown for clarity. A decaying
sinusoidal function of the form
$S(t)=-9\,\text{cos}(2\pi\,6.95\,t)\,e^{-t/2.5}$ is overlaid on the data in
grey. (c) The Fourier transform of the NMR signal without the low-pass filter
applied, and with 150 mHz line broadening.

##  3 Discussion

We have shown that zero- and low-field NMR can be used to measure key steps of
metabolic pathways using hyperpolarized molecules. The signals from the
converted metabolites malate and lactate are lower at elevated (3.8 $\mu$T)
fields compared to zero field, which is not the case for fumarate and
pyruvate. We attribute this to faster relaxation of malate and lactate at
microtesla fields, which may be related to the fact that the rate of hydroxyl
exchange is approximately 350 s-1 at pH 7 and 25∘C.33 This is close to nuclear
spin Larmor frequencies at microtesla field strengths, and so the fluctuating
dipolar field from exchanging protons may act as a relaxation mechanism. We
performed additional experiments in which we formed [1-13C]lactate directly
via sidearm hydrogenation and allowed it to relax for a fixed time at variable
field, followed by measurement of the 13C polarization. From these experiments
we determined that above a field of $\approx$ 30$\mu$T the proposed hydroxyl
exchange relaxation mechanism is no longer dominant. These results are
presented in the Supporting Information.

In the zero-field experiments, the magnetic field sequence to generate the
signals was chosen such that the reaction solution remains at relatively high
field until signal detection. The reason for this is that the
hyperpolarization remains as Zeeman order on the 13C nucleus during the
metabolic transformation so the change in $J$-coupling topology does not
significantly affect the hyperpolarized spin order. We expect that if the
metabolic transformations occurred at zero field, the change in the
$J$-coupling Hamiltonian, which occurs at different time points for each
molecule, would cause loss of coherence and hence significant polarization
losses.34 It is only immediately before signal acquisition that the magnetic
field is switched to zero, and we observe malate/lactate that formed prior to
this, i.e., we do not see the molecules that form during signal acquisition.

Generally, high-field magnetic resonance imaging of metabolism using
hyperpolarized biomolecules is performed using a train of small-angle pulses,
so as not to significantly perturb the hyperpolarized spin order in each
experiment. This allows one to collect a time-series of spectra to study
metabolic flux, and extract information about the reaction kinetics. By
contrast, in the experiments reported here, the magnetic field sequence
converts the hyperpolarized spin order into observable signals which are
detected once; in this sense it is a ‘single-shot’ experiment. An important
next step will be to implement reaction monitoring of the hyperpolarization-
enhanced signals using a magnetic field sequence that allows for weak
perturbation of the hyperpolarized spin bath many times, to collect a series
of spectra. The only limitation for low-field experiments would be signal-to-
noise, which is lower when using small flip-angle pulses. For the zero-field
experiments it is more challenging, since molecular transformations occurring
at zero field change the $J$-coupling network nonadiabatically and likely lead
to irretrievable signal loss. We note that reaction monitoring was previously
demonstrated with zero-field NMR,9 but in that experiment the
hyperpolarization was continually refreshed by the ongoing reaction, which is
not the case for most biologically-relevant reactions involving hyperpolarized
metabolites.

The presence of quadrupolar nuclei at zero field can pose problems. At zero
field, nuclear spins with mutual $J$-coupling become strongly coupled, since
the Zeeman energy differences are absent and the $J$-coupling between them
dominates. Consider two spins with a difference in Zeeman polarization that
become strongly coupled in a nonadiabatic manner (e.g., by quickly turning off
an external magnetic field, or by chemical reaction); the polarization of the
two spins will begin to exchange in an oscillatory manner, with the frequency
given by the $J$-coupling. This oscillating magnetization is the observable in
many zero-field NMR experiments. However, this makes the hyperpolarized spin
order particularly sensitive to the presence of $J$-coupled quadrupolar nuclei
(e.g., 2H or 14N), since polarization that oscillates onto these spins can
rapidly relax.35 In fumarate experiments, the reaction to generate fumarate is
carried out in D2O to prolong the hyperpolarization lifetime, but the
conversion to malate should not be carried out in pure D2O since all malate
molecules would then contain deuterium.111We performed separate experiments in
which the enzyme reaction was carried out in pure D2O, and observed fumarate
signals but no NMR signals from malate. For this reason we used a 1:1 H2O/D2O
mixture as the solvent for the metabolic reaction, so approximately 50% of the
malate molecules are protonated rather than deuterated. Novel methods now
enable decoupling of deuterium nuclei, which should help to alleviate this
problem by suppressing the polarization exchange.36, 37 Regardless, for in
vivo experiments the fumarate would first be purified and then brought into an
H2O solution using established methods.38

The gradiometric detection scheme used in this work is shown schematically in
Fig. 1(b). Taking the sample to be a long cylinder homogeneously magnetized
transverse to the cylindrical axis, the resulting magnetic field takes a two-
dimensional dipole shape, such that the field magnitude is constant at a given
radius from the center of the sample. Hence, in these experiments, the signal
was acquired simultaneously in both the $x$\- and $z$-channels of two QuSpin
OPMs, and during processing the signal difference was taken for each axis.
This gradiometric detection scheme has two advantages: (1) the observable
signal is enhanced by detecting with multiple sensors (up to a factor of 2),
and; (2) acquiring the differential signal is an effective way to cancel
common-mode noise (magnetic noise that is the same at the positions of both
OPMs).

In this work the low-field experiments were carried out at relatively low
frequency ($<$200 Hz) since the bandwidth of the magnetometers here was 135
Hz. This is certainly not a fundamental limitation of the commercial OPMs used
in this work, which have been shown to be capable of operation at up to 1.7
kHz.39

Most experiments were carried out with 5 mm NMR tubes, with a sample volume of
$\approx$600 $\mu$L, and a detected volume of approximately 100-200 $\mu$L. In
the microfluidic experiment we were able to observe a 10 $\mu$L sample in a
single scan, albeit with a reduced signal-to-noise ratio. A quantitative
comparison between the signal in macro and microfluidic experiments is
challenging due to the different experimental procedures that were employed to
obtain the spectra. Although the microfluidic chip used did not involve
fluidic complexity, this is a strength of lab-on-a-chip devices, and indeed it
has been shown that the chemical reaction to hyperpolarize fumarate can be
carried out on a chip40. Microfluidic NMR is hindered in widespread use in
part due to the need for specially-designed probes for high-field
implementation, as well as limited resolution due to magnetic field gradients
at the interface between the chip and sample; ZULF NMR does not suffer from
these limitations, and might prove to be a useful spectroscopic technique in
this field.

##  4 Conclusions

In conclusion, we have shown that biochemical reactions can be quantified by
NMR at zero magnetic field. We used a gradiometer based on optically-pumped
magnetometers to observe the conversion of [1-13C]fumarate to [1-13C]malate
and [4-13C]malate, and [1-13C]pyruvate to [1-13C]lactate at both zero and low
field. We also report zero-field NMR spectroscopy of hyperpolarized
[1-13C]fumarate in a microfluidic chip. To our knowledge, this is the first
demonstration of zero-field NMR in a microfluidic system. Together with the
ability to follow biochemical processes, this opens up interesting possible
applications in the context of lab-on-a-chip cell culture devices.

The particular appeal of OPM detection is that the advanced magnetometer
arrays and image reconstruction algorithms that have been made available for
MEG 15 could be used directly for low-field metabolic MRI. This would, for
example, enable metabolic imaging of patients with medical implants, free from
issues with susceptibility and rf shielding effects. We envision a combined
MEG/MRI modality capable of simultaneously measuring electromagnetic neuronal
activity, brain metabolism, and correlations between the two. The step to in
vivo applications will naturally be challenging as a result of sensitivity
reductions, due to the greater distance between the sensor and reactions
occurring inside the body, and also the lower concentration of biomolecules in
vivo. On the other hand, the ever-improving sensitivity of magnetometers,
developments in pulse excitation schemes, and increasing polarization levels
that can be generated on hyperpolarized biomolecules have consistently
improved NMR sensitivity over the last 70 years, and will likely continue to
do so.

## References

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This project has received funding from the European Union’s Horizon 2020
Research and Innovation Programme under the Marie Skłodowska-Curie Grant
Agreement 766402 and the FET-Open AlternativesToGd Proposal n. 858149. as well
as by the DFG (Project ID 465084791). This work has been supported by an EPSRC
iCASE studentship EP/R513325/1 to SJB, co-funded by Bruker UK Ltd.

## Supplementary materials

Materials and Methods
Spectral simulations
Hyperpolarization decay at low field

##  5 Supplementary Materials

###  5.1 Materials and Methods

All high-field NMR experiments (unless otherwise stated) were performed in a
1.4 T 1H-13C dual resonance SpinSolve NMR system (Magritek, Aachen, Germany).

Parahydrogen at $>$95% enrichment was generated by passing hydrogen gas
($>$99.999% purity) over a hydrated iron oxide catalyst in a cryostat
operating at 30 K (Advanced Research Systems, Macungie, U.S.A.).

For magnetic field sweeps for polarization transfer, an MS-2 four-layer mu-
metal magnetic shield (Twinleaf LLC, Princeton, U.S.A.) was used to provide a
$10^{4}$ shielding factor against external magnetic fields. No static shim
fields were required, since the residual field within the shield was on the
order of 5 nT. The time-dependent applied magnetic field was generated using
the built-in $B_{y}$ shim coil, with current supplied with an NI-9263 analog
output card (National Instruments, Aachen, Germany) with 10 µs time precision.
The guiding magnetic field for sample transport in and out of the magnetic
shield was provided with a handmade solenoid, with current supplied with a
Keysight U8001A current source (Keysight Technologies, Böblingen, Germany).

Fumarate Experiments

The precursor solution for all fumarate experiments was 250 mM acetylene
dicarboxylic acid monopotassium salt, 250 mM sodium sulphite and 7 mM
ruthenium catalyst [RuCp*(CH3CN)3]PF6 in D2O. 250 mM NaOD was added to the
solution to be equimolar with the starting material. All chemicals were
purchased from Sigma Aldrich.

The reactor for fumarate experiments was constructed from stainless steel with
an internal volume of 20 mL. PEEK (polyether ether ketone) tubing of 1/8 in
O.D. was used to flow the para-enriched hydrogen gas, and 1/16 in O.D. 0.5 mm
I.D. PTFE (polytetrafluoroethylene) capillaries were used for all solution
flow. These tubes were connected to the reactor via 1/4-28 PEEK fittings (part
numbers P-249 and P-349, IDEX LLC, Oak Harbor, U.S.A.), and to the gas flow-
control manifold via Swagelok fittings (Swagelok, Frankfurt, Germany). The
reactor was wrapped in two heater mats (part number 798-3753, RS Components,
Corby, U.K.), and these were connected to a power supply, with the current set
to heat the reactor to 85∘C.

For fumarate hydrogenation experiments, a 1.5 mL aliquot of precursor sample
was loaded into the reactor via syringe injection, and given 10 s to reach 85
∘C. The reactor was sealed, and parahydrogen was bubbled into the reaction
solution at approximately 6 L/min for 60 s at a pressure of 8.5 bar. The flow
rate was set by a needle valve at the outlet of the gas manifold. After
bubbling, the sample was pneumatically ejected through a PTFE capillary into a
10 mm NMR tube in the magnetic shield underneath by manually opening a two-way
microfluidic valve. To prevent the sample from passing through any fields that
could lead to undesired state-mixing during sample transport in/out of the
shield, a piercing solenoid was used to provide a 10 $\mu$T guiding field.
Upon landing in the 10 mm NMR tube, the field was nonadiabatically (rapidly)
dropped to 50 nT and then adiabatically increased to 1 $\mu$T in 2 s to
transfer the proton singlet order into 13C magnetization. The solution was
extracted through a 1/16 in PTFE capillary into a syringe.

For the zero-field experiments to observe fumarate (without conversion to
malate), the hyperpolarized fumarate sample was syringe-injected into a 5 mm
NMR tube, and this was dropped into the zero-field spectrometer for signal
acquisition.

For the experiments to observe enzymatic conversion to malate, 150 $\mu$L of
the hyperpolarized fumarate sample was injected into a 5 mm NMR tube
containing a stated amount of fumarase enzyme in 450 $\mu$L 500 mM phosphate
buffer solution at pH 7. The NMR tube was shaken for 5 s and then dropped into
the zero-field spectrometer for signal acquisition.

Pyruvate Experiments

The precursor solution for all pyruvate experiments was 400 mM propargyl
pyruvate and 20 mM rhodium catalyst [Rh(dppb)(COD)]BF4 in a solvent of 95:5
(v/v) CDCl3:ethanol-d6, which was prepared by dissolving the catalyst in the
solvent, and adding the propargyl pyruvate immediately (tens of seconds)
before each experiment. The propargyl pyruvate precursor was synthesized in-
house, and all other chemicals were purchased from Sigma Aldrich.

For pyruvate hydrogenation experiments, a 250 $\mu$L aliquot of precursor
sample was loaded into a 5 mm low pressure/vacuum NMR tube via syringe
injection and the tube was pressurized to 7 bar pH2 pressure. The sample was
heated to 120 ∘C with a heatgun, and then the tube was vigorously shaken for 4
s while under pressure. After shaking, the whole NMR tube was placed in the
magnetic shield for a 4 s magnetic field sweep. After the field sweep, the
solution was ejected from the NMR tube using a valve at the top and the
internal gas pressure to push the solution through a 1/16 in PTFE capillary
into a 10 mm NMR tube containing 300 $\mu$L 400 mM NaOH at 80 ∘C for the
hydrolysis. The resulting mixture was allowed to settle for 2 s and the
aqueous layer was extracted through a 1/16 in PTFE capillary into a syringe
containing 300 $\mu$L acidified 500 mM phosphate buffer solution to neutralize
the pyruvate solution at pH 7.

For the zero- and low-field experiments, this solution was injected into a 5
mm NMR tube, and this was dropped into the zero-field spectrometer for signal
acquisition.

For the experiments to observe conversion to lactate, the syringe used to
extract the aqueous phase from the 10 mm NMR tube contained 200 $\mu$L of
acidified phosphate buffer solution, such that, after mixing, the solution
ended at pH 7. Another 100 $\mu$L of phosphate buffer solution contained 50 mg
NADH and 25 $\mu$L lactate dehydrogenase (Sigma Aldrich, L7525), and this
solution was held in the 5 mm NMR tube. The pyruvate solution was injected
into the 5 mm NMR tube and mixed with the enzyme solution by vigorous shaking
for 5 s, before being dropped into the zero-field spectrometer for signal
acquisition.

A modified experimental procedure from the established protocol reported in
Ref. 41 was adopted to increase the volume of the solution and maximize
pyruvate concentration (and hence signal) for this proof-of-concept
demonstration. For in vivo/in vitro studies, a protocol has to be established
in order to attain a biologically compatible solution of the substrate at high
concentration.

Microfluidic experiment The microfluidic experiment was carried out in an
MS-1LF (Twinleaf LLC, Princeton, U.S.A.) shield. The coil consisted of 10
turns of 0.5 mm O.D. copper wire wound around a former, with a diameter of 35
mm. A QuSpin was held inside and the chip was screwed in place above, with the
sample chamber directly over the sensitive region of the OPM. The chip itself
was made of three layers of polycarbonate, 0.25 mm thick for the top and
bottom layers and 1 mm thick for the middle layer. The layers were bonded
using a plasticiser (5% v/v of dibuthyl phalete in isopropyl alcohol) under
heat and pressure (85∘C, 5 tonnes) for 20 minutes. The chip had inlet+outlet
ports connected to 1/16 in O.D. PTFE tubing via PEEK nanoports (Kinesis GmbH,
Germany). The sample chamber had dimensions of 4 $\times$ 2.5 $\times$ 1 mm,
and hence a volume of 10 $\mu$L. A hyperpolarized sample of $\approx$80 mM
[1-13C]fumarate in D2O was prepared as described above (at $\approx$30% 13C
polarization), and syringe-injected through the PTFE tubing to fill the
microfluidic chip. The pressure was released to allow the fluid to settle for
3 s, after which the solenoid and pulse coil were switched off non-
adiabatically and the signal acquired for 4 s.

Equipment for zero-field NMR experiments

For the zero-field experiments, an MS-1LF four-layer magnetic shield (Twinleaf
LLC, Princeton, U.S.A.) was used to provide a $10^{4}$ shielding factor
against external magnetic fields. To provide a stable current for 3-axis
shimming using the MS-1LF built-in $B_{x}$, $B_{y}$ and $B_{z}$, shim coils, a
CSB-20 3-output current supply (Twinleaf LLC, Princeton, U.S.A.) was used,
which has current noise on the order of 100 pA Hz-1/2. A hand-wound piercing
solenoid produced a guiding magnetic field for sample transport in and out of
the magnetic shield, and provided a stable field at the sample position for
low-field experiments. The $B_{y}$ and $B_{z}$ Helmholtz coils were hand-wound
around a 3D-printed coil former, with 10 turns, and 40 mm coil radius. The
time-dependent Helmholtz fields were produced by a NI-9263 analog output card,
and AE Techron 7228 amplifiers (AE Techron Elkhart, IN 46516 U.S.A.) were used
to amplify the current.

For signal detection, two QuSpin optically-pumped magnetometers were held in
place in the 3D-printed coil former, oriented as shown in Fig. 1(a). The
distance between the center of the sample and the center of each magnetometer
cell was approximately 13 mm. The analog outputs of the QuSpins were read out
by a National Instruments NI 9215 analog input card at 50000 samples/s,
downsampled to 5000 samples/s.

###  5.2 Spectral simulations

Figure 6:  The $J$-couplings used for all simulations.

The simulations of NMR spectra were carried out using the SpinDynamica package
for Mathematica,27 and the $J$-coupling constants shown in Fig. 6. Initial
guesses of the $J$-couplings were determined by high-field NMR, and these were
modified by $<1$ Hz each in all cases, to fit the simulations to the spectra.
Simulations involved propagating an initial density operator through the pulse
sequences shown, and detecting the magnetic signal produced by the sample,
which corresponds to the operator

$\sum_{i}\hbar\gamma_{\text{i}}I^{i}_{z}\text{,}$

where $\gamma_{\text{i}}$ is the gyromagnetic ratio of spin $i$, and
$I^{i}_{z}$ is the $z$ angular momentum operator for the $i$-th spin.

For all simulations relaxation was included phenomenologically (with an equal
time constant for all spins) during detection to match the peak linewidths to
the experimental data. For the low-field simulations of [1-13C]- and
[4-13C]malate, dipole-dipole relaxation between the geminal proton pair was
also included in order to get a better match between simulation and
experimental results. The dipole-dipole relaxation assumed a dipolar coupling
of 25 kHz between the protons, and a rotational correlation time of 50 ps.
This relaxation mechanism was introduced for a 10 s period prior to the pulse,
and during signal acquisition.

###  5.3 Hyperpolarization decay at low field

To better-understand the proposed low-field relaxation of [1-13C]lactate, we
carried out experiments in which we hyperpolarized [1-13C]lactate via side-arm
hydrogenation directly, and allowed it to relax for 5 s at variable field
prior to signal acquisition. We did the same for [1-13C]pyruvate so the
results could be compared.

Hyperpolarized [1-13C]lactate and [1-13C]pyruvate were obtained according to
the procedure already reported by Cavallari et al.42, 43. A solution of
approximately 250 mM of the propargyl ester (propargyl-[1-13C]lactate or
propargyl-[1-13C]pyruvate) and 13.8 mM of the catalyst [Rh(cod)dppb][BF4] in
100 $\mu$L of 95:5 (v/v) CDCl3:ethanol, was loaded into pressurizable NMR
sample tubes, and these were pressurized with parahydrogen gas (86$\%$
enriched, to a pressure of 2 bar at liquid nitrogen temperature). The tubes
were kept frozen (77 K) to prevent any chemical reaction, until the start of
the hyperpolarization experiment. To initiate the hydrogenation reaction, the
NMR tube was heated in a hot water bath at 80 ∘C for 7 s, shaken vigorously
for 3 s, then opened to release the parahydrogen pressure. The tube was then
placed in a mu-metal shield (Bartington TLMS-C200) equipped with a coaxial
solenoid, through which a magnetic field cycle (MFC) was applied, to obtain
the spin-order transfer from the parahydrogen protons to 13C. The magnetic
field profile applied in all the experiments consists of a diabatic passage
from 1.5 $\mu$T (initial magnetic field) to 50 nT, and then up to 10 $\mu$T in
4 s with an exponential profile.

To hydrolyse the 13C-polarized ester (allyl-[1-13C]-pyruvate/lactate) a hot
260 $\mu$L solution of 230 mM NaOH and 50 mM ascorbate was injected with 1.5
bar argon pressure. Hydrolysis of the ester occured in a few seconds and the
aqueous phase containing the hydrolysed pyruvate/lactate was extracted,
whereas the catalyst was retained in the organic phase. An acidic buffer (135
mM HEPES + 60 mM HCl) was added to the aqueous phase to obtain a neutral pH
(7.4).

To investigate the effect of the external magnetic field on the relaxation of
[1-13C]lactate and [1-13C]pyruvate, the hyperpolarized solutions were held at
different magnetic fields (1, 2, 4, 8, and 36 $\mu$T) for 5 s before
acquisition of the 13C NMR spectrum at high field using a 14.1 T NMR Bruker
Avance spectrometer. The protocol is shown in Fig. 7a. The magnetic fields
were generated in the $\mu$-metal shield by controlling the current through
the solenoid coil, except 36 $\mu$T which was the laboratory magnetic field.
Each measurement was performed using a freshly-prepared hyperpolarized sample.
The results are shown in Fig. 7b. There is a reduction in lactate signal after
storage at 2, 4, and 8 $\mu$T field, but this reduction is less pronounced at
1 $\mu$T and 36 $\mu$T. By comparison, the pyruvate signal does not show this
field dependence, and so we posit that the enhanced lactate relaxation is due
to hydroxyl proton exchange. This question is subject to ongoing
investigation.

Figure 7:  (a) External magnetic field strength during the experiment, with
the experimental procedure labelled. (b) Polarization level of [1-13C]pyruvate
and [1-13C]lactate after storage at various fields for 5 s before signal
acquisition.