<table><caption>**Table 7.1:** Experiments list - OD, optical density, and growth phase in the last line. *: an acidic jump stress factor was applied in this experiment.</caption><thead><tr><th>Exp</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8*</th></tr></thead><tbody><tr><th>OD<sub>600</sub></th><td>0.8</td><td>0.9</td><td>1</td><td>1.4</td><td>2.4</td><td>2.5</td><td>2.8</td><td>1.7</td></tr><tr><td></td><td colspan="3">Early exponential</td><td colspan="4">Late exp. & stationary</td><td></td></tr></tbody></table>

## 7.3 DDNP study of glucose metabolism in E.coli K12

For the present study, eight DDNP experiments were performed, using cells grown along the same protocol, albeit harvested at different growth stages. The criterion used to distinguish between the growth stages was the measured OD<sub>600</sub> value of the culture medium. Thus, E. coli samples with OD<sub>600</sub> between 0.8 and 2.8 were used for 8 different experiments (see Table 7.1). In an additional experiment, an acidic jump to pH = 4 was applied to the cell suspension ~ 2 min before the dissolution experiment.

Our DDNP experiments typically yielded time-resolved series of hyperpolarized <sup>13</sup>C spectra as shown in Figs. 7.2b and 7.2c. The most intense peaks originate from [U-<sup>13</sup>C, U-<sup>2</sup>H]-glucose, and were *ca.* two orders of magnitude larger than the remaining hyperpolarized <sup>13</sup>C signals. The *α* and *β* anomers were monitored through the resonance frequencies of their anomeric carbons <sup>13</sup>C<sub>1</sub> (δ(<sup>13</sup>C<sub>1α</sub>) ≈ 93 ppm, δ(<sup>13</sup>C<sub>1β</sub>) ≈ 95.5 ppm). Additional resonances originating from various moieties present in the sample, and observed in these <sup>13</sup>C DDNP spectra, were assigned in a rather straightforward manner thanks to the knowledge of the species involved in the glucose metabolism in E. coli, and their referenced chemical shifts: [33, 245] ethanol (δ(<sup>13</sup>C<sub>1</sub>) ≈ 58 ppm), acetate (δ(<sup>13</sup>C<sub>1</sub>) ≈ 181.5 ppm and δ(<sup>13</sup>C<sub>2</sub>) ≈ 24 ppm). These were consistently observed within seconds after complete in-situ mixing of the hyperpolarized glucose with the cell suspension in the NMR tube. Moreover, for acetate, <sup>13</sup>C<sub>1</sub> and <sup>13</sup>C<sub>2</sub> resonances were doublets with characteristic <sup>1</sup>J<sub>CC</sub> carbon-carbon splittings. Comparison with spectra acquired on the same samples several minutes (~ 10 min) after each DDNP experiment, i.e. on spins at thermal equilibrium (TE), provided confirmation of the previous signal assignments and allowed one to identify additional resonances originating from metabolites that were not present yet in the DDNP experiments, thereby
<figure><img src="image_59.png" /><figcaption>**Figure 7.2:** 7.2a: Schematics of the set up used for the DDNP experiments (see text for details). 7.2b: Typical ¹³C DDNP spectrum experiment, third scan taken from experiment # 3 in Table 7.1. The signal originates principally from hyperpolarized glucose, whilst signals from metabolites are ~ two orders of magnitude smaller. 7.2c: Peak assignment of the DDNP spectrum of exp # 3 in Table 7.1, the superposition of the first 20 scans in the DDNP experiment is displayed. Resonances 1 and 10 were assigned to ¹³C ₁ and ¹³C ₂ resonances of acetate. Peaks 3 and 4 correspond to the β and α ¹³C ₁ anomeric carbon resonances of glucose, whilst labels 6 and 7 indicate the ¹³C ₃⁻₅ and ¹³C ₆ atoms of glucose. Signals labeled 2 and 5 were tentatively assigned respectively δ-PGL which is the first product in the PPP and whereas the very weak unassigned doublets upfield by 1ppm and 4 ppm could correspond to the γ-PGL and the 6PGA directly issued from the δ-PGL. Finally, peak 8 was assigned to ¹³C ₁ of ethanol, and peak 9 to DMSO which served for the chemical shift calibration at 39 ppm. 7.2d: Time evolution of the carbonyl region of the ¹³C spectrum upon hyperpolarized glucose pulse. 7.2e: superposition of a sum of the first 20 one-dimensional spectra of exp # 3, acquired in a typical DDNP experiment(black) and the reference spectra of a sample of unlabeled Acetate (blue); both experiments performed at same pH (7.2) and temperature (310 K) conditions.</figcaption></figure>
<figure><img src="image_60.png" /><figcaption>**Figure 7.3:** E. Coli K12 glucose metabolic pathways - Glycolysis feeds the Mixed Acid Fermentation pathway that leads to the production of multiple end chain metabolites. Only the metabolites of interest for the present study (lactate, formate, ethanol and acetate) - are indicated. [251]</figcaption></figure>

indicating further evolution of the metabolite transformations beyond the DDNP experiment time window, i.e., on the time scale of minutes. One can additionally note that the same resonance peaks were observed in all of the experiments, thereby pointing to the overall repeatability of the experimental procedure. Assignments of lactate, acetate and formate in the DDNP and "post-DDNP" (NMR spectrum acquired in thermally polarized conditions immediately following the DDNP experiment) experiments were confirmed by comparison to reference ¹³C spectra (figure 7.2e in the *Supplementary Information*).

The resonance doublet at ~ 182 ppm detected in the DDNP experiment was thus assigned to acetate, and the additional resonances appearing at ~ 184 ppm and ~ 171 ppm, in the "post-DNP" experiment, to the lactate doublet (¹J<sub>CC</sub>) and the formate doublet (¹J<sub>HC</sub>, no proton decoupling during the acquisition), respectively. This seemed to indicate that the production of lactate and formate by E. coli in our experiments occurred at a significantly later stage than acetate after the injection of hyperpolarized glucose. Finally, as ethanol was found to be also produced in the course of the DDNP experiment (Fig. 7.2c), it was inferred that acetate and ethanol were both produced at an earlier stage than lactate and formate. Note that resonance peaks were assigned based on the knowledge of published chemi-
cal shifts, or available from databases[252] and of the glucose metabolic pathways that lead
from its uptake by *E. coli* to the PPP, glycolysis, to various products of the mixed acid fer-
mentation pathway. Indeed, the latter starts from phosphoenolpyruvate, produced through
glycolysis, to yield lactate, formate, ethanol and acetate (for an extensive compilation of
references on *E. coli* K12 metabolism, see ref. [253]). Note that neither CO₂ (125 ppm) nor
HCO₃⁻ (161 ppm) were observed in our DDNP experiments. A schematic summary is de-
picted in Figure 7.3.

The remaining metabolite resonance observed in the carbonyl region of the ¹³C spec-
trum (~174 ppm) during the DDNP experiment matches that of the ¹³C ₁ resonance of the
δ-phosphogluconolactone (δ-PGL), [33] and the ¹J<sub>cc</sub> = 43 Hz is identical to the one observed
on a DDNP spectrum of δ-PGL enzymatically produced from glucose, and observed inde-
pendently. This assignment is supported by the presence of a triplet corresponding to δ (¹³C
₂) ≈ 80 ppm) of δ-PGL with again ¹J<sub>cc</sub> = 43Hz. The remaining δ-PGL resonances are buried
under the glucose ¹³C ₂–₅ signals. However, the presence of δ-PGL in our experiments was
rather surprising, as the latter is expected to be transformed into 6-phosphogluconic acid
through the action of the 6-phosphogluconolactonase (6PGL) in the oxPPP.[254] Indeed,
in the DDNP experiments performed by Meier and coworkers on *E. coli*, no δ-PGL could
be observed in K12 strain whereas its accumulation was demonstrated on BL21 cells that
lack the *pgl* gene encoding 6-phosphogluconolactonase. [245] However, it has been shown
that a tenfold increase of δ-PGL production can be induced in K12 *E.coli* cells by a glucose
pulse[255]. Such a fast increase of δ-PGL production could explain the early and transient
accumulation of δ-PGL resonances in our experiments. Additional arguments supporting
the presence of δ-PGL in the obtained DDNP spectra will be discussed below.

7.3.1 The decay rates of the α/β-glucose anomeric signals are mark-
ers of the cellular metabolic response to a glucose pulse

In an attempt to probe the metabolic state of the cells, we analyzed the kinetics of the de-
cay of the DDNP-enhanced NMR signals of the injected glucose – the primary substrate in
<figure><img src="image_61.png" /><figcaption>**Figure 7.4:** Typical ¹³C₁ signal evolution of the β (blue) and α (red) anomers of glucose (experiment 3 in Table 7.1, OD₆₀₀ = 1). Experimental measurements (diamonds) acquired after complete injection of the hyperpolarized glucose sample (vertical dotted line) are fitted to an exponential (continuous line)</figcaption></figure>

our experiments. Glucose is present in the extracellular medium only and absent from the cytosol, as it is phosphorylated upon cell intake, during transport through the cytoplasmic membrane, to yield glucose-6-phosphate (G6P). [256, 257] In addition, glucose signals are by far the most intense ones in these experiments and strategies targeting G6P were impeded by weak signal amplitudes. The (intracellular) G6P resonances were undetectable, and the doublet of ¹³C₆ was not observed (~ 63.5 ppm).

We investigated the possibility to use the observed decay rates of the extracellular α- and β-Glc signals as indicators of their relative uptake by the cells, and as markers of the cell metabolic response to a sudden excess of glucose, given the growth (therefore metabolic) state in which they were prepared. In all experiment, the ¹³C₁ signal intensities of both anomers exhibited clear exponential decays with time (see Fig. 7.4), consistent with the assumption of a pseudo first-order kinetic model of glucose uptake. The decay rates are the sum of the ¹³C₁ relaxation rate rα (rβ) and α- (β-) glucose uptake rate kα by E. coli: rα,β + kα,β. The longitudinal magnetization Mα of the ¹³C₁ of the α anomer therefore evolves with time as:

$$ \frac{dM_{\alpha}(t)}{dt} = -r_{\alpha}M_{\alpha}(t) - k_{\alpha}M_{\alpha}(t) \qquad (7.1) $$

(with a similar expression for Mβ). The time evolution of the NMR signal is therefore:

$$ S_{\alpha}(t) = cnst \times \cos^{n-1}(\theta) M_{\ge 0,\alpha} e^{(-r_{\alpha} - k_{\alpha})t} \times \sin(\theta) \qquad (7.2) $$
where $M_{z0,\alpha}$ is the initial $^{13}$C$_1$ glucose magnetization, cnst is a constant characteristic of the spectrometer, $n$ is the number of experiments performed at time $t$, and $\theta$ is the read pulse flip angle. In order to study the anomeric uptake ratio in each experiment, we computed and fitted the signal ratio of glucose anomers with the following expression :

$$ \frac{S_{\alpha}(t)}{S_{\beta}(t)} = \frac{M_{z0,\alpha}}{M_{z0,\beta}} e^{(-r_{\alpha}-k_{\alpha}+r_{\beta}+k_{\beta})t}, \qquad (7.3) $$

from which the differences $(r_{\beta} + k_{\beta}) - (r_{\alpha} + k_{\alpha})$ between the global decay rates $r_{\alpha,\beta} + k_{\alpha,\beta}$ of the $\alpha$ and $\beta$ $^{13}$C$_1$ signals, were extracted. These decay rates were then compared to a reference experiment performed on a sample of hyperpolarized glucose, in the absence of cells, giving access to the difference $r_{\beta} - r_{\alpha}$. The difference of the time constants obtained in an experiment performed in the presence of E. coli and the reference thus provided the anomeric differential uptake rates of glucose by the cells, $k_{\beta} - k_{\alpha}$. Results are summarized in Figure 7.5. Interestingly, in our experiments, the ratios $\frac{S_{\alpha}(t)}{S_{\beta}(t)}$ were linear in time in all experiments, indicating that the defined pseudo-first order kinetics of glucose uptake can be also analysed as a zero order, linear kinetics. The linear behaviour simply means that the approximation $e^x \sim 1+x$ may also be used in our experiments.

It is seen that in experiments 1 to 3 (see Table 7.1), when cells are in early exponential phase and harvested at OD$_{600} \le 1$, the difference $k_{\alpha} - k_{\beta}$ exhibits positive values. In contrast, in experiments #4-#8, where cells were grown to higher densities, with OD$_{600}$ in the range 1.4 – 2.8 (late exponential or stationary phase, and possibly subject to an applied external stress, such as in experiment 8), lower, negative, differential anomeric glucose uptake rates $k_{\alpha} - k_{\beta}$ were consistently observed. Thus, when compared to experiments 1-3, these results suggest that the cell uptake of $\beta$-Glc is favored when cells are grown to higher cell densities, indicating significant changes in the glucose metabolism upon sudden exposure to a glucose excess. Thus, these experiments seemed to allow for the direct observation, in real-time, of the distinct roles of the $\alpha$- and $\beta$- glucose anomers in the metabolism of E. coli.

The above discussion relies implicitly on the assumption that the different time evolu-
tions of the glucose anomers inside the cell can be monitored through the observation of
the *extracellular* signal of glucose, and obey first order kinetics. This hypothesis implies that
the uptake of glucose, which includes its transfer to the intracellular medium through the
outer and cytoplasmic membranes, can be modeled as a simple first order kinetic process.
This is supported by known facts of glucose uptake mechanism. Indeed, the diffusion of glu-
cose through the outer membrane into the periplasmic space is a passive process that takes
place through channels formed by the specialized, transmembrane porin proteins.[258, 259]
It is then internalized into the cytoplasm of *E. coli* through the cytoplasmic membrane by
an active mechanism involving the phosphoenolpyruvate:sugar Phospho-Transferase Sys-
tem (PTS).[256, 257] The PTS comprises an integral protein part and a soluble protein that
combine their actions to simultaneously transfer α- and β- glucose anomers through the
cytoplasmic membrane and phosphorylate them to yield intracellular G6P. In the perspec-
tive of our analysis, the crucial point is that this transfer is also known to have anomeric
selectivity, which has been observed by NMR.[72] It has been suggested that glucose uptake
by the PTS could be modeled by a two-site model where each site shows specificity towards
a single anomer.[30] Moreover, as also shown in the latter reference, the approximation of a
steady-state glucose:protein complex was made and, as cytosolic phosphate concentration
was assumed constant, the irreversible phosphorylation step was modeled as a first-order
kinetics.

The results of our analysis can be interpreted in the perspective of the relative metabolic
fluxes of G6P towards the glycolysis and of the pentose phosphate pathway (PPP). Indeed, a
number of studies have shown that glycolysis and the PPP are anomer selective.[260] Thus,
the yeast glucose-6-phosphate dehydrogenase (G6PDH), the first enzyme of the PPP that
transforms glucose-6-phosphate into δ-phosphogluconolactone has β-glucose specificity.[74]
A direct proof of this result was shown recently, in more physiological conditions, us-
ing DDNP.[226] Such a specificity has also been demonstrated in such diverse organisms
as human erythrocytes[261] and *Pseudomonas fluorescens*.[262] Alternatively, the first en-
zyme of the glycolysis pathway, the yeast glucose-fructose isomerase (PG-isomerase), has
<figure><img src="image_62.png" /><figcaption>**Figure 7.5:** Uptake rate differences of glucose anomers extracted from experiments performed on cells grown to various OD stages. In red, values indicate larger α anomer uptake, and in blue, larger β anomeric consumption by the cell. Black empty circles indicate values obtained from two reference experiments. Values cluster in two clearly visible groups, according to $OD_{600} \le \sim 1$ and $OD_{600} \ge \sim 1.5$. Error bars result from a Monte Carlo estimation.</figcaption></figure>

an anomeric selectivity towards the α anomer of G6P.[74, 263] In the light of these facts, our observations suggest that the first key enzymes of the phosphoglucose metabolism in *E. coli*, G6PDH and PG-isomerase, also verify the properties evidenced in other species. The differential rates $k_α - k_β$ obtained from the $^{13}C_1$ glucose signals, due to the substrate selectivity of these enzymes, therefore provide information on the relative consumption of both anomers by the cells, and indirectly inform on the relative activities of glycolysis and the PPP upon the applied glucose pulse.

These experiments exploit the large extra-cellular DDNP-polarized glucose signal to monitor the response to *E. coli* cells prepared following a well-codified protocol, to a dynamic perturbation achieved by the sudden injection of glucose. A number of studies have focused on the cell response to a single and sudden excess of glucose,[255] or to repetitive "feast-famine" cycles.[264] Such studies suggest that *E. coli* responds to glucose pulses by a large increase of the PPP flux, as would be needed to match the NADPH needs for cell growth.[255]. Thus, following the previous assumption, our *in vivo* DDNP studies point to the fact that the metabolic response to a glucose pulse induces a rerouting of the metabolic fluxes towards the PPP. In addition, higher cell densities are believed [265] to create anaero-
bic conditions and significant metabolic modifications. Hence, our results show consistency with recent findings that show metabolic flux rerouting of E. coli towards the PPP at later growth states, i.e., at higher ODs.[264]. Thus, information extracted from our experiments may also be relevant to the metabolic conditions of the cells prior to the DDNP experiment.

### 7.3.2 Quantitative kinetic analysis of metabolite signals

The time-resolved analysis of DDNP experiments is necessarily an empirical approach where the cell is treated as a "black box", and the output (metabolite) signal is obtained from the input (the substrate) through a transfer function that describes the combined effects of several metabolic pathways. Because of their weak intensities, with typical maximum signal-to-noise ratios on the order of ≈ 2–3 only (see Fig. 7.6), a kinetic analysis could be performed for a pair of signals only, which, as mentioned above, were tentatively assigned to acetate and δ-PGL.

In all of our experiments, these signals were observed at very early times (~1 s after the beginning of the experiment, when the injection of the hyperpolarized solution is complete), attesting for their fast production by the cells. This observation is consistent with recent studies that suggest an immediate response of the cells to glucose pulses.[266] Moreover, their metabolism was assumed to be “saturated” by the very large glucose amount brought by the pulse during the time course of these experiments. Since the experiments are per-

<figure><img src="image_63.png" /><figcaption>**Figure 7.6:** Signal evolution of ¹³C₁ for α and β anomers of glucose (in gray) compared to the signal evolution of Acetate (in red) and δ-PGL (in blue) multiplied by a factor of 200.</figcaption></figure>

formed in a large excess of glucose and assuming that the cells are readily functioning at
full capacity, a simple kind of zero-order kinetic model, in which the production rate of the compound is independent of the concentration of the substrate, was implemented. The evolution of the z magnetization of a product, say, P₁, thus writes:

$$ \frac{dM_{zP_1}}{dt} = k_1 M_{z0,G} e^{-\rho_{P_1} t} - r_{P_1} M_{zP_1}(t) \qquad (7.4) $$

In this equation, $M_{z0,G} = I_0 \times P_0$ is the initial glucose magnetization where $I_0$ is the concentration of hyperpolarized glucose, which is assumed constant during the DDNP experiment, $P_0$ is the initial glucose polarization, and $r_{P_1}$ is the relaxation rate of the product. $\rho_{P_1}$ represents an effective spin relaxation rate that accounts for the spin depolarization during transfer from the initially hyperpolarized glucose to the product, and $k_1$ is the kinetic constant of the overall process that transforms the hyperpolarized extracellular glucose into a product. From Eq. 7.4 one has:

$$ M_{zP_1}(t) = k_1 I_0 P_0 \frac{e^{-r_{P_1} t} - e^{-\rho_{P_1} t}}{\rho_{P_1} - r_{P_1}}, \qquad (7.5) $$

so that the NMR signal of the product is:

$$ S_{P_1}(t) \propto k_1 I_0 P_0 \frac{e^{-r_{P_1} t} - e^{-\rho_{P_1} t}}{\rho_{P_1} - r_{P_1}} \times \cos^{n-1} \theta \times \sin(\theta), \qquad (7.6) $$

where $\theta$ is the (constant) read pulse flip angle and $n$ is the number of pulses performed at time $t$. Eq. 7.6 involves three parameters that define the evolution of the signal: $r_{1P}$, $\rho_1$ and $K_1 = cnst \times kI_0P_0 \sin(\theta)$. The variations with time of the ¹³C resonance peaks ($P_1$=acetate and $P_2$=δ-PGL) at 182 and 174 ppm were thus fitted to the model of Eq. 7.5. Experimental buildup curves of these signals and the associated fits are depicted in Figure 7.7. However, because of too weak signals, only four out of the eight experiments of table 7.1 were amenable to this quantitative analysis (experiments nb. 2, 3, 4, 7). It is clear from the model used that the values of the kinetic constants cannot be compared between different experiments. This is due to the fact that the absolute kinetics, i.e., the production
<figure><img src="image_64.png" /><figcaption>**Figure 7.7:** Variation of the metabolite signals with time. Experiments were performed on *E. coli* harvested at different stages of the culture growth, and characterized by their respective *OD*<sub>600</sub> = 0.9, 1.0, 1.4 and 2.8, respectively (from a) to d). The associated ratios *k*₁/*k*₂ of the buildup rates of both monitored metabolites are indicated in the figure.</figcaption></figure>

rate of the metabolites in the sample, cannot be disentangled from the absolute substrate
concentration in the sample, which varies from one DDNP experiment to the other. How-
ever, following Eq. 7.6, the ratio of the kinetic rate constants of both products P₁ and P₂,
$k_{P1}/k_{P2}$, can be extracted from a single experiment, since the variation of glucose concentration
is the same for both products. Although for experiments # 2, 3, 4, 7 the signals could be
analyzed, the major source of error for the kinetic study remains the weak signal to noise
ratio of the product's resonances. Hence, the significance of the buildup rate ratio $k_{P1}/k_{P2}$ of
these metabolites was tested by a Monte Carlo (MC) simulation where the experimental
uncertainty was estimated from the noise rmsd. Our analysis shows that this ratio varies
significantly between experiments (Fig. 7.8a), and that $k_{P1}/k_{P2}$ seems to strongly correlate with
the stage at which the bacteria were harvested from the culture medium, as monitored by
its *OD*<sub>600</sub>. This is shown in Fig. 7.8b. As discussed above, the signal at 182 ppm was as-
signed to the <sup>13</sup>C<sub>1</sub> of acetate, whilst the peak located at 174 ppm was typical of the <sup>13</sup>C<sub>1</sub>
resonance of δ-PGL that is produced by oxidation of the G6P. However, one would expect
<figure><img src="image_65.png" /><figcaption>**Figure 7.8:** (7.8a): ratios of the kinetic parameters *k*₁/*k*₂ for (experiments 2, 3, 4, 7, from top to bottom). The parameter distributions were estimated using Monte Carlo simulations with simulated detection noise. The histogram shown in this plot results from 100 iterations; (7.8b): plot of kinetic parameter ratios as a function of the OD₆₀₀ of the E.coli culture at harvest time. On the other experiments of table 7.1, signal intensities were too weak to be analyzed quantitatively by model of Eq. 7.6</figcaption></figure>

to mainly observe 6-phosphogluconate (6PGA) instead, produced upon enzymatic hydrolysis of δ-PGL by 6PGL. Note that a very weak signal at the chemical shift of 6PGA (~179.5 ppm) could be identified, as well as another one, hardly distinguishable from noise, at the expected chemical shift of γ-PGL (~178 ppm) was observed (see Fig. 7.2e). [33, 226]

In their work, Meier *et al.* [245] performed similar DDNP experiments on both BL21 and the K12 strains of E. coli. The genomes of these cell strains differ slightly, but with notable consequences for the case at hand, as BL21 cells, in contrast to K12, do not express the *ybhE* (*pgl*) gene encoding 6PGL. These authors clearly showed in DDNP experiments, that in the former strain, δ-PGL accumulated, whereas in the latter, 6PGA was readily observable, and δ-PGL remained undetected.

In the light of that work, the presence of δ-PGL signal in the ¹³C DDNP spectra presented in the present study was rather puzzling. However, several contextual aspects of the present work seem particularly relevant to interpret our data:

* *The cells, at the beginning of the DDNP experiment, are in a partially anaerobic state.*

This is attested by the early production of acetate, seconds after the mixing with the hyperpolarized glucose solution, as well as ethanol, both detected during the DDNP
experiment. Note, that formate and lactate were observed only several minutes later.

* *The DDNP experiment probes the metabolic response of cells prepared in a defined array of growth states to a glucose pulse, rather than the normal response of the metabolic state itself* - The sudden influx of (hyperpolarized) glucose perturbs the metabolic equilibrium, to which the cells oppose by a post-transcriptional response. Indeed, the production of the mixed-acid fermentation metabolites appear in the first seconds after injection. This delay is much shorter than the time needed for the implementation of enzyme synthesis by the cell, which is on the order of minutes.[267] Therefore, the observed metabolic response of *E. coli* relies on an enzyme content already present in the cells.

* *Recent studies that focused on the investigation of the metabolic phenotypes of several E. coli* strains under aerobic and anaerobic conditions showed the high variability of the metabolic fluxes in a number of basic pathways in the cell, including glycolysis, the PPP, the TCA cycle and mixed acid fermentation.[268] In particular, these authors have confirmed that the PGL flux ($\delta$-PGL $\rightarrow$ 6PGA reaction) in BL21 cells was zero. This is expected, as the BL21 *E. coli* strain lacks the *pgl* (or *ybhE*) gene. However, surprisingly, it was also reported that, whilst K12 cells (which have the *pgl* gene) exhibited a significant PGL flux in aerobic conditions, this dramatically decreased under anaerobic conditions to a similar value.

* Together, these elements suggest that at the time of dissolution, cells are in an anaerobic state where the 6PGL flux is too low to transform the rapidly produced $\delta$-PGL into 6PGA, leading to a transient, weak, and very early accumulation of the former. The fact that this signal is absent from the post DDNP spectra attests for the efficient - but slower - response of the cell to the glucose pulse by enzyme synthesis.

Besides, the simultaneous production of hyperpolarized formate and acetate in reference [245] contrasts with our experiments that showed an early production of hyperpolarized acetate, whilst formate was only identified at a later stage, in the "post DDNP", thermally
polarized, spectrum acquired minutes after the DDNP experiments. Such differences may originate from different culture conditions, which can lead to highly different metabolic cell states. In this respect, it is noteworthy that, as shown in ref. [265] the measured OD₆₀₀ value, which is the commonly used criterion to assess the growth state of the cells, only poorly correlates with their physiological state, which may not be reproducible for OD₆₀₀ ≥ 0.3. For these reasons, variations between experimental protocols that do not permit exact control of the metabolic state of the cells may also contribute to explain the apparent discrepancies between similar experiments.

The technique was able to provide valuable metabolic information through comparison of the *real-time* kinetics of both α-glucose and β-glucose uptake. The analyses of these experiments allowed us to relate the relative glucose uptake of each anomer by *E. coli* to the relative activities of glycolysis and the Pentose Phosphate Pathway (PPP) in the cell. Thus, the routing of glucose towards either of these two metabolic pathways of *E. coli* K12 when the cells are subject to a glucose pulse was shown to correlate well with the growth stage of the cells, as assessed by their OD₆₀₀ (optical density at 600 nm).

We have shown that, in the absence of any available reference signals, the metabolite decay rate differences or ratios within a single experiment could be used as makers of the metabolic response of the cells to a single glucose pulse. Although a biological description was attempted, the major objective of this method is to empirically determine the correlations between the values of the previously defined markers and the metabolic state of *E.coli*.
Conclusion

The main goal of the work presented here was to achieve quantitative kinetic studies of
metabolic reactions and pathways. Kinetic rates had therefore to be extracted from the re-
sulting NMR data. During this work, based on the existing DDNP approach, we adapted
strategies aiming at characterizing kinetic reactions having various degrees of complex-
ity. These kinetic analyses involved finding normalization strategies of the different signal
intensities in each experiment; simultaneous fitting of multiple experiments to better con-
strain model parameters; devising strategies to identify possible markers of the metabolic
response. Limitations due to either technicalities of DDNP or the system complexity were
identified and solutions to overcome them were proposed, both for *in vitro* observations of
selected metabolic reactions and *in cellulo* "global" monitoring of the metabolism on living
cells.

*In vitro* kinetic studies by DDNP

In order to try and characterize *in vitro* enzymatic reactions of the first steps of the oxPPP,
DDNP experiments were performed with changing the activity of one of the enzymes of
the cascade, and by simultaneously analyzing of the experiments. Simultaneous fitting of
the data of both experiments allowed to better constrain the model and to determine plau-
sible values for several parameters. However, some remained undetermined. which Mod-
eling DDNP studies of a complex reaction pathway required simplifying assumptions and
approximations. Moreover, fitted enzyme activities showed inconsistencies, the origin of
which was not unambiguously determined. These may be due, among others, to the use
of an oversimplified kinetic model. These limitations point to the necessity to improve the
technique, but also to issues that are not specific of DDNP, rather to parameter estimation
and data fitting in general.

A simplifying strategy was based on the direct use of [U-¹³C, U-²H]G6P to study the kinetics of the G6P dehydrogenase. This involved the optimization of the purification procedure of enzymatically produced labelled G6P. DDNP experiments using different G6PDH activities, which allowed for the determination of the lodel parameters. In particular, the obtained values for the relaxation and the anomerization rates were also consistent with independent measurements. In particular, the anomerization rate of G6P was extracted from the data. To our knowledge, the value of the anomeric rates α ↔ β is scarcely documented once [75].

Reducing the complexity of the reaction network involved made its analysis easier, and
opens the way to more complex modeling of the reaction mechanisms, including the cofac-
tor concentration, for instance, sources of metabolic regulation.

In cell kinetic studies by DDNP

In principle, DDNP provides a unique means to monitor metabolic reactions in the cell in
real time. The difficulty to extract quantitative kinetic parameters from the observed data
still remains a challenge. In our *E. coli* experiments, we were able to relate the changes of the
metabolic response of the cells changes to the growth phase of the cells. The study relied
on the comparative *real-time* kinetics of both *α*− and *β*-glucose uptake. The analyses of
these experiments allowed us to relate the relative glucose uptake of each anomer by *E. coli*
to the relative changes of activities of glycolysis and the Pentose Phosphate Pathway (PPP)
in the cell. Thus, the routing of glucose towards either of these two metabolic pathways of
*E. coli* K12 was shown to correlate well with the growth stage of the cells, as assessed by
their OD₆₀₀ (optical density at 600 nm). Alternatively, the analysis of the compared real-
time evolution of a couple of glucose metabolites showed that these provide an intrinsic
marker of the glucose metabolic response to the sudden (hyperpolarized) glucose exposure.
Again, the signal evolution of two products in multiple experiments was fitted together and
markers of metabolic states were defined out of extracted kinetic parameters.

This analysis is based on the comparison of kinetic rate ratios extracted from different ex-
periments. These quantities are not affected by possible fluctuations of the polarization
levels or polarization losses during the dissolution or injection stages, from experiment to
experiment. This approach, a limited set of experiments (< 10), therefore suggests the possi-
bility to perform comparative studies of kinetics on cells, and may provide a way to increase
the reliability of the DDNP method as a time-resolved, quantitative technique. Preliminary
developments of this in-cell approach to different substrates and cellular systems are shown
in an appendix *Appendix B* and *Appendix C* of this manuscript. *exemple*
# Appendix A

## DNP mechanisms

The different polarization transfer mechanisms in DNP rely on the dipolar interactions between electrons and nuclear spins. Here we introduce the interactions related to DNP polarization transfer from electron to nuclear-spins. Additionally, a brief description of the DNP mechanisms will be given, focusing mainly in TM mechanism.

### A.1 Dipolar interactions and spectral diffusion

In typical DNP samples, the distances between electrons are so large that their spatial wave functions do not overlap, so that Fermi-contact interactions can be neglected. In the dipolar interaction for two electron spins, the magnetic moment of a spin S induces a magnetic field $\mathbf{B}_S(\mathbf{r})$ at position $\mathbf{r}'_S$ of $S'$, expressed as [269]:

$$ \mathbf{B}_S(\mathbf{r}) = -\frac{\mu_0}{4\pi} \left( \frac{\mu_S}{r^3} - 3 \frac{(\mu_S \cdot \mathbf{r})\mathbf{r}}{r^5} \right) = -\frac{\mu_0}{4\pi} \hbar\gamma_S \left( \frac{\mathbf{S}}{r^3} - 3 \frac{(\mathbf{S} \cdot \mathbf{r})\mathbf{r}}{r^5} \right) \quad (A.1) $$

where $\mathbf{r} = \mathbf{r}_S - \mathbf{r}'_S$, is the vector that connects the two particle positions so that $r = |\mathbf{r}|$ is the distance between them, $\mu_0 = 4\pi \times 10^{-7}$ is the permeability of the vacuum. The electron-electron dipolar Hamiltonian is thus:

$$ \mathcal{H}_{SS'} = -\mathbf{B}_S \cdot \mu_S = -\hbar\gamma_S \mathbf{B}_S \cdot \mathbf{S}' = \hbar \mathbf{S} \cdot \mathbf{D} \cdot \mathbf{S}' \quad (A.2) $$
with:

$$D = \frac{\mu_0}{4\pi} \hbar \gamma_S^2 \left( \frac{1}{r^3} - 3 \frac{rr}{r^5} \right) \qquad (A.3)$$

where **D** is the electron-electron dipolar operator. Note that DNP experiments are performed in solid samples so that nuclear inter-spin distances are fixed and so **r**<sub>I</sub> and **r**'<sub>I</sub> positions can be defined. Similarly, the dipolar Hamiltonian for the nuclear spins is:

$$\mathcal{H}_{II'} = -\mathbf{B}_I \cdot \mathbf{\mu}_{I'} = -\hbar\gamma_S \mathbf{B}_I \cdot \mathbf{I}' = \hbar\mathbf{I} \cdot \mathbf{C} \cdot \mathbf{I}' \qquad (A.4)$$

where,

$$C = \frac{\mu_0}{4\pi} \hbar \gamma_I^2 \left( \frac{1}{r^3} - 3 \frac{rr}{r^5} \right) \qquad (A.5)$$

is the operator for the nuclei-nuclei dipolar interaction, where the tensor **rr** is:

$$\mathbf{rr} = \begin{pmatrix} r^2 - 3xx & -3xy & -3xz \\ -3yx & r^2 - 3yy & -3yz \\ -3zx & -3zy & r^2 - 3zz \end{pmatrix} \qquad (A.6)$$

so that:

$$D = \frac{\mu_0 \hbar \gamma_S^2}{4\pi r^5} \begin{pmatrix} r^2 - 3xx & -3xy & -3xz \\ -3yx & r^2 - 3yy & -3yz \\ -3zx & -3zy & r^2 - 3zz \end{pmatrix} = \begin{pmatrix} D_{xx} & D_{xy} & D_{xz} \\ D_{yx} & D_{yy} & D_{yz} \\ D_{zx} & D_{zy} & D_{zz} \end{pmatrix} \qquad (A.7)$$

and similarly for **C**.

### A.1.0.1 Spectral diffusion

Dipolar coupling between spins can induce flip-flop transitions that propagate throughout the spin ensemble and is responsible for spectral diffusion, of major importance for several DNP processes. For nuclear spins, $\mathcal{H}_{II'}$ permits the transport of polarization among nuclei in the sample, whereas for the electron spin system, efficient spectral diffusion increases the diffusion of $\mu$-wave saturation, of crucial importance for thermal mixing mechanism that
will be introduced below.

To better understand the transitions induced by spectral diffusion, $\mathcal{H}_{SS'}$ is expressed in terms of the step operators $S_{\pm} = S_x \pm iS_y$ and $I_{\pm} = I_x \pm iI_y$. For an isolated pair of spins, we have:

$$ \mathcal{H}_{SS'} = \hbar[D_{zz}S_zS'_z + \frac{1}{2}D_{z+}^*(S_zS'_+ + S_+S'_z) + \frac{1}{2}D_{z+}(S_zS'_- + S_-S'_z) \\ + \frac{1}{4}(D_{++}^*S_+S'_+ + D_{++}S_-S'_-) + \frac{1}{4}D_{+-}(S_-S'_+ + S_+S'_-)] \quad (A.8) $$

where the notations $D_{z+} = D_{zx} + iD_{zy} = D_{z-}^*$, $D_{++} = D_{xx} - D_{yy} + 2iD_{xy} = D_{--}^*$, and $D_{+-} = D_{xx} + D_{yy} = -D_{zz}$ have been introduced. Only the terms containing $S_{\pm}$ and $S'_{\pm}$ in this Hamiltonian induce transitions. The Hamiltonian defining the system of two dipolarly-coupled electron spins has also to consider Zeeman interactions and is therefore:

$$ \mathcal{H} = \mathcal{H}_S + \mathcal{H}_{S'} + \mathcal{H}_{SS'} = \hbar[\omega_{0S}(S_z + S'_z) + \mathbf{S} \cdot \mathbf{D} \cdot \mathbf{S}'] \quad (A.9) $$

where the first two terms represent the Zeeman interactions for spins $S$ and $S'$. The dipolar hamiltonian $\mathcal{H}_{SS'}$ induces transitions between the 4 perturbed eigenstates of the two-spin system $S, S'$ with the energy values displayed in table A.1. According to perturbation theory

<table><caption>**Table A.1:** Eigenvalues (right) of the eigenstates (left), of the dipolarly coupled system of electron spins $S$ and $S'$.</caption><thead><tr><th>|m<sub>S</sub>, m'<sub>S</sub>⟩</th><th></th></tr></thead><tbody><tr><td>|-½, -½⟩</td><td>ω<sub>0S</sub> + ¼D<sub>z</sub>z</td></tr><tr><td>|+½, -½⟩</td><td>-¼D<sub>z</sub>z</td></tr><tr><td>|-½, +½⟩</td><td>-¼D<sub>z</sub>z</td></tr><tr><td>|+½, +½⟩</td><td>-ω<sub>0S</sub> + ¼D<sub>z</sub>z</td></tr></tbody></table>

only the parts of the hamiltonian that do not induce a change of the total magnetic number contribute to the splitting of the energy levels, to first order. One may therefore neglect in eq. A.10 the transitions at $\hbar\omega_{0S}$ or $2\hbar\omega_{0S}$, and retain only transitions between $|+\frac{1}{2}, -\frac{1}{2}\rangle$ and $|-\frac{1}{2}, +\frac{1}{2}\rangle$. These flip-flop transitions also allow for the spin diffusion, in multiple spin
systems. The resulting secular Hamiltonian is thus:

$$ \mathcal{H} = \mathcal{L}_S + \mathcal{L}_{S'} + \mathcal{H}_{SS'} = \hbar[\omega_{0S}S_z + \omega_{0S'}S'_z + D_{zz}S_zS'_z + \frac{1}{4}D_{+-}(S_+S_- + S_-S'_+)] \quad (A.10) $$

The Hamiltonian in equation A.10 can be further simplified by ignoring the term $D_{zz}^{ij}S_z^iS_z^j$ (with the change of notations $S \to S^i$ and $S' \to S^j$) which merely shifts the different energy levels without inducing transitions:

$$ \mathcal{H} = \hbar[\omega_S^i S_z^i + \omega_S^j S_z^j + \frac{1}{4}D_{+-}(S_+^i S_-^j + S_-^i S_+^j)] \quad (A.11) $$

The matrix representation of this Hamiltonian is:

$$ \mathcal{H} = \frac{1}{2} \hbar \begin{pmatrix} \omega_S^i + \omega_S^j & 0 & 0 & 0 \\ 0 & \omega_S^i - \omega_S^j & D_{+-}^{ij} & 0 \\ 0 & D_{+-}^{ij} & -(\omega_S^i - \omega_S^j) & 0 \\ 0 & 0 & 0 & -(\omega_S^i + \omega_S^j) \end{pmatrix} \quad (A.12) $$

When we described how was constituted the EPR line for a given radical, we talked about "homogeneous broadening" which induced fluctuation of $\omega_S$ in time, in a range of $\Delta_h$. Since the fluctuations of $\omega_S^i$ and $\omega_S^j$ are not correlated the difference $\omega_S^i - \omega_S^j$ (appearing in the diagonal terms of the matrix) also fluctuates. The total fluctuation is composed by the convolution of $\omega_S^i$'s and $\omega_S^j$'s individual fluctuations and has a width $\Delta_{SS}$. Additionally, the intensities of the non-diagonal terms in A.12 depend on the coupling of the electron with one single particle, the second electron, and is normally less intense than the convoluted fluctuations of $\omega_S^i$ and $\omega_S^j$ in the range $\Delta_{SS}$. Thus it may be assumed that $\frac{1}{4}\hbar D_{+-}^{ij} \ll \Delta_{SS}$, which means that the dipolar interaction can produce a flip-flop transition if the fluctuations of the field are more intense than the interaction itself. As shown in [187], the flip-flop transitions are much more more likely more likely if the difference between $\omega_S^j$ and $\omega_S^i$ is smaller than $\Delta_h$, hence expressing the conservation of energy.

In conclusion, spectral diffusion is a process that relies on flip-flop transitions that are
<figure><img src="image_66.png" /><figcaption>**Figure A.1:** Diagram of the transitions induced by dipolar couplings. a) Electron dipolar interaction, for a system of two electrons where $|\omega_S - \omega'_S| \le \Delta_h$, allowed transitions are represented in yellow. b) Hyperfine interaction where the transitions in yellow are allowed if $\omega_{0I} \sim \Delta_h$</figcaption></figure>

allowed even without μ-wave irradiation. Spectral diffusion couples a spin to a neighboring one and induces transitions of electrons with close precession frequencies, in the range $\Delta_{SS}$.

### A.1.0.2 Hyperfine coupling

The coupling between nuclei and electrons is due to the hyperfine or super-hyperfine interactions. As mentioned above, Fermi-type interactions are neglected, and so the associated Hamiltonian writes:

$$ \mathcal{H}_{SI} = -\mathbf{B}_S \cdot \boldsymbol{\mu}_I = -\hbar\gamma_I \mathbf{B}_S \cdot \mathbf{I} = \hbar\mathbf{S} \cdot \mathbf{A} \cdot \mathbf{I} \quad (A.13) $$

$$ \mathbf{A} = \frac{\mu_0}{4\pi} \hbar \gamma_I \gamma_S \left( \frac{1}{r^3} - 3 \frac{\mathbf{r}\mathbf{r}}{r^5} \right) \quad (A.14) $$

where $\mathbf{r} = \mathbf{r}_S - \mathbf{r}_I$, is the inter-spin distance.

After including the Zeeman interactions and using the secular approximation, the hyperfine Hamiltonian simplifies to:

$$ \mathcal{H} = \mathcal{L}_S + \mathcal{L}_I + \mathcal{H}_{SI} = \hbar[\omega_{0S}S_z + \omega_{0I}I_z + A_{zz}S_zI_z + \frac{1}{2}A_{z-S}S_zI_{+\frac{1}{2}}A_{z+S}S_zI_{-\frac{1}{2}}] \quad (A.15) $$

The two rightmost terms on the Hamiltonian contain the step operators $I_\pm$ that are responsible for transitions of the type $|m_I\rangle = |-\frac{1}{2}\rangle \iff |+\frac{1}{2}\rangle$, in orange in figure A.1b. These transitions require amounts of energy in the order of $\hbar\omega_{0I}$ that are typically three orders of magnitude smaller than $\hbar\omega_{0S}$. The energy is provided by the hyperfine interaction, which
can match the nuclear Zeeman energy under particular conditions, for more information
see ?? . Hence, in order to increase the rate of transitions between nuclear Zeeman levels
we need to introduce a supplementary source of energy. As a matter of fact, the combined
effect of µ -wave irradiation and the hyperfine interaction could induce such transitions.
Moreover, as we will see in the next section, the introduction of a third electronic spin to
the system can also increase the rate at which transitions are induced between the nuclear
Zeeman levels.

In order to describe the complete set of interactions governing DNP process, we need
to group all the previously introduced interactions and the µ -wave irradiation. Hence, we
define a Hamiltonian considering Spectral diffusion, hyperfine and super-hyperfine inter-
actions, and µ -wave irradiation and we obtain:

$$
\mathcal{H} = \mathcal{L}_S + \mathcal{L}_I + \mathcal{H}_m + \mathcal{H}_{SI} + \mathcal{H}_{SS'} + \mathcal{H}_{II'} \quad (A.16)
$$

This Hamiltonian contains all possible interactions involved in DNP transfer. However,
the polarization process depends on various factors, such as the nature of the radical, the
composition of the sample, and on different thermodynamic parameters. Depending on the
sample, the different interactions cooperate giving raise to different DNP mechanisms.

A.1.1 Solid Effect

Of the various DNP mechanisms, the 'Solid Effect' (SE), described in 1957, represents the
first DNP theory able to account for hyperpolarization experiments [270], [271], [272]. We
only briefly present this mechanism, a simplified diagram of which is depicted in figure A.2.
It relies on a µ-wave irradiation that is tuned at ω_m = |ω_S − ω_I| frequency and induces si-
multaneous spin flips of an electron and the nuclear spin to which it is coupled. Hence, when
the irradiation is tuned at the good frequency the combined effort of the µ-wave irradiation
and the hyperfine coupling induce the simultaneous flip of the electron and the nuclear spin.
<figure><img src="image_67.png" /><figcaption>**Figure A.2:** SE mechanism. At $t_0$, the sample is at equilibrium with electrons almost fully polarized (99%). When the μ-wave irradiation starts ($t_0 + \Delta_t$), both the interaction of an electron with the μ-wave field and the super hyperfine coupling, produce the simultaneous flip-flop of a coupled electron and nuclear spins. Subsequently, the spin flip is diffused to the rest of the nuclear spin population by nuclear dipolar interactions (i.e. nuclear spectral diffusion). Then, the electron spins relax and the process starts again. The efficient polarization transfer of this process depends strongly on the μ-wave irradiation frequency to match SE conditions.</figcaption></figure>

Since the electron spin-lattice relaxation time is much shorter than the one of the nucleus, the electron spin returns to its lower energy state in a short time and can thus polarize another nucleus and so on. Additionally, the polarization can be diffused throughout the rest of the nuclear spin population by nuclear spin diffusion, see figure A.2.

The solid effect depends strongly on the irradiation frequency of the μ-wave. If the condition $\omega_m \approx \omega_S - \omega_{0I}$ is met, the solid effect induces a flip-flop transition (electron spin flip, nuclear spin flop), whereas if $\omega_m \approx \omega_S + \omega_{0I}$, the solid effect induces flip-flip transitions. Finally, in case $\omega_m \approx \omega_S$ the EPR line at $\omega_m$ but no nuclear spin transition is induced.

Other DNP mechanisms involve three-spin processes, two electronic and one nuclear spin, those mechanisms are said to rely on triple spin flips, notably Cross Effect (CE) and Thermal Mixing (TM). The difference between these mechanisms is still a subject of discussion. However, some principal features specific to TM have been identified and will be described above.
<figure><img src="image_68.png" /><figcaption>**Figure A.3:** Figure from M. Goldman and coworkers publication [196]. Figure taken from [196]. NMR signal evolution of lithium and fluorine nuclei in a DNP sample. At time 0 µ-wave irradiation is stopped and ⁷Li NMR signal is saturated. The signal evolution is monitored and shows that there is a polarization transfer from ¹⁹F to ⁷Li causing a build-up of ⁷Li NMR signal after saturation. Eventually both signals decay following longitudinal relaxation.</figcaption></figure>

## A.2 Thermal Mixing mechanism

In 1973, Goldman and co-workers [196] studied the transfer of polarization between two different nuclear spin systems present in a sample during a DNP experiment. The experiment consisted on hyperpolarizing crystals of lithium fluoride to monitor the time evolution of the NMR signals of lithium and fluorines. At some point (time 0 in figure A.3), the µ-wave irradiation was stopped and one of the NMR signals was saturated. Following the saturation of the lithium resonance, a build-up was observed in parallel with the fluorine signal decay (figure A.3). This was explained in thermodynamic terms as the existence of a thermal contact between lithium and fluorine energy spin reservoirs that allowed polarization flowing between them. The associated DNP mechanism was hence termed Thermal Mixing in analogy with thermodynamics.

### A.2.1 Triple spin flips

The elementary process involved in thermal mixing is the coupling between two electron spins $S^j$, $S^i$ and one nuclear spin $I$. This coupling can induce a transition of a nuclear spin, thereby transferring electron spin polarization to nuclei. Such a process is termed a triple
<table><caption>**Table A.2:** Eigenvalues (right) of the different eigenstates (left). States given for the triple spin flip system (two electron spins one nuclear spin).</caption><thead><tr><th>|m<sub>S</sub><sup>i</sup>, m<sub>S</sub><sup>j</sup>, m<sub>I</sub>⟩</th><th></th></tr></thead><tbody><tr><td>|+<sup>1</sup>&frasl;<sub>2</sub>, +<sup>1</sup>&frasl;<sub>2</sub>, -<sup>1</sup>&frasl;<sub>2</sub>⟩</td><td>ω<sub>++</sub> = +<sup>1</sup>&frasl;<sub>2</sub>(ω<sub>S</sub><sup>j</sup> - ω<sub>S</sub><sup>i</sup>) + <sup>1</sup>&frasl;<sub>2</sub>ω<sub>0I</sub></td></tr><tr><td>|+<sup>1</sup>&frasl;<sub>2</sub>, +<sup>1</sup>&frasl;<sub>2</sub>, +<sup>1</sup>&frasl;<sub>2</sub>⟩</td><td>ω<sub>+++</sub> = +<sup>1</sup>&frasl;<sub>2</sub>(ω<sub>S</sub><sup>j</sup> - ω<sub>S</sub><sup>i</sup>) - <sup>1</sup>&frasl;<sub>2</sub>ω<sub>0I</sub></td></tr><tr><td>|+<sup>1</sup>&frasl;<sub>2</sub>, -<sup>1</sup>&frasl;<sub>2</sub>, -<sup>1</sup>&frasl;<sub>2</sub>⟩</td><td>ω<sub>+-</sub> = +<sup>1</sup>&frasl;<sub>2</sub>(ω<sub>S</sub><sup>j</sup> - ω<sub>S</sub><sup>i</sup>) - <sup>1</sup>&frasl;<sub>2</sub>ω<sub>0I</sub></td></tr><tr><td>|+<sup>1</sup>&frasl;<sub>2</sub>, -<sup>1</sup>&frasl;<sub>2</sub>, +<sup>1</sup>&frasl;<sub>2</sub>⟩</td><td>ω<sub>++</sub> = +<sup>1</sup>&frasl;<sub>2</sub>(ω<sub>S</sub><sup>j</sup> - ω<sub>S</sub><sup>i</sup>) + <sup>1</sup>&frasl;<sub>2</sub>ω<sub>0I</sub></td></tr><tr><td>|-<sup>1</sup>&frasl;<sub>2</sub>, +<sup>1</sup>&frasl;<sub>2</sub>, -<sup>1</sup>&frasl;<sub>2</sub>⟩</td><td>ω<sub>-+</sub> = -<sup>1</sup>&frasl;<sub>2</sub>(ω<sub>S</sub><sup>j</sup> - ω<sub>S</sub><sup>i</sup>) + <sup>1</sup>&frasl;<sub>2</sub>ω<sub>0I</sub></td></tr><tr><td>|-<sup>1</sup>&frasl;<sub>2</sub>, +<sup>1</sup>&frasl;<sub>2</sub>, +<sup>1</sup>&frasl;<sub>2</sub>⟩</td><td>ω<sub>-+</sub> = -<sup>1</sup>&frasl;<sub>2</sub>(ω<sub>S</sub><sup>j</sup> - ω<sub>S</sub><sup>i</sup>) - <sup>1</sup>&frasl;<sub>2</sub>ω<sub>0I</sub></td></tr><tr><td>|-<sup>1</sup>&frasl;<sub>2</sub>, -<sup>1</sup>&frasl;<sub>2</sub>, -<sup>1</sup>&frasl;<sub>2</sub>⟩</td><td>ω<sub>-</sub> = -<sup>1</sup>&frasl;<sub>2</sub>(ω<sub>S</sub><sup>j</sup> - ω<sub>S</sub><sup>i</sup>) + <sup>1</sup>&frasl;<sub>2</sub>ω<sub>0I</sub></td></tr><tr><td>|-<sup>1</sup>&frasl;<sub>2</sub>, -<sup>1</sup>&frasl;<sub>2</sub>, +<sup>1</sup>&frasl;<sub>2</sub>⟩</td><td>ω<sub>-+</sub> = -<sup>1</sup>&frasl;<sub>2</sub>(ω<sub>S</sub><sup>j</sup> - ω<sub>S</sub><sup>i</sup>) - <sup>1</sup>&frasl;<sub>2</sub>ω<sub>0I</sub></td></tr></tbody></table>

spin flip. The relevant hamiltonian for the description of three-spin processes is:

$$ \mathcal{H} = \hbar[\omega_S^i S_z^i + \omega_S^j S_z^j - \omega_{0I} I_z + \frac{1}{4}D_{+-}(S_+^i S_-^j + S_-^i S_+^j) + \frac{1}{2}(A_{z-}S_z^i I_+ + A_{z+}S_z^i I_-)] \quad (A.17) $$

which, in the interaction representation with respect to the electron spin $S^j$ gives:

$$ \mathcal{H} = \hbar[(\omega_S^i - \omega_S^j)S_z^i - \omega_{0I}I_z + \frac{1}{4}D_{+-}(S_+^i S_-^j + S_-^i S_+^j) + \frac{1}{2}(A_{z-}S_z^i I_+ + A_{z+}S_z^i I_-)] \quad (A.18) $$

The energy level for every state of this Hamiltonian are displayed in table A.2. The matrix can be split into three blocks:

$$ \begin{aligned} \frac{1}{2}\hbar \begin{pmatrix} (\omega_S^j - \omega_S^i) + \omega_{0I} & -\frac{1}{2}A_{z-} \\ -\frac{1}{2}A_{z+} & (\omega_S^j - \omega_S^i) - \omega_{0I} \end{pmatrix} & \\ \frac{1}{2}\hbar \begin{pmatrix} (\omega_S^j - \omega_S^i) + \omega_{0I} & \frac{1}{2}A_{z+} & \frac{1}{2}D_{+-} & 0 \\ \frac{1}{2}A_{z-} & (\omega_S^j - \omega_S^i) - \omega_{0I} & 0 & \frac{1}{2}D_{+-} \\ \frac{1}{2}D_{+-} & 0 & -(\omega_S^j - \omega_S^i) + \omega_{0I} & -\frac{1}{2}A_{z+} \\ 0 & \frac{1}{2}D_{+-} & -\frac{1}{2}A_{z-} & -(\omega_S^j - \omega_S^i) - \omega_{0I} \end{pmatrix} & \\ \frac{1}{2}\hbar \begin{pmatrix} -(\omega_S^j - \omega_S^i) + \omega_{0I} & -\frac{1}{2}A_{z-} \\ -\frac{1}{2}A_{z+} & -(\omega_S^j - \omega_S^i) - \omega_{0I} \end{pmatrix} & \end{aligned} \quad (A.19) $$
For both of the two 2 × 2 submatrices, the energy difference between the diagonal terms is $\pm\hbar\omega_{0I}$. On the other hand, the 4 × 4 matrix can provide such a compensation if the condition $(\omega_S^j - \omega_S^i) = \pm\omega_{0I}$ is met. However, a third spin, the second electron, is necessary in this case. Such a triple spin flip can occur if $\omega_S^j \approx \omega_S^i - \omega_{0I}$, or if, $\omega_S^j \approx \omega_S^i + \omega_{0I}$. Also, remember that, $\omega_S^i$ and $\omega_S^j$ fluctuate in time in a range of $\Delta_h$. Hence, the energy of dipolar coupling between the two electrons needs to match the nuclear Larmor frequency, in a range up to $\Delta_h$. There are two different kinds of transitions related to the non diagonal therms of this matrix:

* The first case, $\omega_S^j \approx \omega_S^i - \omega_{0I}$ of transition produces a triple spin flip and allows the thermal mixing to happen. The terms proportional to $S_+^i I_+$ and to $S_-^i I_-$ induces the transitions and its related to the hyperfine interaction.

* The second case happens when $\omega_S^j \approx \omega_S^i + \omega_{0I}$. In this case the terms proportional to $S_+^i I_-$ and $S_-^i I_+$ produce the triple spin flip.

There is a third possible transition that does not induce triple spin flips but only an electronic flip-flop transitions. When $\omega_S^j \approx \omega_S^i$, the term $\frac{1}{2}D_{+-}(S_+^i + S_-^i)$ induces this electronic transitions. This is related only to the dipolar interaction between electrons.

### A.2.1.1 Cross effect

The Cross Effect (CE) was first introduced by Kessenikh and coworkers in 1963 [193] and has been largely studied and discussed since [192, 194, 186]. A discussion of the difference between CE mechanisms and TM is beyond the scope of this manuscript. However, some descriptions have given a hint on what might define the efficiency of both CE and TM.

CE relies on the saturation of the allowed triple spin flip transitions by the $\mu$-wave irradiation that rely on the condition $\Delta_{EPR} \le \omega_{0I}$. The latter implies that CE (as for triple spin flips mechanisms in general) depends on the with of the EPR line [195]. Thus, when the inhomogeneous linewidth $\Delta_{EPR}$ is such that $\omega_{0I} < \Delta_{EPR}$, CE becomes an efficient DNP mechanism.

As a matter of fact, the transitions in CE come from the saturation produced by the $\mu$-wave
<figure><img src="image_69.png" /><figcaption>**Figure A.4:** Figure taken from [195]. **a** Population distribution for a conventional three spin system. **b** Population distribution for a system matching CE conditions, μ-wave irradiation saturates the transition for the first electron producing a nuclear negative polarization. **c** μ-wave irradiation saturates, the transition for the second electron</figcaption></figure>

irradiation of the electron transitions. The saturation changes the populations in each level which, depending on the saturated transition, can produce positive or negative polarization [195]. The systems have nevertheless to fulfill the condition $|\omega_S^i - \omega_S^j| = \omega_I$ [192][195], as depicted in figure A.4. The μ-wave saturation is at the origin of CE, a system with low spectral diffusion is thus more adapted for CE mechanism since the saturation is not diffused throughout the EPR spectrum.

On the other hand, for TM, the mechanism depends on efficient spectral diffusion. In this mechanism, the saturation of the μ-wave is diffused through the population of spins until the triple spin flip conditions are matched ((ω_S^j - ω_S^i) = ±ω_0I). Although in TM, the μ-wave is also at the origin of the DNP enhancement, the process of coupling electrons and nuclei depends on the efficiency of spectral diffusion. The manifestation of an out of equilibrium hyperpolarized state depends on the spectral diffusion being faster than the relaxation of the nuclear hyperpolarization with the lattice. This will be further discussed in the next section.

The triple spin flips transitions are depicted in figure A.5. On the left hand side of the figure (reproduced from chapter 6.1.3 of [187]), μ-wave irradiation saturates an electron transition
<figure><img src="image_70.png" /><figcaption>**Figure A.5:** Two different cartoons depicting the TM mechanism in different contexts. The green arrows represent the spins flipped by conventional spectral diffusion and the yellow arrows are the triple spin flips. On the left side, the triple spin flip is directly induced by the μ-wave irradiation at $t_2$. The hyperpolarization is then transferred to the other nuclear spins by nuclear spin diffusion. Electron spin diffusion keeps flipping electron spins through the entire EPR line (if the EPR line is continuous). One of the features of TM is that it does not depend on the μ-wave irradiation frequency. On the right side, we have an example in which the μ-wave irradiation saturates a frequency of the EPR line (flipping the electron spin in red) at time $t_0$. Then, spectral diffusion flips subsequent electron spins until matching triple spin flip conditions at time $t_2$ ($\omega_{t1} = \omega_{S1} - \omega_{S3}$).</figcaption></figure>

that triggers directly the triple spin flip. On the right hand side, μ-wave irradiation saturates the electron spin system at a particular frequency, after spectral diffusion $|\omega_S^i - \omega_S^j| = \omega_{I0}$ condition is matched. Although the left side displays spectral diffusion (and can also occur in TM conditions), the direct irradiation of the electron spins involved in the triple spin flip corresponds more to CE scheme. μ-wave irradiation frequency can be set to saturate different transitions depicted in figure A.4.

## A.2.2 Spin temperature exchange and μ-wave irradiation

In a publication entitled "Spin Temperature", by A. Abragam and W. G. Proctor, [200] the concept of spin temperature was discussed. Its formalism is fundamental for the understanding of DNP phenomena among others. In section 2 of the review, [189], Abragam and M. Goldman state that "The basic hypothesis in spin-temperature theory is that the evolution of an isolated system of a large number of interacting spins leads to a state of equilibrium characterised by a temperature, i.e. a Boltzmann distribution of the populations of its various energy levels." It was also claimed later on, that the concept of spin temperature is only meaningful if the process exciting spins out of equilibrium is faster than the spin-lattice re-
<figure><img src="image_71.png" /><figcaption>**Figure A.6:** Scheme depicting the heat exchanges between the different reservoirs of energy involved in TM context under μ-wave irradiation. The main nuclear relaxation source comes from the coupling with the electron spins that also relax through spin-lattice relaxation (1). The direct nuclear spin-lattice relaxation is not an efficient process (2). Tipple spin flips couple the electron non-Zeeman reservoir and the nuclear Zeeman reservoir due to the dipolar and hyperfine interactions between the different electron and nuclear spins. The μ-wave irradiation cools down the electron non-Zeeman reservoir and creates a contact between the electron Zeeman and the electron non-Zeeman reservoirs (yellow arrow). Due to the coupling, the microwave cools down the nuclear Zeeman reservoir indirectly. If TM is efficient the invers spin temperature of both the nuclear Zeeman, and electron non-Zeeman reservoirs will homogenize. This last phenomenon is responsible for the hyperpolarization of the nuclear spin systems.</figcaption></figure>

laxation [189]. In this scenario, a process affecting the population difference of the different energy levels produces a variation in spin temperature. Hence, the spin temperature can be defined in terms of the polarization of the spin system. Yet if the polarization can be determined by a Boltzmann distribution, the system can be considered at equilibrium and so, spin-temperature and lattice temperature are equal. Indeed, the first requirement for TM is that mutual interactions must lead to establishing a local stationary state in a time short with respect to the spin-lattice relaxation time [189]. In this case, there may exist a spin temperature $T_S$ different from the lattice temperature $T_L$.

In the thermal mixing picture, several energy reservoirs are typically defined. Thus, for the electron spin system the *Electron Zeeman reservoir* is defined, to which is associated a temperature $T_Z$. The rest of the energy, contributed by the other interactions defines a second temperature for the system and constitutes the *Electron Non-Zeeman reservoir*, with its temperature $T_{NZ}$. In addition, a nuclear Zeeman reservoir is defined.

Note that for the electron-spin system, in the absence of μ-wave irradiation, the major energy contribution comes from the Electron Zeeman reservoir, which therefore determines the spin temperature, in this case, the lattice temperature. Several descriptions of
TM have been proposed in the literature to describe the behavior of electron and nuclear polarization under μ-wave irradiation in particular conditions, such as high-temperature approximation [273] or strong μ-wave irradiation [197]. More recent work, inspired by the previous descriptions, has tried to describe systems under less constrained conditions, beyond high-temperature approximation [202], or under partial saturation of the μ-wave irradiation [198]. The final objective is to give a description of the TM mechanism in order to predict the evolution of the polarization in DNP systems.

If spectral diffusion is fast enough for a local equilibrium to establish, the electron spin polarization can be determined in function of two spin temperatures $α = ħ/k_B T_Z$ and $β_{NZ} = ħ/k_B T_{NZ}$, the inverse electron Zeeman temperature, and the inverse electron non-Zeeman temperature respectively[273][189]. It has been discussed how triple spin flips create a contact between $β_I = ħ/k_B T_I$, the inverse spin temperature for nuclear spins, and $β_{NZ}$,[189] [188][198]. It can be shown that in TM conditions, when the thermal mixing process is very fast compared with all other relaxation mechanisms involved in the DNP processes, after reaching local equilibrium spin temperatures tend to $β_I = β_{NZ}$. The previous phenomenon is related to the energy conservation rules for triple spin flips, $ω_s^j ≈ ω_s^i + ω_{0I}$ and $ω_s^j ≈ ω_s^i - ω_{0I}$ introduced in the previous section, as demonstrated in [188] and [187].

The DNP process originates on the μ-wave irradiation which adds energy to the electron spin system. The dipolar coupling between electron spins distributes the energy to both the electron Zeeman reservoir and the electron non-Zeeman reservoir. This energy contribution produces a heating of the electron Zeeman reservoir while the electron non-Zeeman reservoir cools down. Triple spin flips create a contact between the electron non-Zeeman reservoir and the nuclear Zeeman reservoir, which is cooled down as well. Hence, the nuclear spins are polarized, as described in chapter 8 of [187]

As a matter of fact, you can express the inverse spin temperature of your electron spin system with the previous assumption:

$$ω_Sβ(ω_S) = ω_0α + (ω_0 - ω_S)β_{NZ} \quad (A.20)$$
Where $\omega_S$ is the resonance frequency of a given spin, and $\omega_0$ is the frequency at the center of gravity of your EPR spectrum. In [188], the development of the previous expression gives:

$$P_S(\omega_S) = \tanh\left(\frac{1}{2}(\omega_0\alpha + (\omega_0 - \omega_S)\beta_{NZ})\right) \quad (A.21)$$

Where we can see the contribution of the electron non-Zeeman and electron Zeeman reservoirs. Is important to remind that $\omega_S$ is affected by the homogeneous broadening and so, it fluctuates inside $\Delta_h$. With the objective of predicting the evolution of the polarization under $\mu$-wave irradiation, multiple theories have described the evolution of the spin temperatures ($\alpha$ and $\beta_{NZ}$) using approximations related to the intensity of the $\mu$-wave and the efficiency of the triple spin flips. As reviewed in T. Wenckebach 2017, if an intense $\mu$-wave irradiation is considered we have:

$$\alpha = -\frac{\omega_m - \omega_0}{\omega_0} \beta_{NZ} \quad (A.22)$$

Which, inserted in equation A.21, in a frame rotating at the $\mu$-wave's frequency, gives:

$$P_S(\omega_S) = \tanh\left(\frac{1}{2}(\omega_S - \omega_m)\beta_{NZ}\right) \quad (A.23)$$

And so, with the $\mu$-wave irradiation you can define the polarization of the electron spin system with a single inverse spin temperature $\beta_{NZ}$. Additionally, since triple spin flips homogenize the nuclear Zeeman and the electron non-Zeman reservoirs' temperature, we got that:

$$P_I = \tanh\left(\frac{1}{2}\omega_{0I}\beta_{NZ}\right) \quad (A.24)$$

This conclusion reproduces Borgini's expression of $P_I$ in [197] which is pertinent since we do not consider the ratio between the number of nuclear spins and the number of saturated electron spins (like proposed in [198]) and therefore we describe a system under strong $\mu$-wave irradiation. For the different spin systems, reaching the lattice temperature depends on a series of relaxation mechanisms. Electron spins relaxation with the lattice follows a process that affects all electron spins at the same rate $\frac{1}{T_{IS}}$. The relaxation process homog-
<figure><img src="image_72.png" /><figcaption>**Figure A.7:** Reservoirs of energy involved in the heat exchange between the different spin systems for the Goldman and coworkers experiment (performed in [196]). 1 and 2 correspond to the spin-lattice relaxation processes. It is important to precise that nuclear spin-lattice relaxation (2) is a very slow process, the main source of nuclear relaxation is due to the interaction with the electrons and the fluctuating field (introduce in previous paragraphs). In 3 we got the indirect contact between the different nuclear Zeeman reservoirs. The exchange of spin temperature is faster than the relaxation processes producing the transfer of polarization from one nucleus to the other. Eventually, the lattice pumps enough energy for the system to get to equilibrium and reach, for the different spin systems, the lattice temperature.</figcaption></figure>

enizes the spin temperature of the electrons with $\beta_L = \hbar/k_B T_L$. The evolution of electrons polarization follows:

$$ \frac{\partial P_S}{\partial t} = \frac{1}{T_{1S}} [P_S - P_L] \qquad (A.25) $$

Where, as expected, $P_L$ is the polarization given by the Boltzman distribution. In the case of nuclear spins the coupling with electron spins is the major source of relaxation, their direct lattice-relaxation process is too slow ($1/T_{1I}$ many times smaller then $1/T_{1S}$). Multiple relaxation mechanisms are fundamental for the complete understanding of DNP and NMR in general, however their complexity makes them not to be detailed in this manuscript. Some minor descriptions will be given in chapters to come. For the moment we only precise that the main source of nuclear relaxation comes from their dipolar coupling with the electron spins, which relax directly with the lattice.

We saw that through TM $\beta_{NZ}$ and $\beta_I$ homogenize. If there are multiple nuclear species all nuclear Zeeman reservoirs can homogenize their spin temperature with the electron non-Zeeman reservoir [187]. When the triple spin flip process is efficient, i.e. the spin temperature exchange is faster than the electron spin-lattice relaxation, TM produces a transfer of spin temperature between multiple nuclear Zeeman reservoirs. This effect is at the origin
of the polarization transfer seen in Goldman and coworkers' experiments (in figure A.3). A cartoon depicting the exchange between the reservoirs is presented in figure A.7. The indirect contact responsible for the polarization transfer between nuclear reservoirs is represented by the arrow in 3.

Multiple of the mechanisms that have been presented can occur simultaneously in the same sample. However, we can use the efficiency of the spin temperature transfer between different nuclear species to evaluate the predominance of TM.

## A.3 Characterizing TM via cross-talk between spin reservoirs

During my masters internship directed by Dennis Kurzbach, a method to evaluate the actual contribution of TM to DNP in a given sample was developed. The objective was to use the fact that the contact between the nuclear Zeeman and the electron non-Zeeman reservoirs tends to equalize the spin temperature of both reservoirs in TM conditions, hence, if the polarization transfer takes place on a time scale that is faster than the nuclear relaxation rate. In such conditions, if different types of nuclei are present in the sample, heat can flow spontaneously from one nuclear reservoir to another via the non-Zeeman electron reservoir. Therefore, under TM, polarization transfers between different nuclear species are expected to follow the simple laws of heat propagation as shown in the experiments of [196] and depicted in figure A.3. In practice, however, DNP often results from a combination of different mechanisms that may be difficult to disentangle. In order to determine if TM is the predominant DNP mechanism we performed experiments on samples containing different nuclear species. The samples for the different experiments contained protons $I = ^1H$ and a second nuclei $I' = ^2H, ^{13}C$, or $^{31}P$, depending on the experiment.

Two complementary experiments were performed: (A) the polarization buildup curves
<figure><img src="image_73.png" /></figure>

**Figure A.8: a)** Energy reservoirs involved in experiment A that monitors the build-up of the polarizations P(I = ¹H) and P(I' = ¹³C) after switching on the saturation of the EPR spectrum by microwaves (μw), and their decay after interruption of the μw irradiation. The μw irradiation cools down the non-Zeeman dipolar electron reservoir e NZ; as a result, the ¹H and ¹³C spins are polarized simultaneously via heat exchange between the reservoirs. Nuclear relaxation proceeds via dissipation of energy to the lattice. **b)** DNP build-up curves and decay of polarizations after switching off the (μw)-field (at the delays indicated exemplarily for ¹H and ¹³C in the panel of 100 mM TEMPOL) for a sample containing I = ¹H and I' = ¹³C nuclei. The polarizations are expressed in terms of inverse spin temperatures, 1/Tj. Traces shown in lighter color indicate the ranges of experimental errors.

of both nuclei were monitored under microwave irradiation, then their return to thermal
equilibrium after switching off the microwave irradiation was observed; (B) we reproduced
the experiment proposed [196] (see figure ??) and initially performed on single crystals of
lithium fluoride, and applied it to amorphous samples that are used in current DNP appli-
cations. In the latter experiment, two different nuclei were simultaneously hyperpolarized
(I = ¹ H, and I' = ² H, ¹³C or ³¹P). After reaching the maximum stationary polarization,
one of the nuclei was saturated by means of RF pulses, and the time-evolution of polariza-
tions P(I) and P(I') were observed. For A and B experiments, we used the nitroxide radical
TEMPOL which is characterized by a broad inhomogeneous EPR line (ca. 0.5 GHz). The
TEMPOL concentration was varied in the range of 10 – 100 mM.
### A.3.0.1 Reaching a common spin temperature

The first test consisted in verifying that both nuclear Zeeman reservoirs (for *I* and *I*') reached a common spin temperature. Figure A.8a displays schematically the flow of spin order in experiment A. Through *μ*-wave irradiation, the non-Zeeman dipolar electronic ($e_{NZ}$) energy levels are polarized, thus cooling down the corresponding heat reservoir. Consequently, triple spin flips tend to equalize the $e_{NZ}$ spin temperature and the nuclear spin temperature of both $^{1}$H (SS'I flips) and $^{13}$C (SS'I' flips) reservoirs. After switching off the *μ*w irradiation, both nuclear polarizations $P(^{1}H)$ and $P(^{13}C)$ decay and equilibrate at the lattice temperature. Typical DNP build-up curves of these nuclear spin polarizations and their subsequent decays, obtained for different concentrations of TEMPOL, are shown in figure A.8b for sample 2.

Results shown in figure A.8b for $I(^{1}H)$ and $I'(^{13}C)$ indicate that, for TEMPOL concentrations above 50 mM, both nuclei converge to a common spin temperature after the initial build-up. In contrast, at lower radical concentrations (10-40 mM), the $^{13}C$ spin temperature is significantly higher than the proton one, thus indicating that TM is not the dominant mechanism since the condition above is not fulfilled anymore.

The fact that TM no longer dominates at low radical concentrations originates from reduced spectral diffusion, as the average distance between radicals increases. When electron spectral diffusion slows down due to decreasing flip-flop probabilities, the electron spins cannot be treated anymore using thermodynamic concepts. The rate of triple-spin flips decreases dramatically and becomes lower than the relaxation rates of the different spin species, leading to the breakdown of the thermodynamic description of DNP.

### A.3.0.2 Heat transfer between the nuclear Zeeman reservoirs

We can evaluate the presence of triple-spin flips at different radical concentrations by experiment B, schematically depicted in figure A.9a. Triple spin flips offer a mechanism through which the transfer of polarization, i.e., of heat from one nuclear reservoir to another via the $e_{NZ}$ reservoir, can take place. Hence, a spontaneous heat flow from a warmer to a colder
<figure><img src="image_74.png" /><figcaption>**Figure A.9:** a) Energy reservoirs involved in experiment B that monitor the transfer between the polarizations P(I = $^1$H) and P(I' = $^{13}$C) after the interruption of the µw irradiation and saturation of either I or I' nuclear reservoirs. Via triple spin flips, the polarization flows from $^1$H to the non-Zeeman dipolar electron reservoir, and is then transferred to $^{13}$C spins via SS'I' triple spin flips. These processes are accompanied by relaxation to the lattice (omitted in the flow diagram.) b) Time evolution of the inverse nuclear spin temperature 1/TI. First, a polarization P(I = $^1$H) is generated by DNP. Subsequently, after the µw irradiation is interrupted, the $^{13}$C spins are saturated and a spontaneous flow of polarization from $^1$H to $^{13}$C reservoirs is observed. Spontaneous transfer of heat from the $^1$H to $^{13}$C reservoir is indicative of triple spin flips SS'I and SS'I'.</figcaption></figure>

spin reservoir attests for the presence of triple-spin flips. Through our experimental setup, we could observe the transfer of polarization from 1H to 13C, i.e., as the 1H reservoir heats up, the 13C reservoir cools down. When the rate of triple spin flips is high, the two nuclear and the eNZ reservoirs reach a common spin temperature before they relax to the equilibrium temperature. This is exactly what is observed in figure A.9b between 40 and 100 mM where the 13C polarization of sample 2 reaches a maximum when the temperatures of the two nuclear reservoirs become equal (the time traces cross). To our surprise, the transfer of polarization between the two nuclear reservoirs is not entirely suppressed even at a radi-
<figure><img src="image_75.png" /><figcaption>**Figure A.10:** a) Characteristic build-up times, $t_B$U for P($^1$H) and P($^{13}$C) polarizations at different TEMPOL concentrations, obtained by fitting experimental build-up curves to mono-exponential functions. At low radical concentrations, the build-up of P($^{13}$C) is faster than the build-up of P($^1$H), indicating a change of the dominant DNP regime (see text for details). b) Dependence of the inverse steady-state spin temperatures $1/T_I(^1H)$ and $1/T_I(^{13}C)$ as a function of the radical concentration. At a TEMPOL concentration of 50 mM these inverse spin temperatures are similar within experimental error, indicating that TM is predominant, while below 40 mM this is no longer the case. c) Characteristic polarization transfer times from P($^1$H) to P($^{13}$C) obtained by fitting the first part of the $^{13}$C time dependence in experiment B to mono-exponential build-up functions. The dashed lines are to guide the eye.</figcaption></figure>

cal concentration as low as 10 mM. Thus, even though the signature features of a common spin temperature and an efficient heat transfer are not fulfilled, we observe triple spin flips, indicating a non-TM regime with a reduced rate of such transitions.

At TEMPOL concentrations of 50 mM or above all characteristic features of TM, are observed, while at lower concentrations the nuclear reservoirs do not reach a common spin temperature and the heat transfer is inefficient despite the occurrence of triple spin flips. The characteristic build-up times and steady-state spin temperatures at the end of the build-up (experiment A) as well as the transfer times (characteristic cooling times of the $^{13}$C reservoir in experiment B) are summarized in figure A.10. Note that heat transfer becomes faster with increasing radical concentration (figure A.10c), thereby confirming the dependence of the triple spin flip rate on the TEMPOL concentration.

In conclusion, combining experiments A and B yields a strategy for the determination of TM contributions to DNP, corresponding to the limiting case where the spin temperatures of all spin reservoirs tend to a common value $T_I$ for $t \to \infty$ due to triple spin flips and the spontaneous heat transfer between different reservoirs. This strategy allows one to assess the presence of the TM regime, understood as a situation where a common nuclear spin temperature emerges from a spontaneous heat flow, through triple spin flip transitions. We want to stress that the sole occurrence of triple spin flips, or of spontaneous heat transfer, is
not indicative of strict and predominant TM, if the spin temperatures of the different nuclei
in the system do not converge. Moreover, it can be stated that TM is the dominant mecha-
nism at high TEMPOL concentrations (≥ 50 mM) at 4.2 K and 6.7 T, while for lower TEMPOL
concentrations (≤40 mM) the spin temperatures of the different reservoirs tend to different
values. From the experimental point of view, it is important to note that the lowest ¹³C
spin temperature can be reached at TEMPOL concentrations of 50 mM due to low ¹H spin
temperatures and the dominance of TM. Yet, even lower 1H temperatures can be reached at
a lower TEMPOL concentration of 40 mM because favorable saturation factors[274][199].
This information is crucial for users who cannot rely on cross-polarization techniques. In
this situation TM-DNP can be a remedy, since it not only allows one to hyperpolarize pro-
tons, but also homogenizes their spin temperatures with various other nuclei potentially
increasing the final achievable hyperpolarization level.

.
# Appendix B

## Pyruvate into Ecoli ATCC and 2,4-DNP

The methodology introduced in the last chapter can be extended to a wide range of organisms and substrates. The principal conditions for this methodology to be applied are:

* The organism has to survive the mechanical shock produced in the injection of the dissolved DNP sample.

* The relaxation times of the substrates have to be long enough for the metabolic process to be observed.

* The substrate has to be internalized and metabolized by the organism.

Although glucose has a fundamental role in metabolism, its $T_1$ is shorter than other metabolites containing carbonyl groups. As a matter of fact, multiple in cell DDNP studies use Pyruvate due to its $C_1$ particularly small relaxation rate. Additionally, pyruvate is a metabolite that is commonly uptaken and metabolized by most living organisms since it plays a central role in multiple metabolic pathways (see subsection 1.1.1.1). Hence, for methodological development we chose pyruvate as substrate to perform our first in cell DDNP experiments.
<figure><img src="image_76.png" /><figcaption>**Figure B.1:** Superposition of the first 25 scans of the injection of hyperpolarized [¹³C]pyruvate into a suspension of *E.coli*. In this spectrum, resonances **1** and **5** are C₂ and C₁ of pyruvate respectively, **2** is acetate's C₁, **3** is pyruvate hydrate's C₁, **4** formate, **6** HCO₃⁻ or bicarbonate, **7** CO₂ and, **8** and **9** are glycerol's C₁ and C₂, **3** respectively.</figcaption></figure>

## B.0.1 Experiment n°1, no cell treatment

The culture of *E.coli* ATCC followed the same standard steps than the ones presented in section 7.2. Using lysogeny broth as medium, bacteria precultures were grown overnight. Cultures were then inoculated into 50 mL of LB and grown to OD₆₀₀ = 0.9. After reaching desired growth, cells were harvested by centrifugation at 3500 G-force for 10 minute, washed in PBS 1x buffer and resuspended in 1 mL of PBS 1x buffer pH = 7.2 inside a 10 mm NMR tube instants before the DDNP experiment.

The DNP sample for pyruvate had been previously optimized in our laboratory, it is composed of a mixture of H₂O, D₂O, and Glycerol-d₈ at 10:40:50% in volume respectively. This mixture was prepared with a stock solution of D₂O at 200 mM TEMPOL, to obtain a final concentration of 50mM TEMPOL. ¹³C₁-pyruvate was added to the final solution to reach a concentration of 1.5 M. The hyperpolarization of ¹³C₁-pyruvate was obtained with a CP sequence for approx. 45 min under µ-wave irradiation at 187.9 GHz with a orwer of
<figure><img src="image_77.png" /><figcaption>**Figure B.2:** Signal evolution of the different metabolites observed in pyruvate metabolism by *e.coli*. Products of pyruvate metabolism, HCO₃⁻ in top, CO₂ in the middle and acetate in the bottom, all end products of the citric acid fermentation pathway. For all products the SNR is very low, kinetics can not be analyzed. B.2b Spontaneous hydration of pyruvate. Pyruvate C₁ in black, pyruvate hydrate in blue, signal is multiplied, ×50.</figcaption></figure>

350 mW. The μ-wave irradiation was modulated with a saw-tooth function over a range of 100 MHz with a modulation frequency of 1 or 2 kHz.

To transfer the sample, 5 mL of PBS 1x at pH = 7.2 were inserted in the dissolution box, heated at 403 K and pressurized at 10.5 bar. The mixing of the hyperpolarized solution with the *E.coli* suspension is done in a 10 mm NMR tube, inside a 10mm BBO probe. Only 1H decoupling was performed by means of a WALTZ16 pulse sequence. The results presented in this section consist on ¹³C pseudo 2D experiments with a 1 s time interval between scans using 10° read pulses. Resulting FID's were treated following the same steps than for the previous chapter.

The resulting pseudo-2D spectrum displayed signals of the hyperpolarized substrate and of different products of *e.coli*'s metabolism. The cells seem to be metabolizing the injected pyruvate, this experiment was the first successful in cell DDNP experiment of our team. A projection of the first 25 scans is displayed in figure B.1. The peak were assigned by compar-
ison with literature and by the knowledge of the species involved in pyruvate's metabolism by E.coli. After integration of the different resonance, the time evolution of each metabolite's signal was reconstructed. The results are displayed in figure B.2. Although different products can be identified, the signal to noise ratio is very weak. Any kinetic analysis would be hardly affected by the noise. However, some comments can be given. The results suggests an early production of formate and acetate, both end chain products of acetyl-CoA (see figure 7.3). The former is eventually degraded into CO2 and subsequently produces bicarbonate. Accelerated excretion of bicarbonate can also also reflect and imbalance in the acid/base conditions of the solution due to excretion of acetic acid, lactic acid, etc...

## B.0.2 Experiment n°2, addition of 2,4-dinitrophenol

A second experiment was performed with pyruvate into *E.coli*. The aim was to increase the signal to noise ratio of the products. Since it had been previously optimized, the DNP sample was conserved (from last experiment). The different DNP related parameters were also conserved (μ-wave frequency etc..). The bacteria, on the other hand, followed a different treatment. After reaching desired growth OD₆₀₀ = 1.1, 2,4-dinitrophenol (2,4-DNP) was added to the culture medium to reach a concentration of 1.5 mM, 30 min before dissolution experiment. Subsequently, cells were harvested by centrifugation at 3500 G-force for 10 minute, washed in PBS 1x buffer and resuspended in 1 mL of PBS 1x buffer pH = 7.2 containing also 1.5 mM of 2,4-dinitrophenol. The 1 mL resuspension was inserted inside a 10 mm NMR tube instants before the DDNP experiment.

The new experiment also displayed proof of metabolism. In figure B.3a we have the superposition of the first 20 1D-spectra. The resonances observed in the spectra evidence a different metabolic behaviour from the obtained in the first experiment with pyruvate. The increment of the acetate resonance's signal suggest that the production of acetate is enhanced. On the other hand, the production of formate seems to diminish and its resonance's decreased signal seems to be covered by pyruvate C₁₁ signal. Additionally, we see the ap-
<figure><img src="image_78.png" /><figcaption>**Figure B.3:** B.3a Superposition of the first 20 scans of the injection of hyperpolarized [1³C]pyruvate into a suspension of *E.coli* previously treated within 2,4-DNP for 30 min. In this spectrum, resonances **1** and **6** are C₂ and C₁ of pyruvate respectively, **2** is lactate's C₁, **3** is acetate's C₁, **4** pyruvate hydrate's C₁ **5**, **7** CO₂ and, **8** and **9** are glycerol's C₁ and C₂, **3** respectively. ??</figcaption></figure>

partition of 2 new resonances assigned to lactate and .... . CO₂ is still being produced which confirms formate's production, however we cannot see its conversion into HCO₃⁻, probably related to a lower hyperpolarized signal of CO₂ that relaxes before producing HCO₃⁻.

In the first experiment, the maximum of CO₂ was obtained around 25 s after the start of the dissolution. In this second experiment with 2,4-DNP, the maximum of CO₂ is obtained around 16 s after start. The same effect is observed for acetate's production for which the maximum is obtained approximately 4 s before in experiment 2. The production processes of both CO₂ (and so formate) and Acetate seems to accelerate in presence of 2,4-DNP. Addition of 2,4-DNP, also seems to enhance lactate's production. The latter can be originated by an enhanced in pyruvate metabolism in the same hypoxic conditions of experiment 1. Conditions at the origin of lactate production, see ??.

2,4-DNP is an uncoupler of oxidative phosphorylation which are compounds able to produce a proton transport across biological membranes. The latter has an impact on nutrient transport, ATP synthesis, and other endergonic reactions at the cell membrane [275]. Addition of 2,4-DNP to cellular medium has shown to affect metabolism (strongly dimishing
production of ATP) and increasing the efflux of multiple metabolic products such as acetate
[276]. The enhanced metabolism towards acetate production and efflux might be at the ori-
gin of acetate resonance's signal increase in experiment 2. Different studies have shown
how the uptake of some carbon sources is reduced in the presence of 2,4-DNP [275]. How-
ever, it has been proven that the inhibitory effects of 2,4-DNP on substrate uptake are not
related to inhibition of the transmembrane transport but to the regulations of metabolism
due to lack of ATP production (and so, low glycolitic rate). Glucose consumption has been
shown to slow down in the presence of 2,4-DNP [276]. An effect of 2,4-DNP compound on
pyruvate uptake has also been observed. Previous research has shown how pyruvate uptake
is dependent on the pH gradient across the membrane [277]. In this work, they claim that
the proton transport through membrane produced by 2,4-DNP reduces the pH gradient in
a limit in which pyruvate transport can get completely inhibited. Our results are not nec-
essarily in contradiction, the pulse of pyruvate create a metabolic shock with an enhanced
efflux of acetic and lactic acid. The pH variation of the medium affects the gradient across
the membrane that can be at origin of an enhanced pyruvate uptake. Our results qualita-
tively show that, the pulse of hyperpolarized pyruvate enhances the production of acetate
and lactate for cells grown with 2,4-DNP. The substrate is thus being uptaken by the cells
in presence of 2,4-DNP and the metabolism towards acid fermentation seems to be acceler-
ated. Although, for E.coli K12, glucose metabolism has been shown to slow down by addition
of 2,4-DNP [276], in our experimental conditions, 2,4-DNP seemed to enhance acetate and
lactate production with pyruvate as substrate.
# Appendix C

## Glucose into Macrophages

Most of prokaryotic cells have a double membrane separating the inside from the external environment. The double membrane can help the organism resist mechanical shocks. Multiple cellular systems without this double membrane would not be able to resist the shock during DDNP's injection with our experimental setup. However, we were able to perform DDNP experiments on eucariotik cell systems. In this section we want to present experiments performed on eukaryotic cells aiming to observe macrophages metabolism of glucose. Macrophages are highly versatile cells with a range of functions depending on their location and activation status. Between the different functions of macrophages are, anti-bacterial and anti-tumor activity, secretion of a wide variety of regulatory peptide factors, prostanoids, and enzymes. The activation of macrophages has been shown to be dependent on the carbon sources and oxygenation [278]. As a matter of fact, glucose is a critical component in the proinflammatory response of macrophages[279]. Other research has shown the major role of oxygenation and metabolic regulation in macrophage's antitumor activity [280]. This cellular system is a very interesting subject of study that has recently been focused by oncology research[280]. The first experiments that we performed on macrophages focused on the study of glucose metabolism. The results presented here are preliminary work, no quantitative kinetic analysis has yet been performed on this system. However, some features of macrophage's metabolism can already be observed.
<figure><img src="image_79.png" /><figcaption>**Figure C.1:** Pictures of the observation of RAW culture with microscope. In the left cells are in low confluency conditions, in the right, cells are at high confluency conditions.</figcaption></figure>

### C.0.1 Cell culture and DDNP setup

All the studies were performed using macrophages from mouse, RAW 267 bought from ATCC. The vials containing the cells were stored in liquid nitrogen at -150°C. From the opening of the vials all operations were done in the cell-culture room, in complete aseptic conditions. For the first use the vials were thawed until liquefaction on a water bath at 37 °C and subsequently decontaminated with ethanol 70%. The content of the vials was transferred to a falcon containing 9 mL of warm (37 °C) culture medium. The ~ 10 mL solution was centrifuged at 125 g for 7 min and supernatants were discarded. Cells were then resuspended in 1 mL of warm culture medium prior to transfer to the culture flask (T75 for adherent cells). Flasks were filled with 14 mL of culture medium and set in the incubator during the procedure. Cells were finally resuspended in the culture flasks to reach a final volume of 15 mL. We used DMEM + 10% FBS as culture medium. Viability of cells was monitored every day by cell counting, the medium was renewed every two days. Pictures of low and high confluency (x5 as many cells) are displayed in figure ???. The process from cell's inoculation to high confluency state takes between 2 and 3 days. Before the dissolu-
tion experiment, cells were scratched from the culture flasks with a cell scraper, without addition of trypsin, and centrifuged at 125 g for 7 min. Cells were subsequently washed with HEPES 100 mM and resuspended into 0.5 mL of HEPES 100 mM in the 10 mm NMR tube, instants prior to the dissolution experiment. For the DNP experiments different cell ammounts were used (from 1 to 8 flasks depending on the experiment), with all cell systems at high confluency conditions.

For the experiments with macrophages, the DNP sample were prepared with a mixture of 10:35:55% in volume of H₂O, deuterated DMSO and D₂O respectively. The mixture was prepared with a stock solution of D₂O at 200 mM TEMPOL to reach 40 mM TEMPOL concentration. [U-¹³C, U-²H]-glucose was added to the solution to have a final concentration of 1 M. The DNP sample consisted on 75 µL of the previously described solution, inserted in a sample-holder and placed in the bath of liquid helium. Hyperpolarization was achieved by means of a CP sequence, see subsection 4.2.3.2. The sample was set at 1.27 K under µ-wave irradiation at 187900 MHz and 350 mW. The dissolved sample was pushed with 5 ml of D₂O warmed at ~140°C.

NMR experiments consisted on series of 1D detections with 1 s time interval using read excitation pulses of 10°. All NMR spectra were recorded with simultaneous ¹H and ²H decoupling, achieved using a WALTZ16 pulse sequence[159]. The obtained FID's were apodized using a 5 Hz exponential window, and zero filling was applied prior to Fourier transformation. Processing of the NMR data was performed using the NMRPipe software [231].

### C.0.2 Glucose metabolism in macrophages

The experiments with which we obtain the preliminary results presented in this section had to be further optimized. The resulting data sets have the first scans damaged by saturation and so results are displayed after enough hyperpolarization has relaxed, thus the first 12 1D spectra were lost. However, the different DDNP experiments on macrophages still showed
<figure><img src="image_80.png" /><figcaption>**Figure C.2:** C.2a Superposition of the first 20 scans of the DDNP experiments performed on macrophages at different cell concentrations. First line from top to bottom is an experiment with *E.coli* K12 at OD<sub>600</sub>=1 to compare the produced and observable metabolites for different cellular systems. 1 lactate, 2 acetate, 3 δ-PGL. C.2b Integrated resonances to reconstruct the signal evolution of the different metabolites. In black lactate, in red acetate and in blue δ-PGL. Signal evolution displayed after scan n° 8.</figcaption></figure>

proof of metabolism. In figure C.2a are displayed the superposition of the first 20 1D spectra (after saturation at scan n° 12) for experiments done with cells at different concentrations. The peak assignment for acetate and lactate was done by means of bibliographic research [134]. In this preliminary work the third doublet is assigned provisionally to δ-PGL. However, further investigation has to be done. Acetate and δPGL resonances observed in the experiments with macrophages are also observed in the experiments on *E.coli*. The observation of δ-PGL could be explained by the pulse of glucose during the dissolution experiment, which has been previously documented to cause a 10 fold increase of δ-PGL's production in other cellular systems [255].

The cell cultures used in all experiments were prepared at the same growth phase, high confluency. Since we varied the cellular concentration for different experiments, the confluency is expected to evolve differently in each experiment during the minutes between harvesting and dissolution. In figure C.2a, a variation of the relative intensities of lactate and acetate doublets can be observed. This variation seems to depend on the concentration of cells. As a matter of fact, for the two experiments with 57 and 238 M of cells, the
production of acetate and lactate seems to inverse. This effect can be explained by the intensification of hypoxic conditions when there is a 4-fold increase of cell's concentration. Lactate production is enhanced to supply the NADH needed for the glycolitic process to continue (see ??). It has been demonstrated that macrophages adapt very fast to hypoxic conditions [281], which explains the fast variation of the metabolic response in our observations. The experiment performed with 1350 M of cells represents a ~ 20 fold increase of cellular concentration. The metabolism shows similar signal intensities for both acetate and lactate productions.

The lost of data due to miss-calibration of the experiments limit the kinetic analysis of these results. For the moment no further analysis will be done. The experiments have to be optimized and repeated. Never the less, observing changes in metabolism related to hypoxic conditions are a very interesting result. As a matter of fact, recent studies have related hypoxic conditions and lactate accumulation to the development of a pro-tumor phenotype in macrophages. The key role of lactate accumulation in cancer was shown to be related to the anaerobic glycolysis enhanced during the accumulation of macrophages around tumors [280]. Characterizing metabolic phases for macrophages is of central interest to determine their action on damaged or inflamed tissues with low levels of oxygenation (malignant tumors, dermal wounds, etc... ).
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