<figure><img src="image_1.png" /></figure>

HAL
open science

# Application and development of dissolution dynamic nuclear polarization techniques for kinetic studies of metabolic reactions

David Guarin

<figure><img src="image_2.png" /></figure>

## To cite this version:

David Guarin. Application and development of dissolution dynamic nuclear polarization techniques for kinetic studies of metabolic reactions. Chemical Sciences. Ecole normale supérieure - ENS PARIS, 2021. English. NNT: . tel-03985370

HAL Id: tel-03985370

https://hal.science/tel-03985370

Submitted on 13 Feb 2023

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_3.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_4.png" /></figure>

École Normale Supérieure

Doctoral school n° 388 : Chimie Physique et Chimie Analytique de Paris Centre

Laboratoire des Biomolécules (LBM), UMR 7203

Application and development of dissolution dynamic
nuclear polarization techniques for kinetic studies of
metabolic reactions.

DAVID O. GUARIN

Thesis presented for the degree of Doctor of Philosophy

Directed and supervised by DANIEL ABERGEL

Co-supervised by DENNIS KURZBACH

Jury members

<table><tr><td><b>Daniel Abergel</b></td><td>Professor, Sorbonne Université</td><td>Thesis director</td></tr><tr><td><b>Mathilde Lerche</b></td><td>Senior Researcher, Technical University of Denmark</td><td>Reviewer</td></tr><tr><td><b>Patrick Giraudeau</b></td><td>Professor, Université de Nantes</td><td>Reviewer</td></tr><tr><td><b>Konstantin Ivanov</b></td><td>Professor, Novosibirsk State University</td><td>Examiner</td></tr><tr><td><b>Sami Jannin</b></td><td>Professor, Université de Lyon 1</td><td>Examiner</td></tr><tr><td><b>Rachel Katz-Brull</b></td><td>Professor, Hebrew University of Jerusalem</td><td>Examiner</td></tr><tr><td><b>Dennis Kurzbach</b></td><td>Professor, Universität Wien</td><td>Co-supervisor</td></tr></table>
<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /></figure>
Abstract

Cellular metabolism involves regulatory mechanisms that allow the cell to adapt to its en-
vironment, thus modifying its phenotype accordingly. Understanding how this metabolism
adapts provides fundamental information to develop and improve diagnostic and treatment
methodologies for several diseases. However, growing evidence suggests that even the
quantification of a complete set of metabolites is not sufficient to predict cell's phenotype.
On the contrary, knowledge of metabolic fluxes is necessary to understand how cells adapt
to their environment.

NMR is a unique observation tool that relies on the interaction between nuclear spins and magnetic fields, and is therefore non-invasive and non-destructive. However, NMR spectroscopy suffers from its intrinsic lack of sensitivity, which can be compensated to some extent by signal averaging, which in turn decreases the sampling rate of the reactions. To circumvent this constraint, Dissolution Dynamic Nuclear Polarization (DDNP) methods were introduced at the beginning of the century. Indeed, this technology allows real-time monitoring of dynamic processes by allowing NMR sampling rates < 1 Hz, while capitalizing on the intrinsic atomic resolution of NMR spectroscopy. The objective of this Ph.D. work is to implement and optimize a DDNP-based methodology to perform kinetic studies of metabolic reactions in both in vitro samples and in living cells.

Initially, we focused on the study of the oxidative stage of the PPP (oxPPP). The objective was to characterize the enzyme kinetics of glucose-6-phosphate dehydrogenase. We have therefore performed experiments by monitoring the NMR signals of the different metabolites involved in the transformation. The analysis of these experiments allowed us to extract the different kinetic parameters of the reaction. The consistency of the values obtained was
evaluated using statistical tools, by comparison with independently measured references and with bibliography. Between the extracted parameters, we were able to characterize the anomerization kinetics of G6P, which seems to be a contribution to the current knowledge of the system.

In a second approach, we set up a procedure to perform DDNP experiments on living cells. We focused however on the study of glucose consumption and metabolism by E.coli K12. The characterization of the phenotypic response by E.coli was made possible by analyzing the real-time kinetics of hyperpolarized [U-¹³C; U-²H]glucose and its metabolic products. Analyses of these experiments allowed us to relate the extracellular ¹³C anomeric signals of glucose to the relative glucose uptake of each anomer by E. coli, and so, to the relative activities of glycolysis and the pentose phosphate (PPP) pathway in the cell. Moreover, the analysis of the real-time evolution of a couple of products' signal intensities showed to depend on cellular growth stages and hence also provided an intrinsic marker of the *E.coli* metabolic response to a sudden (hyperpolarized) glucose exposure. As proof of concept, additional experiments were performed with multiple substrates on different cell systems. The results suggests that different metabolic characteristics can be observed on such systems using DDNP techniques.

## Keywords

Nuclear Magnetic Resonance, Metabolism, Dynamic Nuclear Polarization, Enzyme kinetics,
Résumé en Français

Dans le métabolisme cellulaire interviennent des mécanismes de régulation qui permettent
à la cellule de s'adapter à son environnement, donc de modifier son phénotype en con-
séquence. Comprendre la façon dont ce métabolisme s'adapte fournit des informations fon-
damentales pour développer et améliorer les méthodologies de diagnostic et de traitement
pour plusieurs maladies. Cependant, de plus en plus de preuves suggèrent que même la
quantification d'un ensemble complet de métabolites ne suffit pas pour prédire le phéno-
type cellulaire. Au contraire, la connaissance des flux métaboliques est nécessaire pour
comprendre comment les cellules s'adaptent à leur environnement.

La RMN est un outil d'observation unique qui repose sur l'interaction entre les spins nucléaires et les champs magnétiques, et est donc non invasive et non destructive. Cependant, la spectroscopie RMN souffre de son manque intrinsèque de sensibilité, qui peut être compensé dans une certaine mesure par la moyenne des signaux, qui à son tour diminue le taux d'échantillonnage des réactions. Pour contourner cette contrainte, les méthodes de polarisation nucléaire dynamique par dissolution (DDNP) ont été introduites. En effet, cette technologie permet de suivre en temps réel des processus dynamiques en permettant des taux d'échantillonnage RMN < 1 Hz, tout en capitalisant sur la résolution atomique intrinsèque de la spectroscopie RMN. L'objectif de ce travail de doctorat est de mettre en œuvre et d'optimiser une méthodologie basée sur la DDNP pour réaliser des études cinétiques des flux métaboliques à la fois dans des échantillons in vitro et par observation de cellules vivantes.

Dans un premier temps, nous nous sommes focalisés sur l'étude de l'étape oxydative de
la PPP (oxPPP). L'objectif étant de pouvoir caractériser la cinétique enzymatique de l'enzyme
glucose-6-phosphate déshydrogénase. Nous avons donc réalisé des expériences en suivant
les signaux RMN des métabolites impliqués dans la réaction. L'analyse de ces expérience
nous a permis de caractériser les différents paramètres décrivant la cinétique de la réac-
tion. La cohérence des valeurs obtenues a été évaluée au moyen d'outils statistiques, par
comparaison avec des références mesurées de manière indépendante et par comparaison
avec les valeurs documentés. Entre les paramètres extraits, nous avons pu caractériser les
cinétiques d'anomérisation du G6P, ce qui semble être une contribution à la connaissance
actuelle du système.

Dans un deuxième temps, nous avons mis en place une procédure permettant de réaliser
des expériences de DDNP sur des cellules vivantes. Cependant, nous nous sommes concen-
trés sur l'étude de l'absorption et du métabolisme du glucose par E.coli K12. La caractérisa-
tion de la réponse phénotypique par E.coli a été rendue possible par l'analyse de la cinétique
en temps réel de traces de glucose [U-¹³C; U-²H] hyperpolarisé et de ses métabolites. Les
analyses de ces expériences nous ont permis de relier les signaux 13C anomériques extra-
cellulaires à l'absorption relative de glucose de chaque anomère par E. coli, et aux activités
relatives de la glycolyse et de la (PPP) dans la cellule. En outre, l'analyse de l'évolution en
temps réel de l'intensité des signaux de quelques produits métaboliques a montré que ceux-
ci fournissent un marqueur intrinsèque de la réponse métabolique du glucose à l'exposition
soudaine au glucose hyperpolarisé. Comme preuve de concept, des expériences supplémen-
taires ont été réalisées avec de multiples substrats sur différents systèmes cellulaires. Les
résultats suggèrent que différentes caractéristiques du métabolisme peuvent être observées
sur de tels systèmes au moyen des techniques DDNP.

Mots Clés

Resonance Magnetique Nucléaire, Métabolism, Polarization Dynamique Nucléaire, Ciné-
tique Enzymatique
<figure><img src="image_7.png" /></figure>
# Contents

Abstract I

Résumé en Français III

Physical and Chemical Constants XI

Physical and chemical constants XIII

Introduction 1

I Metabolism studies and NMR 7

1 Overview of the studies on metabolism 8

1.1 Metabolism 8

1.1.1 Presentation of some fundamental metabolic pathways 10

1.1.1.1 Glycolysis 12

1.1.1.2 The Pentose Phosphate Pathway 15

1.2 Study of metabolome, a functional approach 17

1.2.1 Metabolomics 17

1.2.2 Fluxomics 19

2 NMR 23
<table><tr><td>2.1</td><td>NMR in metabolomics and fluxomics</td><td>25</td></tr><tr><td>2.1.1</td><td>In vitro and ex vivo studies</td><td>25</td></tr><tr><td>2.1.1.1</td><td>NMR spectroscopy to study enzyme kinetics in real-time</td><td>25</td></tr><tr><td>2.1.1.2</td><td>Ex vivo metabolomics by NMR</td><td>27</td></tr><tr><td>2.1.2</td><td>In vivo studies</td><td>29</td></tr><tr><td>2.1.2.1</td><td>NMR in vivo assignment with bioreactor</td><td>30</td></tr><tr><td>2.1.2.2</td><td>NMR in cell kinetic study</td><td>31</td></tr><tr><td>2.2</td><td>The Dissolution DNP technique</td><td>33</td></tr><tr><td>2.2.0.1</td><td>The invention of Dissolution DNP</td><td>34</td></tr><tr><td>2.2.1</td><td>Advantages and known limitations of DDNP methodology</td><td>35</td></tr><tr><td>2.2.1.1</td><td>Fast sampling technique ideal for fluxomic studies</td><td>35</td></tr><tr><td>2.2.1.2</td><td>Reproducibility problems of a complex experiment</td><td>36</td></tr></table>

## II A review of the basics of DNP and DDNP 39

### 3 Short review of DNP 41

<table><tr><td>3.1</td><td>Polarization</td><td>41</td></tr><tr><td>3.1.1</td><td>Density Matrix</td><td>43</td></tr><tr><td>3.1.1.1</td><td>Boltzmann distribution</td><td>45</td></tr><tr><td>3.1.2</td><td>Spin polarizations at cryogenics temperatures</td><td>46</td></tr><tr><td>3.2</td><td>Polarization Transfer</td><td>46</td></tr><tr><td>3.2.1</td><td>EPR spectrum</td><td>47</td></tr><tr><td>3.2.2</td><td>DNP mechanisms</td><td>50</td></tr></table>

### 4 The Dissolution DNP system 52

<table><tr><td>4.1</td><td>DNP Hardware</td><td>52</td></tr><tr><td>4.1.1</td><td>Bruker, 6.7 T polarizer</td><td>52</td></tr><tr><td>4.1.1.1</td><td>Magnetic field and cryogenics</td><td>52</td></tr><tr><td>4.1.1.2</td><td>Probe, RF circuit and μ-wave irradiation</td><td>54</td></tr></table>
<table><tbody><tr><td>4.1.2</td><td>Cryogen-free 9.4 T Polarizer</td><td>55</td></tr><tr><td>4.1.2.1</td><td>Magnetic field and cryogenics</td><td>55</td></tr><tr><td>4.1.2.2</td><td>Probe, RF circuit and μ-wave irradiation</td><td>57</td></tr><tr><td>4.2</td><td>Dissolution DNP experiment</td><td>58</td></tr><tr><td>4.2.1</td><td>Sample preparation</td><td>58</td></tr><tr><td>4.2.2</td><td>Dissolution experiment</td><td>59</td></tr><tr><td>4.2.3</td><td>NMR sequences</td><td>62</td></tr><tr><td>4.2.3.1</td><td>Liquid-state NMR sequences</td><td>62</td></tr><tr><td>4.2.3.2</td><td>Cross-polarization sequences</td><td>64</td></tr></tbody></table>

# III In-vitro studies of enzymatic reactions by DDNP 67

## 5 Enzymatic cascade with glucose as substrate 69

<table><tbody><tr><td>5.1</td><td>Context of the experiment</td><td>69</td></tr><tr><td>5.2</td><td>The reaction scheme</td><td>71</td></tr><tr><td>5.3</td><td>Materials and methods</td><td>73</td></tr><tr><td>5.3.1</td><td>Sample preparation and DNP experiment</td><td>73</td></tr><tr><td>5.3.2</td><td>Reaction medium and NMR</td><td>74</td></tr><tr><td>5.4</td><td>Results and Analysis</td><td>75</td></tr><tr><td>5.4.1</td><td>Individual analysis of the experiments</td><td>77</td></tr><tr><td>5.4.2</td><td>Simultaneous fit</td><td>80</td></tr></tbody></table>

## 6 Characterization of G6PDH with labeled G6P 85

<table><tbody><tr><td>6.1</td><td>Production and purification of [U-<sup>13</sup>C; U-<sup>2</sup>H]G6P.</td><td>85</td></tr><tr><td>6.2</td><td>Kinetic analysis</td><td>94</td></tr><tr><td>6.2.1</td><td>Characterizing G6PDH activity and G6P anomerization rate</td><td>96</td></tr><tr><td>6.2.2</td><td>Pseudo-first order, complete reaction scheme</td><td>99</td></tr></tbody></table>
<table><tr><td><b>C</b></td><td><b>Glucose into Macrophages</b></td><td><b>155</b></td></tr><tr><td>C.0.1</td><td>Cell culture and DDNP setup</td><td>156</td></tr><tr><td>C.0.2</td><td>Glucose metabolism in macrophages</td><td>157</td></tr><tr><td></td><td><b>References</b></td><td><b>160</b></td></tr></table>
Physical and chemical constants

<table><tr><td>Planck Constant</td><td>k<sub>B</sub></td><td>6.62607004 × 10<sup>-34</sup></td><td>m<sup>2</sup>.kg.s<sup>-1</sup></td></tr><tr><td>Boltzman Constant</td><td>k<sub>B</sub></td><td>1.38064852 × 10<sup>-23</sup></td><td>J.K<sup>-1</sup></td></tr><tr><td>Bohr Magneton</td><td>μ<sub>B</sub></td><td>9.274009994 × 10<sup>-24</sup></td><td>J.T<sup>-1</sup></td></tr><tr><td>Vacuum Permeability</td><td>μ<sub>0</sub></td><td>1.256637062 × 10<sup>-6</sup></td><td>H.m<sup>-1</sup></td></tr></table>

<table><thead><tr><th>Gyromagnetic ratios</th><th>γ<sub>i</sub></th><th>rad.s<sup>-1</sup>.T<sup>-1</sup></th></tr></thead><tbody><tr><td>e<sup>-</sup></td><td>176.085 × 10<sup>8</sup></td><td></td></tr><tr><td><sup>1</sup>H</td><td>267.522 × 10<sup>6</sup></td><td></td></tr><tr><td><sup>2</sup>H</td><td>41.065 × 10<sup>6</sup></td><td></td></tr><tr><td><sup>13</sup>C</td><td>67.282 × 10<sup>6</sup></td><td></td></tr><tr><td><sup>15</sup>N</td><td>-27.116 × 10<sup>6</sup></td><td></td></tr><tr><td><sup>31</sup>P</td><td>108.291 × 10<sup>6</sup></td><td></td></tr></tbody></table>
Acronyms and Notations

2,4-DNP - 2,4-dinitrophenol

6PGA - 6-Phosphogluconic acid

6PGL - 6-phosphogluconolactonase

ATP - Adenosine triphosphate

ADP - Adenosine diphosphate

AMP - Adenosine monophosphate

BIRD - Bilinear rotation decoupling

CP - Cross polarization

CE - Cross effect

CEp - Capillary electrophoresis

DNP - Dynamic nuclear polarization

DDNP - Dissolution dynamic nuclear polarization

DE - Differential Evolution

EPR - Electron Paramagnetic Resonance

FPLC - Fast protein liquid chromatography

G6P - Glucose-6-phosphate

G6PDH - Glucose-6-phosphate dehydrogenase

GC - Gaz chromatography

HGP - Human Genome Project

HPLC - High performance liquid chromatography

LB - Lysoginy broth

LC - Liquid chromatography

MC - Monte Carlo

MG - Micro wave guide

MS - Mass spectrometry

MFA - Metabolic flux analysis
**NMR** - Nuclear magnetic resonance

**oxPPP** - Oxidative phase of the pentose phosphate pathway

**PEP** - Phosphoenolpyruvate

**PPP** - Pentose phosphate pathway

**PS** - Phase Separator

**PTS** - Phosphotransferase system

**R5P** - Ribose 5-phosphate

**RF** - Radio frequency

**SE** - Solid effect

**SEC** - Size exclusion chromatography

**SNR** - Signal to noise ratio

**TM** - Thermal mixing

**VTI** - Variable Temperature Insert
<figure><img src="image_8.png" /></figure>
Introduction

Living organisms display exceptional attributes that allow them to adapt to and replicate
in changing environments. To this end, they evolutionary developed complex reaction net-
works that enable energy production by consumption of nutrients and respiration (chapter
13 [1])[2, 3, 4]. The French chemist Antoine Lavoisier already noticed this phenomenon
in the 18th century by realizing that animals transform chemical fuels into heat. He wrote:
"[...] respiration is nothing but a slow combustion of carbon and hydrogen, which is entirely
similar to that which occurs in a lighted lamp or candle [...]"[5]. Evidently, when trying to
understand the chemistry of life, it is of major importance to understand the biochemical
processes that determine the conversion of nutrients consumed by living organisms. Al-
though studies of the conversion of starch into sugar were already undertaken in the early
1800s [6], the first description of biochemical degradation of nutrients was given by Pasteur
only by 1850. Indeed, he initially documented the conversion of sugar into alcohol by yeast
and the catalysis of the conversion by "ferments". Molecules with related catalytic functions,
i.e. enzymes, were later identified and named by Buchner [4] and Kühne [7] in 1897. Today,
thousands of enzymes have been isolated and studied, and their structure, reactions and
mechanisms elucidated. These reactions form the metabolic network, the complete set of
enzymatic reactions at the center of cell adaptability is called metabolism [8, 9, 1]. The term
'metabolism' denotes the complete ensemble of enzymatic and non-enzymatic reactions oc-
curring in an organism. Etymologically (from greek *metabolê*, "change") the "metabolism"
defines a system that undergoes constant changes [10]. Interestingly, one of the first uses
of the word 'metabolism' (in the chapter *History of metabolism* written by Graham Lusk
[11, 10]), all the different appearances of the word "metabolism" (in German *Stoffwech-*)
sel) were systematically translated from German to English as "metamorphosis" [8]. Indeed, chemical reactions involved in the metabolic network are under constant change, their variability enables cellular adaptability and survival [1, 12].

In this thesis, I focus on the use of nuclear magnetic resonance (NMR) spectroscopy to study metabolic networks and reactions. To this end, several particularities render NMR a unique tool. One of its main advantages is based on the fact that NMR makes use of interactions between nuclear spins and magnetic fields, and is therefore non-invasive and non-destructive.

The versatility of this observation technique enabled its use in a wide range of applications, ranging from material science[13, 14], to the study of intact cells[15, 16], or the conformational analysis study of biological macromolecules [17, 18]. From the early years of NMR, studies on biochemistry research were developed. Mildred Cohn developed the first enzymology NMR based studies in 1962 [19]. Moreover, in the end of the 1960s, applications focusing on the study of amino acids and peptides were published by Oleg Jardetzky [20, 21]. Contributions to the study of the metabolism had also been given in the early stages of NMR by Robert G. Shulman and coworkers [22].

Biology and NMR have decades of common history [23]. During these years, the use of NMR has contributed to the characterization of a wide set of intermediate molecules in the metabolism i.e., metabolites [24, 25, 26]. Although having a description of the set of metabolites involved in metabolism can give fundamental information about the cells' conditions [27, 12], the mere identification of a complete set of metabolites does not suffice to predict the cellular phenotype. The complexity of the reaction network operating in the ensemble of metabolic processes requires the direct monitoring of metabolic reactions. This is necessary to provide a quantitative analysis of the fluxes of metabolites, and to directly establish the relations between metabolic changes and variations in the environment. NMR has proven to be well suited for this purpose, as it is able to observe in a non-invasive manner multiple metabolites simultaneously[25, 27]. However, NMR spectroscopy suffers from its intrinsic lack of sensitivity, which can be compensated to some extent by signal averaging, which in
turn increases the duration of each detection, i.e. decreases the sampling rate of the reac-
tions. Various strategies have been developed to circumvent this issue in order to study the
evolution of metabolic reactions, with conventional NMR, and without the need of a real-
time observation[28, 29, 30]. The studies of metabolic transformations, or metabolic fluxes,
are mainly based on stoichiometric analyses of ¹³C labeled substrates to determine reaction
rates [31]. Since the 1990s, a vast field focusing on the study of such fluxes have developed
[32]. However, this technique relies mostly on the analysis of the isotopomer distribution of
labeled metabolites, which at the same time depends on an untangled network of multiple
metabolic processes. Other strategies slow down reactions to the scale of the NMR sampling
rate [33, 29] Performing direct observations of fast metabolic reactions near physiological
conditions often remains a challenge with conventional NMR.

Increasing NMR sensitivity has been one of the main motivations for the development of NMR methodology and instrumentation over the years [34, 35, 36, 37]. Some years ago, Dis-solution Dynamic Nuclear Polarization (DDNP) technique was developed. The technique was able to provide tremendous sensitivity enhancements, by several orders of magnitude (up to four)[38], to conventional NMR experiments. Such a methodological leap forward has stimulated a wealth of possible applications, among which the study of metabolism [39, 40, 41, 42, 43]. Indeed, in 2003, it was demonstrated that the polarization gain achieved by DNP at cryogenics temperature could be transferred to ambient temperature to perform liquid-state NMR. With such a high signal enhancement DDNP enables one to monitor re-actions with a time resolution on the order of the second or lower. It therefore becomes pos-sible to study the various metabolites’ time evolution, with high-spatial and high-temporal resolutions. [44, 45, 46, 47]. DDNP has found applications in the study of the metabolism, mainly in the characterization of metabolic fluxes and in the kinetic study of enzymatic re-actions [48, 49, 50, 51, 52]. The interest in this technique has grown in recent years, several studies have been performed on different biological systems, and the methodology keeps being optimized[47, 45, 53, 54].
The objective of this Ph.D. work was to implement and optimize a methodology based on DDNP to perform kinetic studies of metabolic reactions. To perform this study two main approaches were undertaken.

The first approach relied on the study of a metabolic reaction or a series thereof. The strategy consists of performing enzymatic reactions *in vitro*, while using DDNP to monitor their evolution in time. The principal objective is to quantitatively characterize the kinetics of enzymatic reactions.

The second approach aims to perform a global observation of the metabolism by monitoring the uptake and transformation of a hyperpolarized substrate in living cells. The objective is to implement the DDNP methodology to the study of living systems in real-time and, if possible, identify biological markers to elucidate correlations between changes in metabolism and variations in cellular conditions. Hence, both approaches aim to perform quantitative kinetic studies of metabolic reactions.

The DDNP experiment is rather complex and requires the combination of multiple techniques. To start with, the hyperpolarization of the sample has to be optimized which requires an understanding of the fundamental processes giving rise to DNP phenomena. The hyperpolarization process has to be coordinated with liquid-state NMR, and with the preparation of the samples containing the biological and biochemical systems to be studied. The experiments thus require to define a protocol to prepare the *in vitro* samples or the cell cultures. Moreover, the objective is to perform a quantitative analysis of kinetic reactions. The latter implies that models reproducing the chemical reactions have to be defined and numerical tools have to be implemented in order to extract the relevant information present in the resulting NMR data.

The results obtained in my Ph.D. work and the methodologies used will be presented in this manuscript in four principal parts.

The first part is an introduction to metabolism and to the use of NMR in the study of metabolism, it includes a presentation of the strategies used to study the metabolome and
the fluxome.

A theoretical description of DNP phenomena is of fundamental importance for the un-
derstanding of DDNP methodology. Thus, in the second part, we will give a quick overview
of the DNP phenomenon. The subject is further developed in Annex A, together with a
study of thermal mixing mechanism. The experimental setup for dissolution DDNP will
also be presented in the second part.

The third and fourth parts deal with DDNP metabolic studies performed in the course
of this work. It includes the results obtained with both approaches to the kinetic study of
the metabolism.
<figure><img src="image_9.png" /></figure>
# Part I

## Metabolism studies and NMR
# Chapter 1

## Overview of the studies on metabolism

A fundamental characteristic of living organisms is their ability to adapt to the environment. In order to better understand the mechanisms underlying cellular adaptability, it is of major importance to characterize the metabolic pathways involved. These complex networks of chemical reactions enable living organisms to extract and transform chemical energy from the environment, to adapt to variations in their surroundings, and to replicate and assemble [1, 55, 9]. This is true for the simplest living organism, the cell. Both prokaryotic cells (that do not possess a nuclear membrane [1]), and eukaryotic cells [56] exhibit many differences, yet share many common metabolic pathways.

### 1.1 Metabolism

The complex networks of enzymatic reactions composing the metabolism is regulated by the homeostasis principle, according to which, in the cell, some quantities are maintained in a defined range (pH, osmolality, ...)[57, 58, 59]. Different metabolic processes allow the cell to uptake nutrients from the environment, and ensure their transformation and use for multiple purposes (energy production, nucleic acid synthesis, and synthesis of bigger macromolecules). This is in general achieved by cross-regulations of various coupled enzymatic reaction pathways[60, 61, 62].

The complete set of metabolites present in a system is defined as the metabolome[63].
<figure><img src="image_10.png" /><figcaption>**Figure 1.1:** Scheme representing a part of the metabolism of an eucaryotik cell. Each dot is a metabolite, each line is an enzymatic reaction and each color is a metabolic pathway. In this scheme, the complexity of the reaction network involved in metabolism can be observed.</figcaption></figure>

The metabolism of an organism is a very complex system to study, it is estimated that the number of metabolites associated with enzymatic reactions range from ~ 600 in yeast metabolism, to approximately 200 000 in humans and plants[64, 1]. The extreme complexity of this reaction network is illustrated in figure 1.1 for a eukaryotic cell (reproduced from reference [1]). A typical eukaryotic cell can produce up to 30 000 proteins involved in thousands of catalyzed reactions, organized in metabolic pathways[1]. The reduced representation of metabolism, displayed in figure 1.1, shows how multiple metabolites (each dot) are involved in different metabolic pathways (in different colors). A number of metabolic pathways are common or similar for all types of cells whilst others are specific to some cellular organisms[65, 66, 1]. In the following paragraph, some of the more general metabolic pathways that are related to the studies presented in this work will be briefly introduced.
<figure><img src="image_11.png" /><figcaption>**Figure 1.2:** Scheme of the metabolism cycle. The catabolism that stocks chemical energy under the form of different small molecules (in red) and the anabolism that consumes chemical energy for synthesis of larger molecules (in blue).</figcaption></figure>

1.1.1 Presentation of some fundamental metabolic pathways

Cells can be categorized according to the types of energy sources and nutrients they use.
Autotrophs, such as photosynthetic bacteria, vascular plants, and green algae, use CO2
from the atmosphere as their only source of carbon, energy is provided by the sun through
photosynthesis[67, 1]. Alternatively, most microorganisms are heterotrophic, as they use
nutrients found in the environment (sugars, fatty acids, etc...) as carbon sources [67, 1].

The chemical energy obtained from different sources is then stored and used in the dif-
ferent metabolic processes as free energy and is therefore converted into heat. In catabolic
reactions, organic nutrients are converted into smaller molecules, a process associated with
a conversion of energy that is stored in the form of ATP, or molecules with a reducing power
such as NADH and NADPH (see chapter 14 of [1]). Alternatively, anabolic reactions con-
tribute to the biosynthesis of various biomolecules such as lipids, proteins, nucleic acids,
etc...) from smaller-sized precursors. These processes consume chemical energy stored in
the form of ATP, NADH, NADPH, etc... [1]. Figure 1.2 displays a summarized scheme of the
anabolic-catabolic cycle.

For many heterotrophs, glucose is a fundamental nutriment [3, 68, 60]. Its degradation
produces high quantities of free energy (for a general reference, see chapter 13 of [1]) and
can also be stored as a polymer (glycogen) and be released in case of increased energy
demand[69, 70].

Glucose uptake in *E.coli*

Multiple cellular systems have different glucose uptake mechanisms. For *E.coli*, the mechanism has been repeatedly studied and described [71, 72, 73]. The phosphoenolpyruvate-carbohydrate phosphotransferase system (PTS) is at the origin of transport and phosphorylation of different sugars in *E.coli*, namely glucose[71, 73, 72, 30]. PTS activity controls the preferential uptake of glucose over other sources of carbon[71]. The phosphoryl group transferred to glucose by the PTS originates from phosphoenolpyruvate (PEP), an intermediate product of glycolysis [73]. This transfer occurs through a series of enzyme-catalyzed reactions that result in the production of glucose-6-phosphate (G6P). Interestingly, glucose phosphorylation takes place within the membrane, upon translocation of the sugar towards the cell interior, so that it reaches the cytoplasm as G6P[72, 73, 30]. Moreover, studies have pointed to the anomeric selectivity of the glucose transfer through the membrane in *E.coli* [72, 30]. The work of S. Benthin et al. [30] suggested that glucose transfer by PTS relied on two independent anomer specific transport systems (see figure 1.3). Both glucose and G6P undergo spontaneous anomerization processes at particular rates to reach an anomeric equilibrium. This equilibrium depends on the conditions of the system (pH, temperature, etc.) [74, 75].
<figure><img src="image_12.png" /><figcaption>**Figure 1.3:** Glucose anomer selective uptake in*E. coli*. Both uptake and phosphorylation of glucose are done by the Phosphotransferase system. The phosphoryl group is provided by phosphoenolpyruvate metabolite in order to produce G6P. Both glucose and G6P can anomerize spontaneously.</figcaption></figure>

1.1.1.1 Glycolysis

The main glucose catabolic pathway is glycolysis, it was discovered in 1897 on yeast fer-
mentation [4] and was completely described for yeast by Otto Warburg [76]. This metabolic
pathway was the first discovered metabolic pathway and probably the most studied one[68,
65, 76]. Through glycolysis, a molecule of glucose is degraded to produce two molecules
of pyruvate. Part of the released energy is stored in the form of ATP and NADH. Glycol-
ysis comprises two phases. In the first phase, glucose is phosphorylated into glucose-6-
phosphate (G6P)(step 1 in fig. 1.4), 2 molecules of ATP are consumed and one hexose is
cleaved into two molecules of 3 carbons each (step 5 in fig. 1.4). In the remainder of the gly-
colytic sequence, the payoff phase[1], four molecules of ADP are phosphorylated into four
molecules of ATP (steps 7 and 8), two molecules of NADH are produced (step 6), such as two
molecules of pyruvate (step 8). For the complete scheme of glycolysis see figure 1.4. During
complete glycolysis, considering both phases, two molecules of ATP and two molecules of
pyruvate are thus produced, and two molecules of NADH are reduced.

After glycolysis, pyruvate is catabolized along three different routes [1, 65]. For most cel-
lular systems (most bacteria[77], mammalian cells [60, 78] and multiple plants [68]), while
<figure><img src="image_13.png" /><figcaption>**Figure 1.4:** Transformation of glucose into pyruvate through glycolysis. The yellow dotted line separates the "preparatory phase" and the "payoff phase" of glycolysis (see chapter 14 of [1]).

**1** Phosphorylation of glucose by *hexokinase* enzyme with consumption of one molecule of ATP and subsequent transformation into fructose 6-phosphate (F6P) by *phosphoexose* isomerase calytic activity.

**2** Phosphorylation of F6P into fructose 1,6-biphosphate by consumption of a second molecule of ATP, catalyzed by *phosphofructokinase-1*.

**3** 6-carbon structure divided into two 3-carbon structures.

**4** Beginning of the payoff phase, production of two glyceraldehyde 3-phosphate molecules.

**5** Transformation catalyzed by *glyceraldehyde 3-phosphate dehydrogenase* and yields two molecules of NADH.

**6** Transformation catalyzed by *phosphoglycerate kinase*, where two molecules of ADP are transformed into ATP.

**7** The final reaction of glycolysis produces two molecules of pyruvate and two molecules of ATP. The reaction is catalyzed by the enzyme *pyuvate kinase*.</figcaption></figure>
in aerobic conditions, pyruvate produces acetyl-coenzyme A which is then completely catabolized into multiple molecules of CO2 by the transformations occurring in the citric acid cycle [1, 79]. These transformations yield multiple molecules of ATP. On the other hand, under anaerobic conditions, pyruvate follows either degradation into lactic acid or degradation into ethanol (and CO2) after fermentation [78, 76]. In 1861, Pasteur discovered that the consumption rate of glucose in Yeast was increased in anaerobic conditions[3], which evidenced the regulation of the metabolism according to the cell environment. The "Pasteur Effect" was later understood as a metabolic control mechanism to ensure a constant ATP level both in aerobic and anaerobic conditions, i.e., to maintain homeostasis [2]. Under anaerobic conditions, glycolysis yields two molecules of ATP, whereas in aerobic conditions, the total oxidation of glucose through the citric acid cycle produces 30 up to 32 molecules of ATP (ref. [1], chap. 14), which represents a ~ 15 fold increase of ATP production.

For *E.coli* in aerobic conditions, pyruvate is converted to acetyl-CoA and CO2 by the pyruvate dehydrogenase complex. This enzyme is regulated under anaerobic conditions depending on the NAD+/NADH ratio [80]. Acetyl-CoA is further processed within the citric acid cycle to produce additional ATP and reducing equivalents.

In anaerobic conditions, *E.coli* uses a wide variety of substances (since no oxygen available) as electron acceptors [81]. However, the absence of oxygen leads to the inactivation of the citric acid cycle that causes an increased production of acetate and formate [62]. Under such conditions, the production of succinate, formate, acetate, lactate, and ethanol is enhanced, which maintain the oxido-reduction balance [62], through the *mixed acid fermentation* pathway.

As has been mentioned, glucose is a fundamental nutrient for a majority of cellular systems. Since glucose supply is not always sufficient, there is a pathway through which glucose can be synthesized called gluconeogenesis. Gluconeogenesis is an anabolic pathway that transforms pyruvate, lactate, and oxaloacetate (or any compound that can be converted into one of these three) back into glucose. In the glycolytic pathway, seven enzymatic reactions are reversible and three reactions are not (steps 1, 2, and 8 in figure 1.4). Gluconeoge-
nesis follows the seven reversible enzymatic reactions of glycolysis, and replaces the three
non reversible reactions by introducing new enzymes. Although gluconeogenesis requires
the consumption of 4 molecules of ATP and 2 of NADH, the total energetic rendering is
positive. The latter is true since in different conditions, without gluconeogenesis, pyruvate
would be excreted from the cell and the production of multiple molecules of ATP (by the
degradation of pyruvate in aerobic conditions) would not happen[82, 1]. Moreover, both
glycolysis and gluconeogenesis are regulated allosterically or by phosphorylation of an en-
zyme so that when one is activated the other one is inhibited and conversely[82, 1].

1.1.1.2 The Pentose Phosphate Pathway

A second catabolic route for glucose after phosphorylation into glucose-6-phosphate (G6P)
is the Pentose Phosphate Pathway (PPP). This pathway is composed by two consecutive
stages. The first, the oxidative stage (OxPPP) represents the main source of NADPH, a
major reductive agent in the cell [1, 83, 84]. In non photosynthetic cells, the oxPPP is a
major source of NADPH, that is used in fatty-acid synthesis and in the uptake of inorganic
nitrogen[85], for instance. The production of NADPH through the PPP, a main source of
reductive power in the cell, maintains the redox potential necessary to protect the cellular
system against oxidative stress [84]. In figure 1.5, a scheme depicting the oxPPP is presented.
During the oxPPP two molecules of NADPH are produced in a chain of reactions that also
yields a molecule of ribose 5-phosphate (R5P) and a molecule of CO2. R5P can then be used
as a precursor for other cellular processes like nucleic acid synthesis.

However, for some organisms that primarily require NADPH (like cellular systems in
tissues) and that have a mechanism to regenerate NADP+, the ribose-5-phosphate is recy-
cled to produce hexose phosphates again, namely G6P[61, 66, 1]. As a matter of fact, one of
the last steps of the PPP in such systems produces fructose-6-phosphate which is converted
into G6P, thus closing the cycle. For the structure of 6 carbons to be recovered, six molecules
of pentose phosphates (R5P and xylulose 5-phosphate) are transformed into five molecules
of hexose phosphates (G6P), after which the cycle starts again[83, 61].
<figure><img src="image_14.png" /><figcaption>**Figure 1.5:** oxPPP. The PPP starts with phosphorylated glucose (produced by hexokinase). The complete oxydative phase renders a molecule of CO₂, two molecules of NDPH and a molecule of D-ribulose 5-phosphate (R5P). Although R5P can be used as precurosor in multiple cellular processes, the cycle can also continue after producing R5P through the non oxidative PPP, after which G6P is produced again (blue dotted line). [66]</figcaption></figure>

Glucose-6-phosphate is the common precursor of glycolysis and PPP, its respective use for both pathways is under the control of various regulatory mechanisms[80, 68, 62, 83, 61]. In the first place, NADP⁺ is needed for the first reaction of the oxPPP, the dehydrogenation of G6P by the enzyme G6PDH. Similarly for glycolysis, two molecules of ATP are required in the preparatory phase. The availability of both NADP⁺ and ATP is a form of metabolic regulation. Moreover, the relative concentrations of NADP+/NADPH have an allosteric effect on the first enzyme of the PPP, G6PDH. Hence, if the cell produces large quantities of NADP+, the high concentration allosterically stimulates G6PDH activity, increasing the flux of G6P through the PPP [61]. Other alterations of the PPP activity can be induced by several diseases. For instance, in human cells, decreased activity of G6PDH has been related to the presence of diabetes and hypertension [86]. Additionally, for cancer cells, the
reduction of pyruvate into lactate is prioritized over its aerobic degradation through the citric acid cycle. This phenomenon is called the Warburg effect [78, 76].

PPP and glycolysis regulations are dependent on the conditions of the organism, the availability of nutrients, etc... The cellular processes depending on these metabolic pathways are therefore dependent on cellular conditions in such a way that the observation of these pathways' activities could lead one to identify nutrient deficiencies or the presence of diseases.

## 1.2 Study of metabolome, a functional approach

Since, metabolic processes originate in enzymatic reactions, characterizing these reactions is expected to shed light on the cell phenotypic response to external stimuli or genetic variations. Such knowledge of metabolism can lead to advances in diagnosis and in the treatment of multiple diseases[87].

### 1.2.1 Metabolomics

Metabolomics (a term first introduced by O. Fiehn in 2002 [12]), i.e. the metabolome analysis, designates the ensemble of studies aiming at the identification and quantification of all the metabolites of an organism [12, 88, 89]. The suffix "-omics" has been recently used to characterize multiple fields of research in biology. Genomics (illustrated in particular by the Human Genome Project (HGP) [90]), transcriptomics [91], proteomics[92] and metabolomics [88, 64], each point to an important aspect of the cell function. Importantly, variations on the transcriptome or the proteome alone do not necessarily imply changes in the phenotype [64]. In this perspective, metabolomics is of particular relevance, as it can bridge the phenotype-genotype gap [12].

Multiple metabolomic strategies have been categorized by Nelsen and coworkers [93] into two main approaches. In the first approach metabolites are identified to define metabolic profiles of the studied samples, *metabolic profiling*. In the second approach quantitative
analysis is performed on a set of metabolites of a known system, "targeted metabolomics".
For both approaches, multiple observation techniques are used. However, the most pop-
ular are NMR and Mass Spectrometry (MS) [94, 88, 95, 27]. The latter can be coupled to
multiple separation techniques such as CEp (capillary electrophoresis) or, GC and LC (gas
chromatography and liquid chromatography), which have found widespread applications
[96, 97, 98, 99, 100, 101].

For LC techniques, the separation of the sample components is done in liquid-state and
so, samples need minimal pretreatment [102]. LC-MS have been recently used for mul-
tiple applications in metabolomics [98, 99, 57] The metabolite profiles obtained with this
technique, typically contain hundreds of components and their analyses require the use of
advanced statistical tools[103]. Another separation method that has been combined with
MS is capillary electrophoresis. In this technique only small amounts of sample are needed
and is well suited to polar, ionizable, molecules [104, 99]. CEp-MS has been used to per-
form quantitative metabolome analysis on B. subtilis [96]. In Soga et al., a CEp-MS method
was proposed, it enabled the identification and quantification of a large set of metabolites
of B. subtilis. CEp-MS technique has however proven multiple drawbacks related to sam-
ple sticking to the capillary wall, lack of separation, or decreased species stability, which
leads to problems in the quantitative aspects of the method[105]. Alternatively, Fourier
transforms infrared spectroscopy (FT-IR) has also been used in metabolomics. The advan-
tages related to FT-IR technique are the small amount of sample needed, the rapidity of the
analysis, and the lack of long and time-consuming pre-treatment of the sample [106, 107].
The technique has been used in multiple studies of metabolism [107, 108]. The resulting
profiles obtained with this technique are nevertheless composed of overlapping signals, dif-
ficult to disentangle[107, 109]. To date, the measurement and identification of the total set
of metabolites and the complete network of metabolic pathways have not been possible.
The latter is not surprising since no single methodology enables the observation and deter-
mination of all metabolites in a sample[64]. Since no single technique can be used for all
metabolic studies, it is difficult to define databases with complete spectral information and
identification of metabolites. Recently, efforts have been made to develop databases con-
taining metabolomic spectral analyses combining several observational techniques. The
Human Metabolome Database (HMDB) [110](https://hmdb.ca/) and the Spectral Database
for Organic Compounds (SDBS) of the National Institute of Advanced Industrial Science
and Technology, Japan, (https://sdbs.db.aist.go.jp), are good examples of such efforts. They
recompile information of the metabolome obtained by means of several techniques.

Although metabolomic applications of the previously introduced techniques are still
being developed, their combination has nevertheless enabled partial descriptions of the
metabolome, hence elucidating multiple features of metabolism [111, 99, 88]. Still, the mul-
tiple intricate metabolic pathways are dynamic processes, their evolution in time determine
the concentration of the different metabolites involved in the different cellular functions.
Hence, a way to observe metabolisms evolution in time is fundamental, especially since for
cells the distinct metabolic processes are regulated and strongly interconnected. Quantita-
tive analysis of the fluxes of metabolites and metabolic reactions is necessary to get a better
understanding of the regulation of the metabolic pathways, it would also evidence correla-
tions between regulatory mechanisms and cellular functions. The study of these fluxes is
also an "-omics" field of research and is called fluxomics.

**1.2.2 Fluxomics**

The study of metabolic fluxes to better understand variations of the phenotype adds com-
plexity to what was already a very complicated system. Novel approaches to biology have
been developed to construct a more holistic way of describing biological systems and liv-
ing organisms. An example of such is systems biology which aims to predict the possible
behavior of a biological system based on its different components. Systems biology re-
lies on an interdisciplinary approach to characterize biological systems of multiple scales
(cell, tissues, organs) by using the molecular components, the physiological functions, and
the complete phenotype to create thorough quantitative computational models that can be
tested with high technology observation techniques [112]. System biology has been used in
the characterization of both the fluxome and the metabolome [64, 113, 114].

Fluxomic studies depend on observation techniques able to track the fate of a set of
metabolites. To the date, the most frequently employed techniques depend on the use of
¹³C labeled substrates[32, 28, 114]. This approach consists of feeding the studied organisms
(tissues, cells, etc...) with ¹³C labeled substrates to trace the transformation of the substrate
into new metabolites. Different strategies implement the selective labeling of substrates in
order to better identify what kind of transformation is taking place (what carbon structure is
being transferred). As mentioned in the previous section, glucose is a fundamental nutrient
in a majority of living organisms and is therefore one of the most commonly used labeled
substrates in fluxomic studies [64, 28].

A major drawback of ¹³C labeled fluxomic analysis is that, even with selective labeling of the substrate, the contribution of several metabolic pathways acting simultaneously on the substrate is hard to differentiate. The analysis is then limited to substrates intervening on the central carbon metabolism following metabolic transformations that are already known and can therefore be identified and traced in the sample[64].

Metabolic flux analysis (MFA) is another name given to the characterization of fluxes[32,
28]. Different methods have been developed to analyze metabolic fluxes and to describe
their role in metabolic processes[64]. The first approach consists of a comparative analy-
sis of metabolic fluxes. The system is studied under varying conditions and compared to
reference samples. It does not give precise quantitative information about the evolution of
metabolic reactions but helps to establish the impact of different fluxes in a cell's pheno-
type, sometimes called MIDA (mass isotopomer distribution analysis). Other approaches
develop integrative methodologies to follow the transformations of the labeled substrates
and reconstruct, through mathematical models, metabolic processes. For both approaches,
practical examples will be given later in this chapter. A complementary approach to the
analysis of the fluxome is to characterize individual reactions by studying enzyme kinetics
and their impact on the metabolic pathways. In this respect, the characterization of inhibi-
tions, regulations, and variations of enzyme activities are clearly important ingredients for
the description of the fluxome and contributes to the elucidation of the cell phenotype.

The different methodologies mentioned above have been used individually or simulta-
neously to characterize the fluxome of a big diversity of organisms, some examples are :

*   **1998 L. Agius**: Description of the activity of produced and purified glucokinase enzyme from rat hepatocytes. Study of the enzyme activity in presence of different inhibitors and precursors. The activities of glucokinase were assayed following different methodologies adapted to experimental conditions. Activities were extracted from samples with: varying concentrations of glucose as substrate, with different glucose analogs as substrate, in presence of different glucokinase inhibitors. From the extracted enzyme activities multiple features of the enzyme were deduced, features directly related to phenotypic changes of the cell. For example the translocation of glucokinase from the nucleus of the cell to the cytoplasm due to an increase in glucose phosphorylation. [115]

*   **2001 - M. Dauner et al.** : First combined study using NMR and MS observation techniques among others. Evaluation of the energy consumption and dissipation on [U-¹³C]-glucose metabolism of *Bacillus subtilis* bacteria. The system was tested under various conditions: carbon in excess, carbon limitations, nitrogen limitations and phosphorus limitations. The metabolic reaction of the bacteria was assayed to determine the concentration evolution of multiple products, the consumption of oxygen and glucose, and the relative concentrations of intracellular ATP/ADP. They observed that for cultures with carbon excess at big dilution rates (low cellular concentrations) there are no mechanisms that dissipate ATP different from the principal metabolic pathways (gluconeogenesis, etc.). On the other hand, for low dilution rates, almost 20% of the energy is dissipated through alternative mechanisms. It was also the case for samples with phosphorus or nitrogen deprivation [31]. Description of the alternative ATP dissipating mechanisms are given.

* **2001 - W. Wiechert et al.** : Proof of concept, use of a quantitative methodology to study different anaplerotic reactions in *Corynebacterium*. Labeled glucose was used
as a substrate, with different labeling strategies. In this work, they use ¹³C-FLUX methodology, a strategy to make quantitative studies of fluxes. It follows a series of optimization steps: giving a biological description of the system, define a mathematical model to characterize flux evolution, perform statistical analysis, optimize the experimental design for observation and evaluation of the biological system [28].

* **2004 - S. Marin et al.** : Study of glucose metabolic network in rat hepatocytes. It uses MIDA and [1,2-¹³C] labeled glucose. Cell samples were prepared with variations in the incubation conditions, different metabolites were added to the incubation medium in addition to selectively labeled glucose. For some samples, the metabolites added to the medium are substrates of the gluconeogenesis pathway. At the end of incubation, samples were frozen and subsequently processed to extract metabolites. After mass spectroscopy analysis, the isotopomer distribution showed a different flux of glucose through the glycolytic/gluconeogenetic pathways depending on the metabolites available in the sample. This example is a comparative study that gives a description of rat hepatocytes phenotypic variations related to substrate conditions [116].

Multiple methodologies rely on different observation techniques to describe the fluxome of an organism [32, 64, 28]. However, few techniques defined fluxes in terms of kinetic parameters and time domain observations. For the majority of strategies, the fluxes are determined by analysis of the isotopomer distribution after metabolism of ¹³C-labeled substrates[116, 32, 31]. Fluxes were inferred from analytical models of metabolic pathways or comparative approaches. Direct observation of metabolic reactions would require an efficient high-throughput, quantitative technique, or an alteration of the sample to slow down metabolic processes. Having a technique that allows fast sampling (ideally larger than 1 Hz) would simplify quantitative approaches and elucidate the reactions involved in metabolic processes.
# Chapter 2

## NMR

The purpose of the work presented in this manuscript is to develop a technique to perform kinetic studies of metabolic reactions. We aim therefore to develop a methodology focused on the characterization of the fluxome. For this purpose, NMR presents multiple advantages as an observation technique. The non-destructive nature of the technique, the capability of defining structures [17, 117], and the option for quantification [118, 119, 120], are characteristic features of NMR. Moreover, there is no need of isolating the analytes which implies that samples can be easily prepared [121]. Finally, NMR allows the simultaneous observation of several analytes in a mixture [120, 121]. All of the previously mentioned features have made this technique a fundamental tool in multiple domains like material science [13, 14], pharmacy [122, 123], food industry [124, 125] etc. NMR has also contributed to the metabolomics and fluxomics fields of research and is, with MS, one of the two main observation techniques[111, 126, 32]. However, it seems that for these two '-omics' fields of research, MS has been more frequently used[127, 128, 111]. The characteristic features of both techniques have been repeatedly compared and discussed [99, 32, 129, 130, 64, 111]. The benefits of both techniques have even been combined in metabolomics and fluxomics studies [31, 126].

However, major drawbacks in NMR related to the low sensitivity [64, 128, 32], low resolution [131, 132, 111] or hardware cost [133, 32] seem to reduce the use of NMR technique in these fields of research. This problematic was addressed in a recent review by Patrick
Giraudeau [128]. It seems that the previously mentioned limitations as well as a lack of historical collaboration between both scientific communities are at the origin of the limited use of NMR in metabolomics and fluxomics fields. Moreover, W. Wiechert, in a review about MFA and fluxomics, claims that "The optimization of NMR measurement parameters and the proper interpretation of all the peak fine structures in a spectrum require a skilled NMR specialist" [32]. The latter implies that the technicalities of NMR method limit its use in groups in which NMR is not a usual tool. P. Giraudeau also mentions that the limited use of NMR in metabolomics also originates from the lack of collaboration between researchers in both fields, "limited connections between the historical NMR groups [...] and the large community of NMR users who are involved in practical metabolomics studies[...]"[128].

NMR field is nonetheless experiencing major developments to address multiple of its major limitations. For the study of samples heavily charged with different metabolites, techniques have been developed to avoid or disentangle the signal overlapping. Although increasing the magnetic field [35, 128] or relying on alternative nuclei (namely ¹³C or ³¹P)[134, 32, 135, 136] have been focused to circumvent this issue, other new strategies have been recently implemented. These new strategies rely on decoupling techniques[137, 138] and multi-dimensional NMR [139, 140, 141, 142] to spread and differentiate overlapping resonances.

To overcome the high budget related to NMR hardware, companies have developed low field, benchtop NMR spectrometers [143, 133, 128]. The new devices not only are less expensive (< 100 000 €) but also are less heavy and have smaller dimensions (<100 kg) than conventional spectrometers[128]. Although the low field related to such devices implies a loss of sensitivity and resolution, these spectrometers can still be used in metabolomics. As a matter of fact, benchtop NMR spectrometers have already been used in metabolomics to make metabolic profiles of urine samples for patients with type II diabetes [144].

Finally, multiple strategies to increase NMR sensitivity have been addressed in recent years. Not only NMR hardware has advanced [34, 35], but also techniques relying on increasing nuclear polarization have been developed and implemented [36, 145, 146] to over-
come NMR sensitivity problems. Between these techniques, Dynamic Nuclear Polarization (DNP) has had a big impact in the NMR community and will be further developed in the remaining of this manuscript.

## 2.1 NMR in metabolomics and fluxomics

The major advances presented in the previous paragraph have brought the fields of metabolomics and fluxomics closer to NMR. Multiple NMR based strategies have been used to contribute the characterization of metabolism.

### 2.1.1 *In vitro* and *ex vivo* studies

The study of metabolic processes sometimes depend on the *in vitro* reproduction of the phenomenon. Multiple reasons make living organisms not suited for direct observation. Living organisms are complex systems that cannot always be adapted to the experimental conditions of the observation method, namely destructive methods. Additionally, during detection, the observed system has to be static. For long-duration observations, the evolution of living systems can therefore be problematic. However, reactions in metabolism can be reproduced *in vitro* [19, 75, 72] or analyzed *ex vivo* to characterize a particular metabolic process or to assess the impact of an organism on its environment [147, 148, 149].

#### 2.1.1.1 NMR spectroscopy to study enzyme kinetics in real-time

The easy preparation of samples in NMR, its quantitative nature, and the simultaneous observation of multiple analytes, are ideal features for the study of enzyme kinetics. The first applications of NMR in the study of enzymatic reactions date from the late 1960s [19, 150]. The quantitative aspect of NMR has been used to characterize different enzymatic reactions [115, 75]. The analysis has not been restricted to ¹H NMR, studies relying on ³¹P and ¹³C (between others) [135, 151, 152], together with multi dimensional NMR [75] have contributed to these metabolic characterizations. Most studies are based on deducing enzyme activi-
ties from analytical models [153, 30], and by comparison with reference reactions at known
rates. However, real-time monitoring of the reactions remains scarce due to the low time
resolution of the NMR technique. To overcome this issue, some approaches have focused
on slowing down the observed enzymatic reaction artificially, thus enabling its screening
[33, 30, 29]. This approach was used to characterize the second reaction of the oxPPP [33].
When this work was published, there was a debate over the role of the second enzyme of

<figure><img src="image_15.png" /><figcaption>**Figure 2.1:** Figure taken from [33], concentration evolution of G6P δ-PGL and γ-PGL. Concentration values were deduced from ³¹P NMR signal. The reactions were performed at 5 °C to slow down the process.</figcaption></figure>

the PPP, 6-phosphogluconolactonase (6PGL) enzyme. Supposedly 6PGL enzyme catalyzed
the hydrolysis of the two isomer forms of 6-phosphogluconolactones, δ-PGL and γ-PGL. In
that study, the first 2 enzymatic reactions of the oxPPP were reproduced *in vitro*, in a sample
containing the labeled substrate, [U-¹³C] G6P. A sample without the second enzyme was
also used to assess the spontaneous hydrolysis of δ and γ isomers. Samples were cooled to
5 °C to slow down the enzymatic reaction so as to monitor them in real-time. A two-minute
time resolution was achieved with ³¹P NMR (an averaging of 80 scans was required for each
spectrum).

The ¹³C carbon labeling was used only to identify the reaction products of the G6P dehydrogenation by G6PDH. The curves of the peak intensities versus time provided the kinetics of the different metabolites involved in the reaction (figure 2.1). These experiments demonstrated that the oxidation of G6P by G6PDH yielded only one isomer, δ-PGL. The γ-PGL isomer is mainly observed after all G6P is consumed. A second conclusion was that the only substrate of 6PGL enzyme is δ-PGL. In a subsequent experiment, a sample with both isomers at the same concentration was stabilized (5 °C, pH 6.7). 6PGL enzyme was then added, its activity transformed δ-PGL into phosphogluconic acid (6PGA) and let γ-PGL unchanged proving that only δ-PGL isomer is a substrate for 6PGL enzyme.

The work cited here is an example of how the screening of metabolic reactions can pro-
vide direct qualitative information of enzymatic reactions with simplified models. Moreover,
quantitative information can be easily extracted from the data since the relation between
precursor and product can be directly observed. However, to better reproduce metabolism,
the *in vitro* systems need to be prepared near physiological conditions. The latter implies
that an increased time resolution is required to be able to monitor enzymatic reactions in
real-time.

2.1.1.2 *Ex vivo* metabolomics by NMR

The adaptation of a cellular system to its environment causes variations in the excreted
metabolites. Depending on the organism, the nutrients available, and the active metabolic
processes, different metabolic products can be released to the external medium [148, 149].
Metabolomics has also relied on the characterization of the external medium to evidence
variations in cells phenotype [149, 154]. Ex vivo NMR methodology has been optimized for
different samples like plasma and urine [147, 155, 149]. This ex vivo characterization relies on
the observation of samples heavily charged with metabolites. The peak attribution of such
samples can thus be very challenging due to the multiple overlapping resonances, analyses
therefore use statistical tools for data treatment to overcome this issue [156, 157]. Ex vivo
<figure><img src="image_16.png" /><figcaption>**Figure 2.2:** Figure taken from [? ]. Spectrum on the aromatic region of a sample of mouse urine. 2D ¹H-¹³C pure shift HSQC spectrum (A), compared to a standard HSQC (B).</figcaption></figure>

samples are normally stable for longer periods than living organisms, multi-dimensional NMR experiments can thus be used to facilitate peak attribution [141, 158].

However, in some cases, the scalar coupling of the different nuclei causes the apparition of additional resonances. Hetero-nuclear decoupling standard techniques are commonly employed in NMR[159] and can be used to reduce the sample's resonances overpopulation. Moreover, recent developments use " pure shift NMR" methodologies to perform homonuclear decoupling.

In the work published in I. Timari et al. 2019, they use pure shift NMR to perform homonuclear decoupling on mouse urine samples. The metabolomic characterization is simplified since the spectra become better resolved if the resonances related to the scalar coupling are removed. In figure 2.2, a conventional HSQC spectrum (B) is compared to a pure shift HSQC spectrum (A). The spectra displayed in the aromatic region shows how there are multiple overlaps of different resonances when no decoupling is applied, even at high magnetic fields. One of the particularities of their work is that the optimization of the pulse sequence, gives HSQC spectra with no loss of sensitivity and with the improved
resolution of pure shift.

Hence, *ex vivo* samples are stable for longer periods than living cells or in vitro reproductions of enzymatic reactions. Multiple NMR techniques with enhanced spectral resolutions can thus be used to characterize metabolic profiles. However, *ex vivo* samples have been isolated from the studied organisms and so the organism's evolution cannot be observed.

### 2.1.2 In vivo studies

In this manuscript, when NMR is said to study *in vivo* systems, it also considers samples of isolated cells (in-cell) and isolated tissues. Other magnetic resonance (MR) based techniques, namely magnetic resonance imaging (MRI), has been used to perform *in vivo* studies of the metabolism of living animals and humans [160, 161, 162].

The non destructive characteristic of MR techniques enables the study of *in vivo* systems. Additionally NMR is very versatile with temperature regulation and so, samples can be studied near physiological conditions. Nevertheless, there is a drawback, NMR spectrometry requires a certain time to make a detection, duration in which the sample must be stable. As has been mentioned multiple times in this manuscript, living organisms evolve and adapt to the environment. In order to use NMR as an observation method for *in vivo* applications, the living organism must be put in a steady state or the reactions have to be quenched during the detection time [163, 164, 165].

Moreover, the observation of living cells results in heavily charged spectra. As for *ex vivo*, the presence of a very large set of metabolites makes peak attribution a difficult process. Multiple strategies have been developed in NMR to analyze complex systems and facilitate the attribution of peaks, namely 2D NMR [132, 142]. Heteronuclear MR has been also used for this purpose, in the study of multiple cellular systems [166, 30, 164, 72, 16].
### 2.1.2.1 NMR in vivo assignment with bioreactor

NMR probes have been adapted to the study of living system by developing mechanisms to distribute nutrients and oxygen to the cells, present in the NMR tube [167, 142, 168]. These bioprobes or bioreactors, subminister nutrients at constant intervals and uses the self-regulation of a cellular system to imitate a metabolic steady state in which NMR is used to characterize the metabolome.

In the work presented in *M.T. Anaraki et al.* [142] the use of a bioprobe (or bioreactor), constructed in their group, is used to stabilize the metabolism of a living organism. The bioreactor used in this work is called *Low-volume flow-system*, a complete description is given on [169]. The studied system is *Daphnia Magna* a small crustacean (1.5 - 5 mm) that consumes algae and is eaten by fish. The organism is small enough to be studied with NMR spectrometers in 5 mm NMR tubes and is constantly fed with nutrients and oxygen through the bioreactor. The only food source used was another living organism, algae *Chlamydomonas reinhardtii* which was previously fed with ¹³C enriched nutrients.

The principal objective of this work was to make a complete characterization of the metabolome of a living organism. The NMR spectrometry based description can subsequently be used to characterize the metabolome of other organisms. Multiple NMR strategies were used to identify the very big amount of metabolites present in such a complex biological system. In figure 2.3 we see an HSQC in vivo spectra of ¹³C enriched *Daphnia Magna* with a color coded metabolite attribution. The attribution was made based on supplementary NMR experiments and by comparison with multiple databases and with literature. The peak attribution was very challenging because of the overpopulation of all spectra recorded, as for the majority of *in vivo* metabolomic experiments. In [142], it was mentioned that the attribution "required a laborious manual approach that required checking on a peak by peak basis across numerous spectra and the literature, which was important to avoid misassigning components due to overlap". The multitude of different 2D and even 3D NMR experiments were then used to relate 1D simple ¹H experiments to a complex and
<figure><img src="image_17.png" /><figcaption>**Figure 2.3:** *In vivo* 2D HSQC (¹H-¹³C) spectrum of 13C-enriched *Daphnia magna* with color coded metabolites assigned. Figure taken from [142]</figcaption></figure>

complete peak attribution. This effort constitutes a big contribution to the metabolomics field, feeding databases with a spectral description of a living organism's metabolome and making it accessible to studies with less NMR complexity and without the need of ¹³C labeling. In my opinion, this work is a great example of what is metabolomics true objective as a holistic approach.

### 2.1.2.2 NMR in cell kinetic study

As mentioned above, multiple in-cell studies have been performed with NMR in metabolomics [15, 132, 16]. However, kinetic in cell studies remain scarce due to the low temporal resolution achievable with NMR. NMR has nevertheless been used to perform kinetic studies of metabolism focusing on slow reactions (time scales in the order of tens of minutes to multiple hours) [163, 170, 168]. ³¹P MR has been widely used in-cell to characterize the kinetics of multiple features related to cells' metabolism like substrates consumption, production of
<figure><img src="image_18.png" /><figcaption>**Figure 2.4:** Figure taken from [170]. Time-course analysis of glutathione redox homeostasis in living S. cerevisiae cells upon oxidative stress. The cellular response to oxidative stress was monitored over the course of the experiment by using in-cell NMR spectroscopy, shown here as filled contours from 1D 15N projections summed over $\delta(^1H)=8.0-8.3$ ppm of the $^1H-^{15}N$ HSQC spectra</figcaption></figure>

energy, or internal pH regulation [163, 171, 172, 173]. Other work based on in-cell ¹³C NMR has been documented [72, 174]. ¹³C Isotope labeling is often used to increase signal intensities, enabling also faster NMR detections. ¹³C labeling techniques have also been combined with 2D-NMR in the characterization of dynamic, and interaction properties of proteins in living cells with time resolutions in the order of tens of minutes [175, 176].

In [170], multi-dimensional NMR is used to study the oxidation of ¹⁵N labeled glutathione with a real-time fluxomic approach. Selective pulses were used to reduce the sampling window and so, reduce the time needed for each detection. 2D NMR allowed to separate peaks that overlapped in the ¹H dimension whereas remained well separated in ¹⁵N dimension. The technique was used on *Saccharomyces cerevisia*, which has a specific high-affinity uptake system for glutathione. Pulses were calibrated to allow the quantitative monitoring of the evolution of the different signals. The system was studied under various conditions, to this end cells were treated by the addition of different compounds
$(H_2O_2, AgNO_3, \dots)$ and compared to reference control experiments, see figure ??.

In this work, they were able to study the flux of a metabolic reaction in a living organism. They used non disruptive and quantitative characteristics of NMR, mixed with the increased spectral resolution of 2D NMR and selective isotope labeling to that end. Although the method allowed to successfully identify variations of the glutathione flux in different cellular environments, the reactions observed had characteristic time scales in the order of multiple tens of minutes. Hence, this method is an effective way to perform real-time studies on living cells provided that the reaction observed is a slow process (tens of minutes). However, a vast majority of metabolic reactions in living organisms are characterized by times scales inferior to a second.

Although NMR seems to present multiple advantages to the study of living systems, its time resolution limits the study of fluxes to slow reactions or artificially slowed reactions. In order to develop a more general technique to monitor real-time metabolic reactions, for both in cell and *in vitro* systems, the time resolution of NMR need to be increased, i.e. NMR sensitivity needs to be enhanced.

## 2.2 The Dissolution DNP technique

Developing methodologies for signal enhancement on NMR is of primary importance to overcome the weak sensitivity of NMR, its principal limitation. One of the principal hyperpolarization techniques used to date is dynamic nuclear polarization (DNP), a technique that originated with Overhauser's idea to use electron polarization to increase nuclear polarization [177]. The term dynamic nuclear polarization was given by Abragam, in 1958, while performing experiments on diamagnetic insulators using paramagnetic impurities, the polarization donor system [146]. A review of DNP mechanisms will be given in the next chapter.

Although DNP constituted a methodology that successfully enhanced NMR signal, multiple features of the technique strongly limited the range of applications. The main problem of DNP for a solution state spectroscopist is to use a hyperpolarized sample at ambient
<figure><img src="image_19.png" /><figcaption>**Figure 2.5:** Figure taken from [178], both spectra acquired on the same sample of Urea at 59.6 mM in the same 9.4 T spectrometer. **A:** DDNP experiment. **B:** Urea in thermal equilibrium, averaging over 65 h, 232128 transients. Estimated signal enhancement of $\epsilon = 44\,400$.</figcaption></figure>

temperature whilst it is prepared at cryogenic temperatures.

### 2.2.0.1 The invention of Dissolution DNP

In this perspective, a major technical development was achieved in 2003. When in J.H. Ardenkjær-Larsen et al. a frozen DNP sample was dissolved and transferred to a conventional liquid-state NMR spectrometer [178]. The sample remained hyperpolarized for a duration in which NMR signal was strongly enhanced. Since the hyperpolarized state is not an equilibrium state, when a sample leave DNP conditions the polarization enhancement starts decaying following longitudinal relaxation, characteristic to each nuclear system (proportional to $T_1$ time constant). Experiments were carried on both ¹³C-labeled urea and urea in natural abundance. The spectra displayed on figure 2.5 was acquired with urea in natural abundance, the upper spectrum uses dissolution DNP. Signal enhancement was on the order of 44 400 between hyperpolarized ¹³C and thermally polarized spectra. A

In figure 2.5, the spectrum with no hyperpolarization (i.e. at thermal equilibrium) was averaged over 65 h, 232128 scans compared to 1 scan for the experiment with hyperpolarization. Since the signal intensity determines the time resolution achievable for the monitoring of dynamical processes, hyperpolarization represents a most useful way to observe reactions
with small time scales, on the order of the acquisition time ($\sim T_2^*$). Typically experiments performed with DDNP have a time resolution on the order of a second or less. Hence, DDNP technique has enough time resolution to make real-time studies of metabolic reactions. The labeling strategies used in the multiple fluxomic methodologies can be combined with DDNP or replaced by the contrast between hyperpolarized and thermally polarized compounds[46, 45, 44, 128]. Dissolution DNP technique appears as a very promising technique that has led to a wide range of potential applications, in metabolomics or fluxomics, both *in vitro* and *in vivo* [179, 49, 50, 53, 180].

### 2.2.1 Advantages and known limitations of DDNP methodology

#### 2.2.1.1 Fast sampling technique ideal for fluxomic studies

In DDNP, the anlytes' signal can be monitored for the duration in which the hyperpolarization remains. However, each NMR pulse generates a polarization loss proportional to $1 - \cos\theta$, where $\theta$ is the flip angle. Thus, in DDNP, time sampling of metabolic reactions is achieved using the smallest possible flip angles. The simple NMR pulse sequences used in DDNP provide spectra that can be analyzed quantitatively.

Relying on nuclear species with characteristically long relaxation times has been prioritized in DDNP experiments to avoid the complete relaxation of the hyperpolarized signal. $^{13}$C MR is thus frequently used, which represents also an increase in spectral resolution compared to $^{1}$H MR [47, 45]. Such a technique thus allow the simultaneous screening of a substrate and its metabolic products. It can thus be used to perform kinetic studies of metabolic reactions or to elucidate the reaction schemes of different metabolic processes.

Although DDNP methodology seems to be very promising for applications in multiple domains, some of the major concerns have to be addressed. To start with, as mentioned above, hyperpolarization is not an equilibrium state. When the DNP sample leaves the polarizer (DNP hardware), longitudinal relaxation causes the sample to go back to equilibrium i.e. to thermal polarization. Hence, during the transfer, a part of the polarization enhancement is lost. Naturally, to reduce enhancement loss one can, reduce the duration of the
transfer, slow the relaxation process, or use substrates with characteristic long $T_1$. Different DDNP setups rely on the manual injections of the dissolved sample, characterized by long transfer times (5-10 s duration)[38, 53, 181]. Other setups with automatic injection systems normally push the sample with gas through pipes connected to the NMR tube inside the spectrometer[182, 183]. These systems, have other problems related to the mechanical shock of the injection, which can damage the sample (such as living cells). Pressure regulated injectors are being developed for DDNP applications, to prevent the mechanical shock of the automatized dissolution systems[45, 184, 54, 185]. The usual strategies to increment hyperpolarized signal in DDNP are thus often based on choosing substrates with characteristically long $T_1$ and diminishing the transfer duration. Being forced to choose molecules with functional groups having long $T_1$ is clearly a strong limitation for metabolomic and fluxomic studies since some metabolic pathways are therefore not accessible to DDNP methodology.

### 2.2.1.2 Reproducibility problems of a complex experiment

As will be detailed in the next chapter, DDNP experiments depend on a very complicated set-up. The time needed for the polarization of the sample to attain a maximum hyperpolarization level can vary from tens of minutes to several hours. After reaching maximum polarization, the sample, which is frozen in a bath of liquid helium, has to be dissolved to be transferred to the NMR spectrometer. Thus, samples have to be extracted from chambers filled with cryogenic liquids, where any air leakage would provoke the complete freezing of the system, causing the failure of the DDNP experiment and in most cases the loss of the DNP sample. Moreover, during the dissolution experiment, for a big majority of DDNP systems[182, 185, 183], the dissolution procedure is done manually and so the duration of the dissolution step changes between experiments. The polarization of the sample transferred to the NMR spectrometer is therefore dependent on the experiment and so is not completely repeatable.

Solvents used for the dissolution of the frozen DNP sample are warmed to very high
temperatures (~140 °C) to optimize the amount of sample liquefied and transferred. Hence, the dissolution implies that the DNP sample has to be exposed to extreme thermal conditions which limit the nature of the hyperpolarized compounds that can be used.

As mentioned in the introduction, the principal purpose of my Ph.D. work is to optimize the experimental procedure both technically, by adapting the DNP technique and the hardware to the study of biological and biochemical systems; and analytically, by developing methods to characterize the kinetics of the observed reactions. In the next chapters, after properly introducing DNP and DDNP, the fluxomics projects undertaken during my Ph.D. will be presented, the results serving as an additional proof of concept of the potential contributions of DDNP to the study of metabolism.
<figure><img src="image_20.png" /></figure>
# Part II

## A review of the basics of DNP and
DDNP
<figure><img src="image_21.png" /></figure>
# Chapter 3

## Short review of DNP

As mentioned in the last chapter, DNP is able to increase NMR signal by several orders of magnitude. It was discussed that the enhancement depends on reducing the temperature to cryogenic levels which implies that the studied system must be frozen and so, in solid-state. The Dissolution DNP experiment bridges the gap between DNP hyperpolarization and conventional liquid-state NMR, where *in vivo* and in-cell biological systems, as well as *in-vitro* biochemical systems can be studied. DDNP experiments are complex, as many different issues are encountered, especially regarding the loss of polarisation during transfer of the solution with the hyperpolarized spins. Optimizing the different steps of the experiment is therefore of primary practical interest.

In this chapter, we will review the main mechanisms of DNP hyperpolarization, and some recent aspects of thermal mixing will be discussed.

### 3.1 Polarization

The spin momentum of the electron, $\hbar\mathbf{S}$, is associated to the magnetic moment $\mu_S = \hbar\gamma_S \mathbf{S}$, where $\hbar$ is the reduced Planck constant and $\gamma_S$ is the electron spin gyromagnetic ratio: $\gamma_S = \frac{\mu_B}{\hbar} g_S$; $\mu_B$ is the Bohr magneton and $g_S$ is the g-tensor (isotropic for the free electron). Electrons have half odd spin, and so $|\mathbf{S}| = S = \frac{1}{2}$. Similarly, the nuclear magnetic moment will be noted $\mu_I = \hbar\gamma_I \mathbf{I}$. In the following, we will assume $I = \frac{1}{2}$ as is the case for protons.
In the presence of a magnetic field, the degeneracy of the spin energy levels is lifted, which leads, by virtue of the Boltzmann law, to a population imbalance between the upper and lower states, therefore a spin polarization. It will be shown below that reducing thermal motion can be described by a cooling of the spin system. As a matter of fact, nuclei are difficult to polarize. Efficiently increasing their polarization cannot be undertaken by simply imposing a strong magnetic field, hence the originality of DNP. The qualitative idea of DNP is to achieve a similar orientation for a large population of nuclear spins i.e. to increase the polarization of the nuclear spin system. Hence, polarization is the relative difference of populations in the two states of energy. To quantify the polarization enhancement achievable via DNP, the interactions between the particles and the field need to be introduced.

The Zeeman interaction between the electron spin magnetic moments and the external constant magnetic field **B** is:

$$ \mathcal{H} = -\hbar \mathbf{B} \cdot \gamma_S \mathbf{S} = \hbar \omega_S \mathbf{S} = \hbar(\omega_S^x S_x + \omega_S^y S_y + \omega_S^z S_z), \quad (3.1) $$

where $\omega_S$ is the frequency vector $\omega_S = -\mathbf{B} \cdot \gamma_S$. The spin state vector can be represented by a two-dimensional state vector $\psi_S = \begin{pmatrix} a \\ b \end{pmatrix}$ in the basis of states $\{|m_S\rangle\} = \{|\frac{1}{2}\rangle, |-\frac{1}{2}\rangle\}$

$$ |m_S\rangle = |\frac{1}{2}\rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix} \quad \text{and} \quad |m_S\rangle = |-\frac{1}{2}\rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix} \qquad (3.2) $$

where the three spin operators are represented by the Pauli matrices:

$$ S_x = \frac{1}{2} \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, \quad S_y = \frac{1}{2} \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}, \quad S_z = \frac{1}{2} \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \qquad (3.3) $$

Next, we want to determine the energy related to the electron spin interacting with the field **B**. An externally applied static magnetic field $\mathbf{B}_0$ orients the space and defines z-axis
of a Cartesian coordinate system. In this reference frame, $\omega_{0S} = -\mathbf{B}_0 \cdot \mathbf{\gamma}_S$, and the Zeeman hamiltonian writes:

$$ \mathcal{H}_{0S} = \frac{1}{2} \hbar \begin{pmatrix} \omega_{0S} & 0 \\ 0 & -\omega_{0S} \end{pmatrix} \qquad (3.4) $$

For nuclei, the frequency vector is actually $\omega_{0I} = \gamma_I \mathbf{B}_0$ since $\gamma_I$ is positive and not negative like $\gamma_S$ and:

$$ \mathcal{H}_{0I} = -\frac{1}{2} \hbar \begin{pmatrix} \omega_{0I} & 0 \\ 0 & -\omega_{0I} \end{pmatrix} \qquad (3.5) $$

### 3.1.1 Density Matrix

The description of a statistical ensemble of spins requires the use of the density matrix. For an isolated particle described by its wave function $|\psi\rangle$, the density matrix is defined as the projection operator $|\psi\rangle\langle\psi|$, which, for a single spin 1/2, takes the form:

$$ |\psi\rangle\langle\psi| = \begin{pmatrix} a \\ b \end{pmatrix} (a^*b^*) = \begin{pmatrix} aa^* & ab^* \\ ba^* & bb^* \end{pmatrix} \qquad (3.6) $$

For a statistical ensemble of spins where N copies of the particle occurs with some probability, the density matrix is the average of the projectors over the ensemble:

$$ \rho = \overline{|\psi\rangle\langle\psi|} = \begin{pmatrix} \overline{aa^*} & \overline{ab^*} \\ \overline{ba^*} & \overline{bb^*} \end{pmatrix} = \begin{pmatrix} \rho_+ & \rho_\perp \\ \rho_\perp^* & \rho_- \end{pmatrix} \qquad (3.7) $$
Then, the polarization vector $\mathbf{P}_S = (P_S^x, P_S^y, P_S^z)$ is defined as:

$$
\begin{align*}
P_S^x &= -\frac{1}{S} \frac{\mathrm{Tr}\{\rho S_x\}}{\mathrm{Tr}\{\rho\}} \\
&= -\mathrm{Tr}\left\{ \begin{pmatrix} \rho_+ & \rho_\perp \\ \rho_\perp^* & \rho_- \end{pmatrix} \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \right\} / \left\{ \mathrm{Tr}\left( \begin{pmatrix} \rho_+ & \rho_\perp \\ \rho_\perp^* & \rho_- \end{pmatrix} \right) \right\} = -\frac{\rho_\perp + \rho_\perp^*}{\rho_+ + \rho_-}, \\
P_S^y &= -\frac{1}{S} \frac{\mathrm{Tr}\{\rho S_y\}}{\mathrm{Tr}\{\rho\}} \\
&= -\mathrm{Tr}\left\{ \begin{pmatrix} \rho_+ & \rho_\perp \\ \rho_\perp^* & \rho_- \end{pmatrix} \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} \right\} / \left\{ \mathrm{Tr}\left( \begin{pmatrix} \rho_+ & \rho_\perp \\ \rho_\perp^* & \rho_- \end{pmatrix} \right) \right\} = -i \frac{\rho_\perp - \rho_\perp^*}{\rho_+ + \rho_-}, \\
P_S^z &= -\frac{1}{S} \frac{\mathrm{Tr}\{\rho S_z\}}{\mathrm{Tr}\{\rho\}} \\
&= -\mathrm{Tr}\left\{ \begin{pmatrix} \rho_+ & \rho_\perp \\ \rho_\perp^* & \rho_- \end{pmatrix} \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \right\} / \left\{ \mathrm{Tr}\left( \begin{pmatrix} \rho_+ & \rho_\perp \\ \rho_\perp^* & \rho_- \end{pmatrix} \right) \right\} = -\frac{\rho_+ - \rho_-}{\rho_+ + \rho_-},
\end{align*}
$$

Now, since the components $a$ and $b$ of $|\psi\rangle$ are complex numbers: $a = a_0 e^{i\phi_a}$, and $b = b_0 e^{i\phi_b}$.

The variation of the phase $\phi$ is restricted to $0 \le \phi_a \le 2\pi$, $0 \le \phi_b \le 2\pi$. We can thus express

the density operator (in eq. 3.7) as:

$$
\rho = \begin{pmatrix} \overline{aa^*} & \overline{ab^*} \\ \overline{ba^*} & \overline{bb^*} \end{pmatrix} = \begin{pmatrix} a_0^2 & a_0 b_0 e^{i(\phi_a - \phi_b)} \\ a_0 b_0 e^{-i(\phi_a - \phi_b)} & b_0^2 \end{pmatrix} \quad (3.8)
$$

And by computing the averages we find that:

$$
\overline{e^{\pm i(\phi_a - \phi_b)}} = \frac{1}{(2\pi)^2} \int_0^{2\pi} d\phi_a \int_0^{2\pi} d\phi_b e^{\pm i(\phi_a - \phi_b)} = 0 \quad (3.9)
$$

so that the density matrix therefore adopts the following form:

$$
\rho = \begin{pmatrix} \rho_+ & 0 \\ 0 & \rho_- \end{pmatrix} = \begin{pmatrix} a_0^2 & 0 \\ 0 & b_0^2 \end{pmatrix} \qquad (3.10)
$$
Therefore, $\rho_{\perp} = 0$ and $\rho_{\perp}^* = 0$, hence $P_S^x = P_S^y = 0$ and $P_S = (0,0, P_S^z)$. As expected, the polarization is thus defined by its component along $\mathbf{B}_0$. Now we have, $|P_S| = P_S = P_S^z = -\frac{\rho_+ - \rho_-}{\rho_+ + \rho_-}$ where $P_S$ is the polarization of the electrons.

### 3.1.1.1 Boltzmann distribution

Following the quantum mechanical definition, the probability to find the particle in one of those states is, respectively:

$$P_{+\frac{1}{2}} = \frac{aa^*}{aa^* + bb^*} = \frac{a_0^2}{a_0^2 + b_0^2}, \quad \text{and} \quad P_{-\frac{1}{2}} = \frac{bb^*}{aa^* + bb^*} = \frac{b_0^2}{a_0^2 + b_0^2}, \qquad (3.11)$$

According to the Boltzmann statistics, and by introducing eq. 3.11, the probability of the spin being in one of either states is:

$$P_{+\frac{1}{2}} = \frac{1}{Z}e^{-\frac{1}{2}\beta_S\hbar\omega_{0S}} = \frac{a_0^2}{a_0^2 + b_0^2} \quad \text{and} \quad P_{-\frac{1}{2}} = \frac{1}{Z}e^{+\frac{1}{2}\beta_S\hbar\omega_{0S}} = \frac{b_0^2}{a_0^2 + b_0^2} \qquad (3.12)$$

Here, $\beta_S = \frac{\hbar}{k_B T_S}$, where $k_B$ is Boltzmann constant and $T_S$ is the spin temperature (the concept of spin temperature is defined in Appendix A) here given for electrons. In these expressions, $Z = e^{+\frac{1}{2}\beta_S\hbar\omega_{0S}} + e^{-\frac{1}{2}\beta_S\hbar\omega_{0S}}$ is the partition function. From equations 3.11 and 3.12, we obtain for the electron Polarization:

$$P_S = -\frac{\rho_+ - \rho_-}{\rho_+ + \rho_-} = -\frac{a_0^2 - b_0^2}{a_0^2 + b_0^2} = \frac{e^{+\frac{1}{2}\beta_S\hbar\omega_{0S}} - e^{-\frac{1}{2}\beta_S\hbar\omega_{0S}}}{e^{+\frac{1}{2}\beta_S\hbar\omega_{0S}} + e^{-\frac{1}{2}\beta_S\hbar\omega_{0S}}} = \tanh(\frac{1}{2}\beta_S\omega_{0S}) \qquad (3.13)$$

The expression for the nuclear polarization is defined in a similar fashion. In conclusion, electron and nucleus polarizations under a static magnetic field $\mathbf{B}_0$ at the sample temperature $T_{sample}$ is defined as follows:

$$P_S = \tanh(\frac{1}{2}\beta_S\omega_{0S}) = \tanh(\frac{\hbar\omega_{0S}}{2k_B T_S^2}) \qquad (3.14)$$

$$P_I = \tanh(\frac{1}{2}\beta_I\omega_{0I}) = \tanh(\frac{\hbar\omega_{0I}}{2k_B T_S^2}) \qquad (3.15)$$
Where both spin temperatures $T_S^S = T_S^I = T_{sample}$, the spin system is said to be at *thermal* polarization.

### 3.1.2 Spin polarizations at cryogenics temperatures

The expression of polarization given by equation 3.14 defines the relation between $P_S$ (or $P_I$) and the external magnetic field $B_0$, the spin temperature $T_S$ and the nature of the particle $\gamma_S$ or $\gamma_I$. Boltzmann distribution is defined for a spin system at constant sample temperature $T_{sample}$ and constant $B_0$, the system is considered at equilibrium. Under these conditions the spin temperature equals the sample temperature: $T_S = T_{sample}$. For a sample at $T = 1.2$ K and $B_0 = 6.7$ T the electron and nuclear polarizations are:

$$P_S = 0.99 \qquad (3.16)$$

$$P_I = 0.0016 \qquad (3.17)$$

This shows that, even though the samples are cooled to cryogenic temperatures the polarization obtained for protons is still very weak. On the other hand, in the exact same conditions, the polarization for electrons is almost of 100%. DNP mechanism relies on transferring the polarization of the electronic spins at cryogenic temperatures to the nuclear spins. This transfer is achieved by means of a set of multiple dipolar interactions that will be detailed in the next section.

## 3.2 Polarization Transfer

DNP nuclear polarization enhancement depends on the transfer of polarization from electron spins to nuclear spins by means of microwave ($\mu$-wave) irradiation. The electron and nuclear spins are coupled through dipolar interactions that induce transitions, spin flips. Spin flips also occur within the populations of both electronic and nuclear spins. The phenomenon of diffusion of spin flips is called spectral diffusion.
### 3.2.1 EPR spectrum

In order to understand the polarization transfer processes, it is necessary to describe the interactions of the electron spins with their environment. In DDNP experiments, the paramagnetic impurities are unpaired electrons of the stable radicals used as polarizing agents. As a matter of fact, unpaired electrons act as paramagnetic centers that have an orientation with respect to the magnetic field $B_0$. Although this interaction has a fundamental precession frequency, defined by the frequency vector $\omega_{0S} = B_0\gamma_S$ (introduced in the precedent chapter), some frequency shifts can be induced by the interactions with the environment and by the particular orientation of each paramagnetic center with respect to the magnetic field. The interactions of an electron with the external magnetic field, and with the local magnetic fields created by the magnetic moment of the surrounding particles, gives rise to the Electron Paramagnetic Resonance (EPR) spectrum.

Depending on symmetry properties of the radical, different orientations of the paramagnetic centers can induce variations in its Zeeman response to the external magnetic field. Variations of the Zeeman response related to the orientation of the paramagnetic centers describe an anisotropy of the g-tensor. Moreover, unpaired electrons are affected by the interaction with nearby nuclear spins (intra-molecular), additional electronic spins, and remote nuclear spins. Frequency shifts caused by the g-tensor anisotropy and by the interactions with nearby nuclear spins are responsible for "inhomogeneous broadening". This type of broadening does not fluctuate and hence is time independent. The frequency shifts induced by interactions with other electron spins and more remote nuclear spins lead to "homogeneous broadening". The frequency shifts related to this broadening is fluctuating and so is time dependent. Consequently, the EPR spectrum is affected by the nature of the radical, its interaction with the static magnetic field, and its coupling with other surrounding particles. The EPR spectrum is thus a convolution of both homogeneous and inhomogeneous broadening. The interactions related to the inhomogeneous broadening are larger (up to several orders of magnitude, depending on the sample) and hence cause larger frequency shifts than
<figure><img src="image_22.png" /><figcaption>**Figure 3.1:** Schematic drawing of an arbitrary EPR spectrum. Here, $\Delta_{EPR}$ is the total width of the EPR spectrum, it is determined by the *inhomogeneous broadening* of the radical. $\Delta_h$ is the width of the so called "spin packets"[186, 187] determined by the *homogeneous broadening* that creates a time-dependent fluctuating field i.e. $\omega_S$ varies in time in a frequency range of $\Delta_h$. Slow spin diffusion is responsible of a "Hole Burning"[186, 187], whereby saturation of the EPR line remains local at the $\mu$-wave irradiation frequency.</figcaption></figure>

homogeneous broadening. This is illustrated in figure 3.1, where the maximum width of the EPR line $\Delta_{EPR}$ depends on the "inhomogeneous broadening", and the time dependent shift $\Delta_h$ due to the fluctuating interactions at the origin of the "homogenous broadening", are depicted. The shape of the EPR line of the radical is of major importance for the presence and efficiency of the different DNP mechanisms.

The $\mu$-wave irradiation used for DNP alters the electronic polarization because of the absorption of energy by the electron spins, and thus saturation occurs at the irradiation frequency. Depending on the efficiency of homogeneous broadening the saturation of the $\mu$-wave irradiation can be diffused in the range $\Delta_h$, thus saturating a band of the EPR spectrum and not just a discrete frequency [188, 187].

The Hamiltonian representing the contribution of the $\mu$-wave irradiation along the x-axis has the following expression,

$$ \mathcal{H}_m = 2\mathbf{B}_1\cos(\omega_m t) = 2\hbar\omega_{1S}S_x\cos(\omega_m t) \quad (3.18) $$

where $\mathbf{B}_1(t)$ is the magnetic field created by the microwave, $\omega_m$ is the carrier frequency
of the $\mu$-wave and $\omega_{1S} = -\gamma_S B_1$.

The energy absorbed by the electron spins can be expressed in terms of the thermodynamic potentials. Indeed, for an electron spin with a Zeeman angular frequency $\omega_S$, the free energy is given by:

$$F_S = -\frac{\hbar}{\beta_S} \ln(Z) = -\frac{\hbar}{\beta_S} \ln(e^{+\frac{1}{2}\beta_S \omega_S} + e^{-\frac{1}{2}\beta_S \omega_S}) \quad (3.19)$$

where Z is the partition function. From this expression the entropy $S_S$ and the energy $U_S$ can be derived as:

$$S_S = -\frac{\partial F_S}{\partial T_S} = -\frac{\partial F_S}{\partial \beta_S} \cdot \frac{\partial \beta_S}{\partial T_S} \quad (3.20)$$

$$U_S = F_S + T_S S_S = -\frac{1}{2} \hbar \omega_{0S} \tanh\left(\frac{1}{2} \beta_S \omega_{0S}\right) \quad (3.21)$$

As so, by introducing the expression of polarization derived in the past section, and given in eq. 3.14:

$$U_S = -\frac{1}{2} \hbar \omega_{0S} P_S \quad (3.22)$$

Hence, variations of the polarization are thus related to variations of the internal energy of the spin system. When the $\mu$-wave saturates a band of the EPR spectrum, if no other mechanisms can build up the thermal polarization in the saturated band, it is then said that the irradiation *burns a hole* in the EPR line, in yellow in figure 3.1, (see chapter 3 of [187]). The energy related to the $\mu$-wave irradiation is at the origin of the polarization transfer in DNP. Hyperpolarization phenomena is competing with nuclear relaxation mechanisms. Although normally, at DNP temperatures, nuclear spin-lattice relaxation is very slow compared to DNP polarization transfer, nuclear species can relax through its dipolar coupling with electron spins, sometimes called nuclear relaxation by paramagnetic impurities [189, 190, 191]. Hence, in order to get the nuclear-spin system out of the Boltzman equilibrium state and to enhance its polarization, the rate at which the polarization is transferred from electron to nuclear spins has to be bigger than the nuclear relaxation rate[189, 188, 187].
### 3.2.2 DNP mechanisms

The $\mu$-wave irradiation of the EPR spectrum triggers a transfer of polarization from the almost fully polarized electron-spin system to the nuclear-spin system. The transfer is done through a series of dipolar interactions that define the mechanism of polarization transfer. These transfer mechanisms strongly depend on the shape and width of the EPR spectrum [189, 187, 190, 192, 186] and thus depend on the sample composition, magnetic field, etc. In a given sample, DNP mechanisms determine the achievable nuclear polarization enhancement. Hence, a thorough understanding of the underlying mechanisms is a prerequisite for the optimization of DNP and DDNP experiments. In this section we briefly present these DNP mechanisms, a more detailed introduction is given in Appendix A.

The principal documented DNP mechanisms in solid-state samples are, the Solid Effect (SE)[146, 189, 190, 187], the Cross Effect (CE) [193, 194, 192, 195, 186, 187] and Thermal Mixing (TM)[196, 197, 189, 188, 198, 199, 187].

The SE mechanism, discovered in 1958 [146], relies on the dipolar coupling of an electron spin and a nuclear spin. In this mechanism, the $\mu$-wave irradiation provides energy to the coupled spin system, enabling transitions that otherwise would not be energy-conservative. These $\mu$-wave induced transitions are responsible for the transfer of polarization from the electron spins to the nuclear spins, that under irradiation is more efficient than the nuclear relaxation by paramagnetic impurities [189, 190]. SE mechanism is predominant when the inhomogeneous spectral breath $\Delta_{EPR}$ is smaller than the nuclear Larmor frequency $\omega_{0I}$ [189, 200] (and see Appendix A).

Both CE and TM mechanisms depend on the coupling of three spins, two electron spins, and one nuclear spin. The coupling between the three-spin system can induce transitions (triple spin flips) provided that the difference between the two electron Larmor frequencies matches the nuclear Larmor frequency ($|\omega_S^i - \omega_S^j| = \omega_{0I}$). Triple spin flips thus occur when the inhomogeneous breath of the EPR spectrum is larger than the nuclear Larmor frequency ($\omega_{0I} < \Delta_{EPR}$).

The differences between CE and TM mechanisms have been the subject of discussion
[186, 192]. However, it has been generally agreed that the predominance of one of these two mechanisms relies on the homogeneous broadening linewidth ($\Delta_h$) of the EPR spectrum [186, 195, 192]. For systems with weak mutual interactions between electron spins (and hence weak homogeneous broadening), where $\Delta_h < \omega_{0I}$, CE is the predominant mechanism[186, 195, 201]. On the other hand, for systems with strong mutual interactions between electron spins, where electron spectral diffusion is therefore also enhanced, and $\Delta_h > \omega_{0I}$, TM is assumed to be the predominant mechanism [186, 195, 188, 202].

In TM conditions, $\mu$-wave irradiation is diffused throughout the EPR spectrum. The triple spin-flip conditions are therefore matched for different nuclear species simultaneously, provided that $\omega_{0I} < \Delta_{EPR}$[187]. Surprisingly, under these conditions, transfers of polarization were observed between different nuclear-spin systems [196]. TM mechanism presents multiple particularities that have been largely studied and documented [196, 189, 186, 202, 187]. During my master's internship (also at the LBM, in the team *Paris en Resonance*), and during a part of my thesis, I worked on the characterization of TM regime in DNP samples. The results obtained in my master's are presented in *Appendix A* together with a more detailed introduction to the different DNP mechanisms, namely TM.
# Chapter 4

## The Dissolution DNP system

Performing DDNP experiments remains challenging and requires a complex instrumentation. The dissolution system has been under constant evolution and optimization, aiming to increase the efficiency and reproducibility of the experiments, and to simplify what is a complex procedure. In this chapter, I will describe the complete set-up with which I performed the different experiments presented in this thesis.

### 4.1 DNP Hardware

In our laboratory, two polarizers based on different technologies were used and will be introduced in this chapter.

#### 4.1.1 Bruker, 6.7 T polarizer

The main DNP instrument used was a Bruker 6.7 T polarizer. This hardware prototype developed by the Bruker company was installed 5 years ago with the help of Daniel Abergel, Dennis Kurzbach and Dr. Emanuelle Weber - Ph.D. student at the time.

##### 4.1.1.1 Magnetic field and cryogenics

This polarizer is composed of a cryo-magnet and a cryostat. The cryostat, where the NMR probe and the sample are introduced for experiments, is brought to cryogenic temperatures
<figure><img src="image_23.png" /><figcaption>**Figure 4.1:** Complete scheme of the Bruker 6.7. polarizer with the exchangeable dewar of liquid helium (~100 L) connected to the cryostat. The μ-wave source (and frequency doubler) emitting the irradiation going to the sample through the μ-wave guide. We can also see the cryostat with the phase separator allowing the filling of liquid helium in the sample space, the transfer of liquid helium is regulated by two needle valves releasing helium at different heights in the cryostat. The magnet is isolated from the cryostat by a chamber that is pumped to create void, the external vacuum. When the polarizer is warm, the trap between the cryostat and the external vacuum becomes porous allowing the pumping of impurities in the cryostat. Finally we see the cryo-magnet that is cooled down by a chamber with liquid helium, then in a subsequent chamber liquid nitrogen and ultimately a last chamber pumped to create void isolating the previous chambers from the outside.</figcaption></figure>

by filling it with liquid helium, ¹He. The liquid helium is stored in an external dewar that is connected to the cryostat by means of a transfer line (see figure 4.1). Liquid helium is introduced in the sample area of the polarizer through the so-called phase separator (PS) in which the liquid and the gaseous Helium are separated. Two needle valves are used to control the amount of helium flowing into the remaining part of the cryostat where the sample is located (figure 4.1). The evaporated helium gas goes to a recovery line and is re-liquefied by the Cryogenics Department at the ENS. This service aims to reduce the cost generated by the constant need for liquid helium in DNP experiments.

The typical temperature inside the cryostat, in the sample space is ~4.2 K. However, pumping on the cryostat permits to reach temperatures as low as ~1.2 K by using a pumping system that comprise a forevacuum pump and a Roots pump. The magnetic field of 6.7 T is achieved by a Bruker kind magnet. A number of features are automatized to increase
the reproducibility of DNP and to make it more user friendly. For information, the typical helium consumption on a week of DDNP experiments amounts to ~80 – 100 L of liquid helium.

### 4.1.1.2 Probe, RF circuit and μ-wave irradiation

The probe includes the Radio Frequency (RF) circuit and the Microwave Guide (MG). The MG connects the microwave source with the system, allowing at its terminus the irradiation of the sample. The microwave source is an ELVA1 emitting at ~94 GHz (93800-94200 MHz) which is coupled to a Virginia Diodes frequency doubler so that the output signal is in the range 187.6 - 188.4 GHz. The ELVA1 source maximum power is of 350 mW. Experiments typically used a saw-tooth modulated microwave irradiation with a 100 MHz frequency span. In figure 4.2 a picture of a Proton/Deuterium probe is shown. Most DNP probes have

<figure><img src="image_24.png" /><figcaption>**Figure 4.2:** a) Bottom and Head of a Proton/Deuterium DNP probe. In the bottom part (left side) we see a Helmholtz resonator built in the laboratory. In the structure we see: 1 μ-wave guide, 2 induction coil for one of the two channels, 3 teflon sample holder and 4 airtight cap, this is the entry of the sample stick that holds the sample and introduce it inside the resonator immersed in a bath of liquid helium. b) Scheme showing the perpendicular distribution of the coils for perpendicular directions of the two induced magnetic fields (related to each channel). The perpendicular distribution reduces the possible coupling of the fields induced by the two RLC systems.</figcaption></figure>

two channels, one for protons and a second for an X nuclei. So are the probes we use in the laboratory, which are able to excite simultaneously the magnetization of two different nuclei. Four different radio-frequency coils are arranged in a perpendicular array. The currents circulating in each RLC (Resistor (R), inductor (L), capacitor C) circuit creates two
mutually orthogonal magnetic fields, each circuit at a different resonance frequency. Thus, RF fields tuned at two different frequencies are generated at the Larmor frequencies each nuclei $\omega_L = \gamma_{nuc} \times B_0$.

## 4.1.2 Cryogen-free 9.4 T Polarizer

<figure><img src="image_25.png" /><figcaption>**Figure 4.3:** Image taken from [203], depicting an external view of the Cryogen-free Polarizer. 1 Helium gaz storage tank with a maximum capacity of 200 L. DNP system with the dry magnet, the VTI system and the DNP probe. 3 Dry pump allowing the flow of helium through the entire system. The arrows indicate the helium circuit involved in the cool-down of the polarizer.</figcaption></figure>

The second polarizer used in this work, mounted by M. Baudin [203], is based on a different design and uses a dry magnet and cryostat, which avoids the need for liquid helium, a system inspired on recently developed hardware[204, 205]. Since both the magnet and the VTI (Variable Temperature Insert, the cryostat) are cooled with a recycling loop of helium, the cost related to the consumption of Helium is strongly reduced.

### 4.1.2.1 Magnetic field and cryogenics

In these “cryogen-free” or “dry” superconducting magnets, liquid helium is provided by "built-in" liquefiers. In our setup, a cryo-cooler (Sumitomo Heavy Industries - RDK-415D cold head and F50H compressor) is used to cool the magnet. This kind of magnets can be set at different fields $B_0$ with a principal drawback regarding the homogeneity of the magnetic
field, which is not problematic for these DNP experiments performed on non rotating solids.
In the ENS *cryo-free* polarizer, the magnet is usually ramped up to 9.4 T although it could
be also energized at 3.35 T and 6.7 T The whole process of cooling down the magnet takes
around 30 h (starting at room temperature). Is important to note that even though the
electronic polarization P<sub>e</sub> is stronger at higher fields, some of the mechanisms of polarization
transfer (from electron spins to nuclear spins) may be less efficient.

After the system reaches its base temperature (2.5 K), a circuit of helium is set to cool-
down the cryostat, in green in figure 4.4. The circuit starts with a 200 L storage tank contain-
ing helium gas connected to the cryostat. The helium is then cryo-pumped into a chamber
with a volume of 0.5 L in which it is liquefied, called the helium pot. The liquid helium is
then filled into the VTI space that contains the probe. The volume of liquid helium flowing
in the VTI is regulated by a manually operated needle valve. The circuit goes through two
charcoal traps that filter helium preventing blockages of the circuit due to water or nitrogen
impurities.

Temperatures down to 1.4 *K* can be reached in this cryostat. The evaporated helium goes to the storage tank waiting to be re-liquefied starting again the cycle. The system is depicted in figure 4.3, where the arrows indicate the flow of helium through the circuit. Although the VTI and the probe are in contact, the probe is designed to avoid any leakage of superfluid helium. Thus, the circuit flowing through the VTI is a closed system with no loss of helium. The helium gas inserted inside the probe, i.e. in the sample space, is liquefied through thermal contact with the VTI. Since it is leak-tight the volume of gas entering the probe can be easily controlled. For a conventional experiment, the sample space is filled with ~ 50 L of helium gas. The circuit of helium going to the probe (in blue in figure 4.4) is independent of the other circuits. Any excess of helium gas or evaporation can be recuperated into airtight bags connected to the probe and eventually re-liquefied into the sample space.
<figure><img src="image_26.png" /><figcaption>**Figure 4.4:** Scheme of the different and independent helium circuits of the polarizer. In green, the VTI cooling closed system. In blue, the sample space system refilled with helium gas that liquefies due to the thermal contact with the VTI.</figcaption></figure>

### 4.1.2.2 Probe, RF circuit and μ-wave irradiation

The design of the RF probe used in this set up is very similar to the one described for the 6.7 T Bruker polarizer, based on a Helmholtz design (see figure4.2) with two RF saddle coils tuned at ¹H and X resonance frequencies.

The μ-wave irradiation is achieved through a Virginia Diodes source, with an output power between 0 and 75 mW and a frequency between 262-264 GHz after several multiplication steps (×3, ×2, ×2, ×2), generated from an output frequency of ~ 11 GHz. The μ-wave is modulated using a saw-tooth modulation function, typically in a range of 100MHz. The μ-wave is guided to the sample thought a the μ-wave guide fixed to the probe structure.

This cryogen-free polarizer introduces a major improvement for DNP applications, as the liquid helium autonomy in the sample space increases the maximum duration of a DNP experiment, as helium is constantly re-liquefied. Even though the constant pumping of the different helium circuits represents a cost, the very low helium consumption is highly valuable in view of its scarcity. Although there are major improvements for this new generation of "Cryo-free" polarizers, some models need still to be optimized and automatized to improve the accessibility of the user to the complete system.
## 4.2 Dissolution DNP experiment

The DDNP experiment involves the transfer of a hyperpolarized sample in solid-state, inside the polarizer at cryogenic temperatures, to a solution-state NMR spectrometer operating at ambient temperature. The challenge of keeping the maximum possible polarization throughout requires optimizations and improvements at each stage of the experiment, including sample preparation.

### 4.2.1 Sample preparation

The composition (pH, nature of the substrate, nature of the radicals, ...) of the DNP samples is of major importance for the DDNP experiment, as the level of hyperpolarization, and the relaxation of the hyperpolarization during the transfer depends on it.[206, 207, 208, 46, 209]

DNP samples used for dissolution experiments avoid the complete crystallization of the sample. To this end, the sample is designed to solidify as solid glass. The complete crystallization of the sample has an impact on multiple aspects of DNP. First of all, the separation of the sample in different phases disrupts the homogeneity of the sample and destroys the contact between the radicals and different nuclear species [206, 207] which get separated. Furthermore, the different mechanisms of DNP depend on the environment of the electrons (as explained in the previous chapter) and the rotational freedom of the radicals, a complete crystallization of the sample would extremely influence the latter. In order to prevent complete crystallization, glass forming solvents (or colloquially, glassing agents) are added to the sample. Glycerol, DMSO, ethylene glycol and ethanol are some of the most common for DDNP applications. We prioritize water-soluble solvents and we aim for the most homogeneous samples[210, 206].

Clearly, the optimization of the DNP sample depends on the particular application, on the substrate and the radical used. Nevertheless, the experimental setup (magnetic field, sample transfer) present features that also have to be considered while preparing the sample [207, 201, 206, 211]. The magnetic field, for instance, has an impact on the mechanisms of
<figure><img src="image_27.png" /><figcaption>**Figure 4.5:** Laboratory picture at Paris en Resonance, LBM, framed in red are the different parts of the dissolution system. 1) Bruker 6.7 T polarizer. 2) Dissolution box for Bruker polarizer. 3) Cryo-free 9.4 T polarizer. 4) 0.9 T magnetic tunnel. 5) 400 MHz Bruker NMR spectrometer.</figcaption></figure>

polarization transfer in DNP. The radical nature and concentration are parameters that have
therefore to be optimized in function of $B_0$ [203, 195, 211].

**4.2.2 Dissolution experiment**

DDNP experiments rely on a sequence of steps, each of which is related to a piece of hard-
ware as seen in figure 4.5 and must be optimized to yield satisfactory experiments. There
is also a scheme presented in figure 4.6 with the different steps of a conventional DDNP
experiment. Both figures represent the DDNP setup presently operating at the ENS, *Paris
en Resonance* team. The different steps of the DDNP experiment (fig. 4.6) are:

* **1) Hyperpolarization of the sample:** The DNP sample is inserted in the polarizer. The polarizer is then filled with liquid helium and cooled down to 1.2 K, the μ-wave is set on. Depending on the hyperpolarized nuclei, the DNP sample, and the hyperpolarization strategy, the duration required to reach maximum nuclear polarization can
vary from some tens of minutes to several hours.

2) **Dissolution:** After reaching the maximum of polarization the frozen sample is dissolved and transferred. To this end, a solvent inside the dissolution box (number 2 in figures 4.6 and 4.5) is warmed up and pressurized minutes before the dissolution. Additionally, an overpressure is set inside the cryostat with a flow of helium gas. The overpressure prevents any air leakage that would immediately freeze inside the cryostat. When the cryostat is over atmospheric pressure and the solvent is warm and pressurized (~ 140 °C and 10.5 bar), the cryostat is opened, the dissolution-cane is inserted in the central cavity of a cane leading to the sample holder, connecting the warm solvent with the frozen DNP sample. Subsequently, the warm and pressurized solvent is pushed towards the sample-holder containing the frozen DNP sample which is instantly dissolved. A constant flow of helium gas pushes the dissolved and diluted DNP sample through a magnetic tunnel, inside the NMR spectrometer, and finally injects it inside the NMR tube. The total transfer takes around 3 s.

3) **Sample mixing and NMR detection:** Although the total transfer takes 3 s, the sample reaches the NMR tube 1 second after dissolution step starts. In many applications, the NMR tube is prepared with a solution containing reactants awaiting the dissolved DNP sample. The incoming DNP sample, diluted in the dissolution solvent, mixes with the solution inside the NMR tube. The NMR detection is automatically triggered by the dissolution system upon dissolution, which allows for the observation of hyperpolarized spectra.

The previous description of the dissolution DNP methodology shows the complexity of the experiment. After the dissolution of the sample, it is normally advantageous to maintain a magnetic field during the transfer to minimize relaxation and therefore reduce polarization losses. Avoiding regions of zero magnetic field, where the Zeeman interaction vanishes and the energy levels become degenerate is critical. Zero field regions are very often induced by the shielding of NMR magnets.[208, 212]. For these reasons, a magnetic tunnel was added
<figure><img src="image_28.png" /><figcaption>**Figure 4.6:** Scheme of the DDNP system at *Paris En Resonance* laboratory. The red dotted line indicates the path followed by the heated and pressurized solvent during the dissolution. The solvent is pressurized and pushed through the circuit with a continuous flow of He gas. When the solvent is ejected from the box to the circuit, a trigger starts the NMR detection after a 0.5 s delay. The different steps of the experiment are detailed in the text.</figcaption></figure>

to the dissolution system in our setup[212]. This magnetic tunnel covers a distance of ≈ 4 m, with a magnetic field of 0.9 T (number 4 in picture of figure ?? ).

Although the major problems of this technique are related to the conception of the NMR experiment and the DNP sample, some of the issues one often encounters during the dissolution experiment are:

* Complete consumption of the liquid helium before maximum polarization is achieved, the experiment has to be started again.

* Air leakages or misregulation of the helium gas pressure can cause complete freezing of the system during the dissolution. The DNP sample is usually lost.

* Slow pressurization of the dissolution box (with the dissolution solvent) can cause overheating and burning of the resistance responsible for warming up the solvent.
* Misconfiguration of the 'triggers' causing the NMR sequence not to launch. The hyperpolarized signal is then lost.

Additionally, the amount of sample that is actually transferred to the NMR tube, as well as its polarization, vary depending on the configuration of the DDNP experiment. The composition and volume of the DDNP sample, the temperature and volume of the dissolution solvent, the pressure of the He gas bottle, the duration of the continuous flow of helium during the transfer are, among others, parameters that define the transferred volume of the DNP sample. Although the transferred volume can be calibrated, small variations on the setup can change its value. However, the lost volume can be estimated to vary between zero losses and a third of the DNP sample.

Many efforts are being done towards automatizing the system to ensure better stability and reproducibility of DDNP technique [54, 213, 214, 215, 185, 184].

### 4.2.3 NMR sequences

#### 4.2.3.1 Liquid-state NMR sequences

As has already been mentioned, excitation pulses in NMR kill a part of the hyperpolarization. The amount of magnetization destroyed by each excitation pulse is proportional to $1 - \cos \theta$, where $\theta$ is the flip angle. In the absence of relaxation, the signal after $n$ experiments is written as:

$$S_{Hyp}(t) = S_{Hyp}^{0} \times \cos^{n}(\theta)$$

Where $S_{NMR}^{0}$ is the initial hyperpolaryzed signal. Thus, in DDNP, time sampling of metabolic reactions is achieved using the smallest possible flip angles. Hence, a $\theta = 30^{\circ}$ pulse would destroy ~13% of hyperpolarization in one scan. Therefore, in DDNP, the most common sequences are simple 1D detections that use low angle squared pulses in the relevant spectral window. Each single scan is taken with a time interval (that determines the time resolution), the final sequence of 1D scans composes a 2D experiment in which the second dimension
<figure><img src="image_29.png" /><figcaption>**Figure 4.7:** Figure taken from [218]. Cross polarization pulse sequence performed on ¹H and ¹³C during µ-wave irradiation. After CP, ¹³C signal is acquired. For more information go to [218].</figcaption></figure>

is time. These experiments are said to be pseudo-2 dimensional. DDNP-NMR can be used to observe different nuclei, the most common are ¹³C, ¹H, ¹⁵N and ³¹P. Normally ¹³C is prioritized due to its characteristically long T₁ and its fundamental role in organic molecules. ¹H has shorter T₁ relaxation times that, depending on the dissolution setup, can cause the complete relaxation of the hyperpolarization during the transfer.[46, 44, 45]

However, the versatility of NMR can be used to make slightly more complex experiments in which protons are hyperpolarized and subsequently detected in NMR. A strategy has been to use hyperpolarized water to transfer hyperpolarized protons to particular molecules through chemical exchanges. This technique has been used to study protein structures and protein-ligand interactions, between others [41, 40, 216]. DDNP with hyperpolarized water has also been used to transfer hyperpolarization to alternative nuclei through conventional cross-relaxation [209, 217]. Other NMR strategies have been developed to optimize DDNP and widen the range of applications. The use of gradients has also contributed on the field of DDNP. In recent years a new technique called *Ultra Fast* based on spatial data encoding, allows one to perform multidimensional detections on a single scan. The technique was first proposed in Frydman *et al*. in 2002 [219], today is a technique commonly used in multiple domains. Since 2-dimensional experiments can be recorded on a single scan, the hyperpolarization of the nuclear species can be used. In multiple teams, DNP and ultra-fast techniques have been combined to profit the signal enhancement and the fast acquisition in multidimensional NMR [220, 221].
<figure><img src="image_30.png" /><figcaption>**Figure 4.8:** CP pulse sequence used in all experiments presented in this manuscript. The pulse starts with a series of 90° pulses to destroy any previous polarization called pre-saturation (not needed for CP). 1) Adiabatic pulse of $t_A$ duration set to align spins in the x-axis, both nuclear magnetization is transferred from z-component to the x-component. 2) Spin lock to transfer polarization. The optimal $t_{SL}$ duration depends on the strength of ¹H, ¹³C dipolar coupling. For ¹³C, the pulse is ramped-up and down to efficiently find Hartmann-Hahn match, it has been empirically tested in the lab. 3) Magnetization is brought back to the z-axis with an adiabatic pulse that lasts for $t_A$. 4) 10° squared excitation pulse and acquisition on ¹³C channel to monitor the evolution. After acquisition, a duration $t_1$ of 30-90 s for the spins to relax. The 4th step is repeated 8 times (4-12 min), in the 9th scan the CP is repeated and the sequence starts again.</figcaption></figure>

### 4.2.3.2 Cross-polarization sequences

Two principal strategies are used in DNP to hyperpolarize a sample, "direct hyperpolarization" and "cross polarization" (CP).

CP is used to transfer polarization between different nuclear species. With this technique, the polarization build-up of lower gamma nuclei can be accelerated, and higher polarizations can be achieved. ¹H direct hyperpolarization is usually significantly faster and higher than that of other nuclei (see for instance section A.3), and is therefore commonly used in CP as polarization donor.

The use of CP technique in DNP was introduced in Jannin et al. 2011 [218]. In this publication a pulse sequence is used to transfer polarization from ¹H to ¹³C nuclei. CP transfers magnetization through dipolar coupling from the high-$\gamma$ nuclei ($^1$H) to the low-$\gamma$ nuclei ($^{13}$C) during a "spin-lock" period in which the Hartmann-Hahn condition is met [222]. The CP pulse sequence used in our experiment is based on the reference [218] which is displayed in figure 4.7.

The CP pulse program used consists of 4 steps, 3 of which are simultaneous for both
<figure><img src="image_31.png" /><figcaption>**Figure 4.9: 4.9a** Typical CP profile. The time interval between every scan is 90 s, each CP step is done every 8 scans, i.e. 14 min. This duration is chosen in function of the time needed for protons to polarize, characteristic of the sample.</figcaption></figure>

channels ¹H and ¹³C (depending on the probe, the second channel could be set to ³¹P or ¹⁵N frequencies). In the first step a 90° adiabatic pulse is set for both channels. It is followed by a "spin-lock" pulse that creates a thermal contact (Hartmann-Hahn) between the two nuclei and during which magnetization is transferred. During the spin lock, for one nucleus, the amplitude of the field is swept in order to optimize the Hartmann-Hahn match. The optimal duration for the spin-lock pulse depends on the strength of the dipolar coupling. During the contact period, the µ-wave irradiation is stopped by means of µ-wave gating. In the third step spin magnetization is brought back to the z-axis by a second adiabatic pulse. On the fourth step, a low angle excitation pulse (usually 10° in our experiments) is set on the ¹³C channel to monitor the evolution of the signal. The CP block (first 3 steps) is repeated every 8 scans, between each scan there is a time gap that can vary between 30 and 90 seconds. During this period ¹H polarization build's up until transfer during CP. In figure 4.9a, the signal evolution of a sample under CP is depicted. Each signal 'jump' corresponds to Hartmann-Hahn transfer between ¹H and ¹³C. For each experiment, pulse powers and durations are optimized empirically. The CP is repeatedly tested on the sample, each parameter's value is progressively varied.
<figure><img src="image_32.png" /></figure>
# Part III

## In-vitro studies of enzymatic reactions
by DDNP
# Chapter 5

## Enzymatic cascade with glucose as
substrate

### 5.1 Context of the experiment

The study of metabolic fluxes requires the characterization of enzymatic reactions taking place in a living organism, which requires the knowledge of the role and the functional characteristics of each enzyme, as well as their regulation, an essential aspect to understand the organism's phenotype. Over the past few years, dissolution DNP has been used to monitor the kinetics of fast enzymatic reactions *in vitro* by recording simultaneously the time resolved NMR signal of an hyperpolarized substrate and its reaction products[48, 49, 223, 52]. A brief summary of such investigations is given below, as an overview of the state of the art of DDNP applications to enzyme kinetics. In *A.W. Barb et al.* the transformation of pyruvate into alanine by the catalysis of alanine transaminase was studied *in vitro* by means of DDNP [179]. In this study, both ¹³C NMR and ¹H NMR were used to monitor the signal evolution of labeled pyruvate, the catalytic effect of alanine transaminase was detected and the protonation induced by the enzyme was characterized. However, quantitative kinetic analysis was not performed.

As a proof of concept, the hydrolysis of Na-benzoyl-l-arginine catalyzed by tripsin was studied in reference [49]. In this study the system of reactions was monitored by NMR
for a total of 3 s, during which the reaction rates were characterized. Relaxation of the
hyperpolarized sample was considered and measured independently. For these experiments,
the substrate concentration was chosen so that the reaction kinetics evolved linearly with
time (0 order). Although the kinetic rate of the reaction could be extracted, the method was
tested in a very simplified reaction system consisting of a linear evolution in time of a single
reaction.

DDNP and ¹³C NMR have been compared with ¹⁹F NMR as method to monitor the evolution of enzymatic reactions. In *Eykin and coworkers*, the catalytic activity of carboxypeptidase G2 is studied [48]. The single-step reaction is monitored by ¹³C NMR for the complete duration of hyperpolarization, with 3,5-difluorobenzoyl-L-glutamic acid in natural abundance as substrate. Subsequently, the same reaction is studied by means of ¹⁹F NMR. However, activities are only extracted with the second method, without DNP. A discussion of the pertinence of both techniques is given.

A more complex system involving two successive reactions has been studied by DDNP.
The successive transformation of choline into betaine aldehyde, and betaine aldehyde into
betain, was monitored in [224]. This reaction is catalyzed by choline oxidase enzyme and
was modelized by two subsequent pseudo first order reactions. Kinetic rates characterizing
the reactions were extracted and their values were evaluated by comparison with bibliogra-
phy. The obtained values were in the same order of magnitude than the documented ones.
Some possible inconsistencies of the resulting values were discussed. However, no further
statistical assessment of the validity of the parameters was done.

In this work, real-time DDNP studies on the enzyme kinetics of the oxPPP (subsec-
tion 1.1.1.2) were undertaken. This studies are performed on *in vitro* samples, i.e. enzyme
solutions containing a single or a combination of successive enzymes of this metabolic path-
way. Some aspects of this particular metabolic pathway have been previously studied by
means of DDNP technique[225, 226, 50].

Phosphorylation of glucose into G6P catalyzed by hexokinase enzyme was monitored
in *Miclet et al.*[50]. The evolution of [U-¹³C; U-²H]glucose signal and its [U-¹³C; U-²H]G6P
were recorded for the complete duration of the hyperpolarized signal (~ 20 s). The resulting data was fitted with a simple model to extract the kinetic rates of the enzymatic reaction. The reaction was independently analyzed for both α and β anomers which catalytic rates were successfully determined. The results suggested that hexokinase activity has no anomeric specificity.

A continuation of this work was presented in *Sadet et al.*, where two consecutive reactions catalyzed by hexokinase enzyme and G6PDH enzyme were studied. The experiments were performed with [U-¹³C; U-²H] glucose to produce [U-¹³C; U-²H]G6P and subsequently [U-¹³C; U-²H] δ-PGL. The reactions were reproduced *in vitro* with high enzyme activities in order to force a fast production of δ-PGL. Although the reaction was monitored from the injection of the dissolved hyperpolarized sample of glucose, only the data obtained after complete consumption of the G6P was analyzed (~ 10 s after injection). A kinetic analysis was performed on the spontaneous degradation of δ-PGL and kinetic rates were extracted. Hence, only one-step non-enzymatic reactions were studied.

Kinetic studies of the first steps of the oxPPP remains a challenge. To start with, glucose and G6P resonances have to be identified and integrated, which becomes difficult due to the overlap of their C₁ peaks. Also, multiple spontaneous reactions must be considered in the kinetic study, which adds complexity to the reaction scheme, and makes its numerical analysis more demanding. Here, we undertake a complex study of a cascade of enzymatic reactions while considering multiple additional spontaneous reactions. A first approach we used to the study of this system relied on the direct observation and analysis of the cascade of enzymatic reactions. A second approach will be presented in the next chapter where G6P is hyperpolarized and used as substrate. We therefore bypass the glucose phosphorylation stage and so avoid resonance overlap, as well as simplify the kinetic model.

## 5.2 The reaction scheme

The phosphorylation of glucose and the first reaction of the PPP are enzyme catalyzed reactions in which additional spontaneous reactions are involved. In the first reaction of the
<figure><img src="image_33.png" /><figcaption>**Figure 5.1:** Cascade of enzymatic reactions. The cofactors involved in the two enzymatic reactions are also represented. In dotted lines are represented the reactions that will not be considered in our model. The anomerization rates of G6P are represented in green. Hexokinase enzyme activity rate is represented in blue and G6PDH activity rate in red. $\rho_{PGL}$ in violet represents the rate of $\delta$-PGL degradation due to both hydrolysis and isomerization.</figcaption></figure>

enzymatic cascade, glucose is phosphorylated into G6P by the catalysis of hexokinase enzyme. The second reaction is catalyzed by G6PDH enzyme and transforms a molecule of G6P into a molecule of $\delta$-PGL. More information about this pathway is given in subsection 1.1.1.2.

Glucose and G6P populations have two anomers $\alpha$ and $\beta$, and G6PDH has an anomer specific activity towards $\beta$-G6P [74, 33]. This specificity is taken into account in our analysis. The transformation of $\alpha$-G6P into $\delta$-PGL is therefore disregarded. Several non enzymatically catalyzed reactions have also been included in this scheme. The kinetic rate of the spontaneous $\alpha/\beta$ anomerization determines the evolution of both anomers' concentrations towards a thermodynamic equilibrium. For glucose, this rate has been shown to be on the order of several minutes [74, 227]. Since our DDNP experiments allow us to observe the hyperpolarized analytes for only some tenths of seconds, glucose anomerization may not be considered. Alternatively, the anomerization rate of G6P is much faster ($\le$min) and was therefore taken into account in our model [227]. Besides, $\delta$-PGL is known to isomerize into $\gamma$-PGL and hydrolyzed into 6PGA. [226, 33, 75]. Both isomerization and hydrolysis reactions occur spontaneously on the time scale of the studied enzymatic reactions and were therefore considered. The complete reaction scheme is presented in figure 5.1. In these experiments the dependence of the enzymatic reactions on the cofactor concentrations was avoided by using them in large excess with respect to the substrate. Also, the spontaneous
degradation of $\delta$-PGL and its hydrolysis into 6PGA were accounted empirically by a simple exponential "leakage" term 5.1. Under these conditions, the hexokinase enzymatic reaction rate depends solely on the available concentration of glucose, and is therefore considered as a pseudo-first order reaction. Similarly, the G6PDH catalyzed reaction $\beta$-G6P $\rightarrow$ $\delta$-PGL, is assumed to depend only on the concentration of $\beta$G6P. The set of coupled pseudo-first order reactions, the anomerization of G6P, and the degradation of $\delta$ – PGL determine the concentration evolution of the different metabolites in the reaction cascade.

## 5.3 Materials and methods

### 5.3.1 Sample preparation and DNP experiment

All experiments were performed with the same DNP sample composition. Glucose samples were prepared with a solution of D2O:Eth-Gly at 50:50% volume composition, in which the polarizing agent TEMPOL (4-Hydroxy-TEMPO) was dissolved to reach a final concentration of 40 mM. [U-¹³C; U-²H]glucose was added to the sample to attain a concentration of 400 mM. For each experiment a sample of 75µL was transferred to a PEEK sample holder and was inserted inside the cryostat, in contact with a bath of liquid helium where it solidifies as a solid glass (DNP system described in subsection 4.1.1). Each DNP sample contains 30 µmol of [U-¹³C; U-²H]glucose. A CP sequence was used to hyperpolarize the sample. A maximum of polarization was achieved after ~60 min, with the sample at 1.2 K and under µ-wave irradiation at 187.9 GHz frequency and 350 mW power.

Dissolution was achieved by flushing 5 mL of D₂O previously heated to 403 K at 10.5 bar onto the frozen hyperpolarized sample. The hyperpolarized solutions were transferred from the polarizer to the 400 MHz spectrometer (distant by ~ 5-6 m from each other) upon Helium gas flow. Mixing of the hyperpolarized sample with the solution of enzymes takes place in a 10 mm NMR tube sitting inside the NMR spectrometer, typically began less then one second after dissolution and was complete after 3 seconds.
### 5.3.2 Reaction medium and NMR

A common buffer solution containing the cofactors (ATP and NADP⁺) was prepared for both experiments. The cofactor solution containing both enzyme cofactors consisted on 2 mL of HEPES buffer 200 mM at pH = 7.2, to which 180µmol of ATP and 180µmol of NADP⁺ (90µmol per experiment) and 46 µL of a stock solution at 1 M of MgCl₂ (23 µmol per manip) were added. 400 µL of a solution of NaOH 1 M were added to the mixture to reach a pH of 7.4; 54 µL of HEPES completed a total volume of 2.5 mL which was split into two samples of 1.25 mL per experiment.

The concentration of the cofactors was three times larger than the maximum expected substrate concentration in the NMR tube to match pseudo-first order conditions of the experiments. Enzymes were added in a subsequent step. Commercially available (*Merck*) yeast (*saccharomyces cerevisiae*) hexokinase and G6PDH enzymes were used. Experiments were performed with two different hexokinase activities. In one experiment, 1.26 mg of Hexokinase with a specific activity of 83 u.mg⁻¹, and 0.35 mg of G6PDH with an specific activity of 165 u.mg⁻¹ were used. The experiment contained a total of 104 ± 8.3 u of hexokinase and 57.8 ± 16.5 u of G6PDH. For a second experiment, 50.6 ± 8.3 u of hexokinase and 57.6 ± 16.5 u of G6PDH were weighted and added to the second sample. Thus, hexokinase activity was approximately half for the second experiment. In both experiments the sample containing both cofactors and enzymes was transferred to a 10mm NMR tube and inserted inside the NMR spectrometer some minutes before the dissolution experiment. NMR spectra was recorded at T = 310 K on a 9.4 T Avance III Bruker spectrometer with a 10 mm BBO probe. Each DDNP experiment consisted in a series of 1D ¹³C spectra with 10° read pulses. ²H and ¹H decoupling was performed in all experiments using a WALTZ16 pulse sequence.[159]
<figure><img src="image_34.png" /><figcaption>**Figure 5.2:** ¹³C NMR, superposition of the first 10 scans, for both experiments. a) Experiment 1, u hexokinase and u G6PDH. b) Experiment 2, u hexokinase and u G6PDH. For both experiments the different resonances are: 1 γ-PGL C₁; 2 δ-PGL C₁; 3,4 β-gluc. and β-G6P C₁; 5,6 α-gluc. and α-G6P C₁; and 7* and overlay of all other carbon resonance from Gluc., G6P, and PGL species, both carbons of ethylene-glycol also appear in 7*.</figcaption></figure>

**5.4 Results and Analysis**

¹³C 1D spectra extracted from the pseudo-2D experiments 5 s after injection (5th scan) are displayed in figure 5.2. The carbonyl region exhibit the ¹³C ₁ resonance signal of δ-PGL, which therefore attests for the presence of the reaction cascade. For experiment 1, glucose signals have a faster decay, which is consistent with the experimental conditions, since the activity of hexokinase is twice the one used for experiment 2. Also, for experiment 1, a faster production of δ-PGL, as well as γ-PGL, is observed, as attested by the stronger signals. Although the G6PDH activities in both experiments were approximately identical, the kinetics of the reaction cascade seems to be faster than for experiment 1, which points
<figure><img src="image_35.png" /><figcaption>**Figure 5.3:** Figures taken from experiment 1.5.3a Stackplot of the first 40 scans in which we see the signal evolution of both anomers of G6P and glucose C₁ in the right side. In the left we see the signal evolution of δ-PGL's C₁ and, a weak signal of its isomer γ-PGL.5.3b Deconvolution of α-glucose and α-G6P C₁. The deconvolution was achieved by fitting a summation of 4 lorentzian functions, centered in each peak's position, to the NMR data. The experimental data is represented in black, each lorentzian is represented in red, and the convolution of the four lorentzians is represented in blue.</figcaption></figure>

to the fact that the different reactions are coupled. Both anomers of glucose and G6P C₁ resonances are doublets (due to $J_{CC}^1$ coupling) and overlap, so that, in order to determine glucose and G6P C₁ signal intensities, both signals must be deconvoluted. However, it is interesting to note that ratios of the relative intensities of both anomer signals are inverse in both experiments, which is likely a consequence of the anomeric specificity of G6PDH towards β G6P.

The time evolution of the different metabolite signals is illustrated in a stacked plot of DDNP 1D spectra, in figure 5.3a. The signals of glucose and G6P C₁ were deconvoluted with Lorentzian functions centered on the chemical shift of the peak maxima, with a tolerance of 3 points (~3Hz, each spectrum contained a total of 16384 points corresponding to 150 ppm) for both resonances. An example is displayed in figure 5.3b. The time evolution of the signal intensity was then reconstructed for each metabolite. Through the reaction pathway described above, the magnetization of the various metabolites obeys the following set of
equations:

$$ \frac{d}{dt} \begin{pmatrix} M_{G\alpha} \\ M_{G\beta} \\ M_{G6P\alpha} \\ M_{G6P\beta} \\ M_L \end{pmatrix} = \begin{pmatrix} -k_{H\alpha} - r_{G\alpha} & 0 & 0 & 0 & 0 \\ 0 & -k_{H\beta} - r_{G\beta} & 0 & 0 & 0 \\ k_{H\alpha} & 0 & -k_{\alpha\to\beta} - r_{G6P\alpha} & k_{\beta\to\alpha} & 0 \\ 0 & k_{H\beta} & k_{\alpha\to\beta} & -k_{dh\beta} - r_{G6P\beta} - k_{\beta\to\alpha} & 0 \\ 0 & 0 & 0 & k_{dh\beta} & -d_L \end{pmatrix} \begin{pmatrix} M_{G\alpha} \\ M_{G\beta} \\ M_{G6P\alpha} \\ M_{G6P\beta} \\ M_L \end{pmatrix} \quad (5.1) $$

(the colors used match those in figure 5.1). The parameters $r_x = 1/T_{1,x}$ are the spin-lattice relaxation rates (in $s^{-1}$) of the x metabolite. Parameter $d_l$ corresponds to the lumped decay rate of the $\delta$-PGL signal, which includes both its relaxation and chemical transformations $d_L = r_L + \rho_{PGL}$.

### 5.4.1 Individual analysis of the experiments

We used the model of equation 5.1 to fit both experiments independently. In our model 5 kinetic rates, 5 relaxation parameters and 5 initial signal values, i.e., a total of 15 parameters are fitted. The algorithm chosen for the fit is called Differential Evolution (DE) [228]. DE is an evolutionary kind of algorithm, and thus use a metaheuristic approach in which no assumptions about the system have to be made, i.e. no initial values have to be given. This minimization algorithm thus avoids the target function to be trapped in a local minimum due to its dependence on initial conditions. Note, however, that there is no proof of convergence, unlike strategies based on gradient minimization [228]. Results of the fitting are displayed in figure 5.4 for both experiments, which show that data are well reproduced by the model. The fitted lines (continuous lines) reproduce well the evolution of the experimental NMR signal (dotted lines) for the different metabolites. However, the output parameters display multiple inconsistencies. To start with, some parameters values converge to zero. Some of the model parameters seem to be underdetermined, and so their values cannot be determined independently. This suggests that the system of differential equations is not constrained enough by the data, which therefore suggests that we need to introduce addi-
<figure><img src="image_36.png" /><figcaption>**Figure 5.4:** Independent fit of the data resulting from experiment 1 (in **a**) and experiment 2 (in **b**). The data was fitted individually for each experiment with the model presented in equation 5.1.</figcaption></figure>

tional constraints for the analysis.

A Monte Carlo (MC) simulation to mimic experimental noise (due to NMR detection) was used to evidence potential correlations between parameters. According to standard practice, experimental noise was estimated for each experiment by computing the standard deviation of the signal in a region without resonances. It was then randomly added to each points of each 1D spectrum and the analysis was performed on these new pseudo-experimental data. It is important to precise that with the MC simulation only the error related to the detection noise can be determined, other sources of experimental are thus not estimated.

The MC showed that not all parameters converged to the same values for each realization of the noise. Moreover, significant correlations between some parameters obtained, as illustrated in figure 5.5 for experiment 1. In contrast, the kinetic eigenmodes of the reaction pathway (5.1) were well constrained and consistently extracted from the data. These are:
<figure><img src="image_37.png" /><figcaption>**Figure 5.5:** Example of scatter plots evidencing correlations found for some parameters obtained from experiment 1. Results obtained after 150 MC iterations. See text for more details about the MC. The same correlations are observed for experiment 2.</figcaption></figure>

$$
\left\{
\begin{aligned}
x_1 &= -k_{H\alpha} - r_{G\alpha} \\
x_2 &= -k_{H\beta} - r_{G\beta} \\
x_3 &= -\frac{1}{2}(k_{\alpha\to\beta} + k_{dh\beta} + k_{\beta\to\alpha} + r_{G6P\alpha} + r_{G6P\beta} + \\
&\quad (k_{\alpha\to\beta}^2 + 2k_{\alpha\to\beta}(-k_{dh\beta} + k_{\beta\to\alpha} + r_{G6P\alpha} - r_{G6P\beta}) \\
&\quad + k_{dh\beta}^2 + 2k_{dh\beta}(k_{\beta\to\alpha} - r_{G6P\alpha} + r_{G6P\beta}) \\
&\quad + k_{\beta\to\alpha}^2 + 2k_{\beta\to\alpha}(r_{G6P\alpha} + r_{G6P\beta}) + r_{G6P\alpha}^2 - 2r_{G6P\alpha}r_{G6P\beta} + r_{G6P\beta}^2)^{\frac{1}{2}}) \quad (5.2) \\
x_4 &= -\frac{1}{2}(k_{\alpha\to\beta} + k_{dh\beta} + k_{\beta\to\alpha} + r_{G6P\alpha} + r_{G6P\beta} - \\
&\quad (k_{\alpha\to\beta}^2 + 2k_{\alpha\to\beta}(-k_{dh\beta} + k_{\beta\to\alpha} + r_{G6P\alpha} - r_{G6P\beta}) \\
&\quad + k_{dh\beta}^2 + 2k_{G6P\beta\to6PGL}(k_{\beta\to\alpha} - r_{G6P\alpha} + r_{G6P\beta}) \\
&\quad + k_{\beta\to\alpha}^2 + 2k_{\beta\to\alpha}(r_{G6P\alpha} + r_{G6P\beta}) + r_{G6P\alpha}^2 - 2r_{G6P\alpha}r_{G6P\beta} + r_{G6P\beta}^2)^{\frac{1}{2}}) \\
x_5 &= -d_L
\end{aligned}
\right.
$$

, which shows the various parameters dependencies. These complex relationships between
eigenvalues and kinetic parameters suggest that additional constraints may be needed to
exactly extract all of the model parameters. In particular, independent measurements of
spin lattice relaxation times of glucose relaxation may be used to extract hexokinase kinetic
parameters from eigenvalues x₁ and x₂. However, for the third and fourth eigenvalues there
is no external measurement we can perform to extract the kinetic parameters involved.
### 5.4.2 Simultaneous fit

To try and overcome the underdetermination of the model, both experiments were fitted simultaneously. In this case, relaxation and anomerization parameters are common to both experiments. This is not a strong assumption, as both experiments were performed in the same conditions (temperature and pH of the sample, magnetic field, etc...). Since the two experiments exhibit different kinetics, we could expect the fitting problem to be less degenerated. Moreover, one can expect that, with this strategy, no independent measurements of anomeric rates, or G6P relaxation rates (that could not be measured) should be required, since the data sets are mutually constraining.

For the simultaneous fits we imposed that the parameters, $r_{G\alpha}$, $r_{G\beta}$, $r_{G6P\alpha}$, $r_{G6P\beta}$ and $d_L$; and $k_{\beta\to\alpha}$, $k_{\alpha\to\beta}$ are identical in both experiments. Alternatively, the G6PDH and hexokinase activities were kept as independent parameters in both experiments.

Results of this simultaneous fit are displayed in figure 5.6. It is seen that the data are well reproduced. Here, although individual parameters seem to be better determined, some inconsistencies remained. The MC consisted on 500 iterations with addition of noise, and unconverged trials (82), as attested by significantly larger values of the target function, were discarded. Following this procedure, most of the eigenvalues were well defined, although $x_3$ exhibited a bimodal distribution 5.7. The histograms of the eigenvalues obtained from the Monte Carlo simulation (representing a total of 320 MC iterations) are shown in figure 5.7. For $x_3$, one of the two modes has no physical meaning, the resulting parameter values are many orders of magnitude bigger than what is documented in bibliography or what was prepared during the experiment. The iterations converging to this mode could thus be discarded. The obtained set of parameters are displayed in table 5.1. We can see that, for 7 of the 10 parameters, the distributions have standard deviations of 3% to 10% of the average value of the parameter, and could thus be considered well-defined. Three other parameters, $r_{G6P\beta}$, $k_{\alpha\to\beta}$ and $k_{\beta\to\alpha}$, were less well-defined. Their standard deviation is of ~50% or larger than the average value of the parameter, and exhibited mutual correlations as shown in figure 5.8. It turns out that, for $k_{\beta\alpha}$ and $r_{G6P\beta}$, in 222 and 226 iterations of the MC the
<figure><img src="image_38.png" /><figcaption>**Figure 5.6:** Simultaneous fit of the data resulting from experiment 1 (in **a**) and experiment 2 (in **b**). Only the parameters related to enzyme activities in the model (eq. 5.1) were considered different for each experiment, i.e. all other parameters were considered equivalent for both experiments during the simultaneous fit.</figcaption></figure>

resulting values are lower than 0.001, respectively. For this reason, their histograms seem to be empty. Strategies to further constrain the model in order to extract these parameters will be discussed later. Although the complete set of parameters could not be determined, some parameters could be estimated with an error lower to 10%. The parameters defining glucose relaxation for both anomers are almost equivalent, which is realistic. These values are also similar to documented values of glucose in similar experimental conditions[226] [51]. Regarding the activity of hexokinase, the kinetics of the enzyme are found slightly faster

<figure><img src="image_39.png" /><figcaption>**Figure 5.7:** Histograms of the eigenvalues obtained for experiment 1 (in blue) and experiment 2 (in red). The distributions resulted from an MC simulation consisting of 500 iterations. $X_5$ is defined as equivalent for both experiments and therefore has no color code.</figcaption></figure>
<figure><img src="image_40.png" /><figcaption>**Figure 5.8:** In the first column are displayed the histograms obtained with the MC simulations of the 3 undefined parameters. For both $k_{\beta\alpha}$ and $r_{G6P\beta}$ more than 70% of the values are < 0.0001, their values can be thus neglected. Parameter correlations are displayed on the other 2 columns.</figcaption></figure>

towards the $\beta$ transformation in both experiments, i.e. $\frac{k_{H\beta}^{\text{exp1}}}{k_{H\alpha}^{\text{exp1}}} = 1.4$ and $\frac{k_{H\beta}^{\text{exp2}}}{k_{H\alpha}^{\text{exp2}}} = 1.27$, note that the ratio is very similar for both experiments. Finding such similar ratios is reasonable since we used the same enzyme in the same experimental conditions. Moreover, this value is similar to a value of $\frac{k_{H\beta}}{k_{H\alpha}} = 1.58$ measured in [50].

The kinetic rates for G6PDH catalysis seems to be approximately equal in both experiments, with a value $k_{dh\beta} \sim 0.4$, which is consistent with the fact that samples were prepared with the same G6PDH activities. In addition, the ratios of the hexokinase rate constants for the two anomers vary in a similar fashion between experiments, i.e., $\frac{k_{H\alpha}^{\text{exp1}}}{k_{H\alpha}^{\text{exp2}}} = 5.5$ and $\frac{k_{H\beta}^{\text{exp1}}}{k_{H\beta}^{\text{exp2}}} = 5.3$. This is realistic, as both rates $k_{H\beta}$ and $k_{H\alpha}$ reflect the same enzyme kinetics. However, the values of these experimental ratios was larger than the expected value of $\sim 2$, conditions in which the experiments were prepared.

The latter inconsistency can be related either to errors in the preparation of the samples
or to the presence of non-considered transformations. As a matter of fact, multiple regulation mechanisms have been identified for this chain of reactions. To start with, it has been shown that glucose can be a low-affinity substrate of G6PDH enzyme [74]. Additionally, the ratio between NADPH/NADP⁺ has a regulatory effect on G6PDH activity [61]. Finally, the accumulation of G6P has been documented to have an inhibitory effect on hexokinase activity [50]. In order to properly extract the enzyme activities, these additional reactions have to be considered in the model. However, the model as defined for this experiments does not allow to extract the complete set of kinetic parameters. Adding new parameters is hence not conceivable.

Improving and extending the strategy described in this chapter should involve the combination of additional experiments with different enzyme activities. This implies that all experiments must be done within a short time to avoid enzyme degradation and activity losses, which occurs once in solution. However, in practice, the time required to perform one such DDNP experiment - sample preparation and hyperpolarization (~1h) - amounts to about 2 h with the current instrumentation. Therefore, a set of 3 experiments with different enzyme activities, and a calibration experiment, would then need a total time of 8 h if no setback occurs.

The strategy presented in this section can nevertheless be advanced to a versatile and useful tool for more complex systems in which enzymatic cascades need to be characterized, provided that the different reactions involved in the system, and the relevant regulatory

<table><thead><tr><th></th><th>Parameter</th><th>k<sub>Hα</sub></th><th>k<sub>Hβ</sub></th><th>k<sub>dhβ</sub></th><th>k<sub>α→β</sub></th><th>k<sub>β→α</sub></th></tr></thead><tbody><tr><td rowspan="2">Exp. 1</td><td>Average</td><td>0.095</td><td>0.126</td><td>0.434</td><td>0.052</td><td>0.023</td></tr><tr><td>St. deviation</td><td>0.009</td><td>0.011</td><td>0.042</td><td>0.022</td><td>0.028</td></tr><tr><td rowspan="2">Exp. 2</td><td>Average</td><td>0.018</td><td>0.023</td><td>0.376</td><td>||</td><td>||</td></tr><tr><td>St. deviation</td><td>0.002</td><td>0.003</td><td>0.26</td><td></td><td></td></tr></tbody></table>

<table><caption>**Table 5.1:** Resulting parameters of the simultaneous fit. Average over 352 MC iterations after filtering.</caption><thead><tr><th>Parameter</th><th>r<sub>Gα</sub></th><th>r<sub>Gβ</sub></th><th>r<sub>G6Pα</sub></th><th>r<sub>G6Pβ</sub></th><th>d<sub>L</sub></th></tr></thead><tbody><tr><td>Average</td><td>0.091</td><td>0.092</td><td>0.171</td><td>0.035</td><td>0.104</td></tr><tr><td>St. deviation</td><td>0.0054</td><td>0.0063</td><td>0.062</td><td>0.08</td><td>0.003</td></tr></tbody></table>
mechanism are considered.
# Chapter 6

## Characterization of G6PDH with labeled G6P

It is clear that studying the kinetics of each enzyme individually is much simpler than the complete cascade of events. We therefore decided to focus on the kinetics of G6PDH only. We produced and purified G6P to this aim.

### 6.1 Production and purification of [U-¹³C; U-²H]G6P.

For this study, we optimized a technique previously used in the lab to produce and purify [U-¹³C; U-²H]G6P [229]. Labeled G6P was enzymatically produced from [U-¹³C; U-²H]glucose. To this aim, labelled glucose is simply added to a buffer solution containing Hexokinase, ATP (cofactor) and MgCl₂ [229]. Formerly, a *fast protein liquid chromatography* (FPLC) with an anion exchange column was used to separate the different sample components and to extract the substrate from the reaction medium. Although an effective way to purify labeled G6P, the above strategy is very time consuming. Indeed, due to the saturation of the column, only a limited amount of molecules can be retained, which limits the flow and volume to be processed. The various anionic components of the reaction medium can be adsorbed on the column (ATP, ADP, AMP, buffer, G6P) and therefore contribute to its saturation, where AMP is produced by the spontaneous dephosphorylation of ATP and ADP.
In the work presented in chapter 3 of [229], after optimization of the method a maximum of ~347 µmol of [U-¹³C; U-²H]G6P, could be purified during a total of 17 purifications by FPLC, implying that the complete process lasted for ~11 h 20 min to obtain 94.458 mg of [U¹³C-U²H]G6P.

Another purification strategy developed during this work is presented below. We used size-exclusion (or molecular-sieve) chromatography (SEC)[230]. Here, the separation is based on the differing ability of molecules, depending on their sizes, to go through the pores of the gel-filtration medium, present in a column. Thus molecules at the exit of the column are separated according to their size. Labeled G6P was obtained from the following reaction medium:

* 500 mg [U-¹³C; U-²H]glucose, 2,6 mmol.

* 45 mL of Phosphate Buffer, 100 mM, pH = 7,25.

* 1,71 g ATP, 3.37 mmol.

* 3,1 mL of a 1M MgCl₂ solution corresponding to a final concentration of 3,1 mmol.

* 1,8 mL of a 1M NaOH solution for a final pH of 7,1.

* 200 U of Hexokinase enzyme from *saccharomyces cerevisiae*, representing 5,37 mg.

The enzymatic reaction took place during 48 H at ambient temperature and was subsequently frozen at (-20 C°) once glucose phosphorylation was complete. The masses of these different molecules and of hexokinase (water excluded) add up to $m_{init} = 4,355$ g. After production, the pH was raised to 10.5 to precipitate the magnesium as magnesium hydroxide and magnesium phosphates. Subsequent centrifugation of the reaction medium was used to remove the Mg(OH)₂ and (MgHPO₄) precipitates. The resulting solution was then lyophilized and weighted. The obtained solid has a total mass of 3,9 g suggesting we filtered 455 mg of magnesium salts. The solid was dissolved again in 15 mL of H₂O close to solubility limit to be deposited on the SEC column. We used a column filled with a Sephadex® G25
gel filtration resin (Diameter: 35 mm; Length: 150cm). After being cleaned by a solution of 200 mM NaOH and extensively washed with water, the reaction medium was inserted into the column. Fractions were collected every 5 min (10-12 mL per fraction) with a flow of 2-2,4 mL.min⁻¹. A dehydration reaction was used to identify the fractions containing

<figure><img src="image_41.png" /><figcaption>**Figure 6.1:** Colorimetric test used to reveal the presence of carbohydrates. After spotting each fraction on a TLC silica gel plate, the plate is plunged in a H₂SO₄ solution and heated. The apparition of brown marks confirms the presence of sugars in the different fractions.</figcaption></figure>

sugars (ATP, ADP, AMP and G6P). In figure 6.1, we see that most of the sugars present in the reaction medium are found in fractions #16 to #20. In order to assess the efficiency of the purification method we measured the amount of G6P obtained in each fraction and its purity. The amounts of ATP, ADP and Phosphate buffer were also quantified in order to evaluate the purity of the [U-¹³C; U-²H]G6P obtained. As a first quantification, fractions #16 to #25 were lyophilized and weighted. The resulting masses are presented in table 6.1. Since the TLC plates showed absence or very weak presence of sugar in fractions ≥ #20, we pooled the five fractions #21 to #25 (named fraction #21*). The total mass collected within these fractions was 2.8 g, which corresponds to 70% of the total mass deposited on the SEC column. The remaining 30% (1, 1 g) mg accounts for non-sugar compounds. The HK protein that could be eluted in earlier fractions and in contrast, salts (phosphate, Na, Cl, Mg) could be present in fractions ≥ #25. Subsequently, the solids were dissolved in pure D₂O (in 500 µL for fractions #16 and #17, and in 1 mL for fractions #18-#21), and the amounts of [U¹³C-
<table><caption>**Table 6.1:** Mass of solid obtained after purification by gel filtration of the reaction medium and subsequent lyophilization.</caption><thead><tr><th>Fractions</th><th>16</th><th>17</th><th>18</th><th>19</th><th>20</th><th>21*</th><th>total</th></tr></thead><tbody><tr><td>mass (mg)</td><td>9</td><td>75</td><td>504</td><td>768</td><td>643</td><td>829</td><td>2828</td></tr></tbody></table>

<figure><img src="image_42.png" /><figcaption>**Figure 6.2:** ¹³C NMR spectrum for the peak attribution of fraction n° 17. The lyophilized fraction was dissolved in 500 µL of pure D₂O. **1** glycine C₁, **2** β-G6P C₁ furanose, **3α** G6P C₁ furanose, **4** β-G6P C₁ 5α-G6P C₁, **6*** C₂⁻₅ of both anomers of G6P, peak overlay, **7** G6P C₆, **8** Glycine C₂.</figcaption></figure>

U²H]G6P in these samples were measured by means of ¹³C NMR. The peak assignment is presented in figure 6.2. In the resulting ¹³C spectra we can also identify the furanose form of the G6P, which is a spontaneous transformation of the G6P molecule. The cyclic structure of the sugar consists of a cycle of 4 carbons in the furanose form compared to a 5 carbons cycle in the pyranose form, the most common form for G6P. In this manuscript, when we refer to G6P, we thus refer to G6P in the pyranose form.

We acquired a ¹³C spectra of each fraction in presence of [U¹³C]glycine sample contained in a capillary inside the NMR tube, to serve as a reference for quantitation. The relation between G6P concentration and glycine's ¹³C signal intensity was calibrated by comparison with a reference solution containing a known concentration of [U-¹³C; U-²H]glucose.
<figure><img src="image_43.png" /><figcaption>**Figure 6.3:** ¹³C spectra for quantification of the different fractions collected after purification. Reference used for quantification was [U-13C] glycine, peak in the carbonyl region</figcaption></figure>

The relation is given by:

$$ \frac{S'_{Gly}}{S_{Gref}} = \frac{[Gly]}{[G_{ref}]}, \quad \text{and} \quad \frac{S_{G6P}}{S_{Gly}} = \frac{[G6P]}{[Gly]} \qquad (6.1) $$

$$ [G6P] = \frac{S_{G6P}}{S_{Gly}} \times \frac{S'_{Gly}}{S_{Gref}} [G_{ref}] $$

Hence, the concentration obtained in each fraction [G6P] can be determined in function of the signal ratios in each NMR spectra $S_{G6P}/S_{Gly}$, the signal ratios obtained in the reference experiment with glucose $S'_{Gly}/S_{Gref}$, and the known concentration of glucose [Gref]. After measuring [G6P], the amount of material $N_{G6P}$ can be determined in function of the volume in which the lyophilized fraction was diluted, $N_{G6P} = [G6P] \times V_{samp}$. The ¹³C spectra acquired for the different fractions are displayed in figure 6.3. Since the C1 and C6 resonances of G6P can be integrated separately, we performed three independent quantifications using the un-
<figure><img src="image_44.png" /><figcaption>**Figure 6.4:** Multiple quantifications of G6P's amount of substance, performed with different ¹³C resonances</figcaption></figure>

shielded C1 peaks, the most shielded C6 resonance and lastly the C2-C5 zone. We can thus cross-check the resulting values.

The signal attributed to G6P C₁ was obtained by integrating the resonances of both α and β G6P C₁, the intensities obtained were then added. For the second quantification, we integrated the region 66-77 ppm, in which C₂-₅ resonances of G6P are located. The total signal intensity was then divided by 4. The third quantification was performed by directly integrating C₆ resonance of G6P. The results obtained in the different measurements are displayed in the histograms of figure 6.4. The results presented in the histograms of figure 6.4 show similar values for the quantifications performed with different ¹³C resonances, 1.08-1.28 mmol. Results suggest a loss of 1,32-1,52 mmol, representing 50% to 58% of the original transformed substrate, since the G6P was produced from 2.6 mmol of glucose. Part of the G6P is however present in the furanose form, characterized by higher chemical shifts for the C1 as seen in the ¹³C spectra (see figure 6.3). However, after quantification, the furanose conformers only represent a total of 0.126 mmol. Hence, a significant amount of [U¹³C-U²H]G6P is retained in the remaining fractions or lost during the purification procedure. Since ATP and ADP are not ¹³C labeled, their quantification was performed by means of ¹H NMR. We followed the same strategy to quantify the amount of substance of these two compounds in the different fractions. Glycine was not a good reference in ¹H
<figure><img src="image_45.png" /><figcaption>**Figure 6.5:** 6.5a¹H spectra for quantification of the different fractions collected after purification. The molecule used as reference for quantification was acetic acid and the peak used for the analysis is the one around 2 ppm. 6.5b Possible variation in susceptibility due to changes in the concentration of the different molecules on each fraction.</figcaption></figure>

NMR because of resonances overlaps with the ribose moieties. Therefore, we used acetic acid as the reference compound inside the capillary. The amounts of ATP and ADP were measured together. The resulting ¹H NMR spectra are displayed in figure 6.5. We used the resonances of ATP/ADP in the aromatic region to perform the quantification.

Although all ¹H NMR spectra were acquired at the same temperature, we can however observe a frequency shift for the different fractions. The shift, more evident in the aromatic region (~ 7-9 PPM), could be related to a variation in pH. The pH in each fraction is mainly regulated by the concentration of phosphate buffer. It is therefore normal to see different shifts in each spectrum due to the different compositions of each fraction. The frequency shift was considered in the determination of the signal intensities used in the quantification. Moreover, there seems to be a smaller frequency shift in the acetic acid peak (~ 1 ppm). Since the acetic acid is inside a capillary, the pH should not change between fractions. A variation in the magnetic susceptibility can cause a frequency shift for the reference resonance, and a modification of its shape, see figure 6.5b. The significant changes in composition, density and viscosity, between fractions may account for this magnetic susceptibility shift which, however, have no impact on the quantification. The results
<figure><img src="image_46.png" /><figcaption>**Figure 6.6:** Comparison of the quantity of ATP/ADP vs G6P per fraction. G6P plot results from the quantifications done with the ¹³C₆ peak.</figcaption></figure>

of the measurements of ATP/ADP quantities are displayed in table 6.2 together with the results of the quantification of G6P. Originally, we added 3.37 mol of ATP and at the end we only recover a total of ATP and ADP of 1.54 mol. These results suggest that a only the half of ATP/ADP was present in the fractions 18-20. Figure 6.6 suggests that a remaining mass should be present in later fractions (after #20). We can already observe that the fractions #17 and #18 have bigger concentrations of G6P, the presence of ATP/ADP seems to be not significant. For later fractions, the quantity of ATP/ADP overtakes G6P and these fractions have to be further purified. A summary of these observations is presented in figure 6.6.

To evaluate the presence of the phosphate buffer in these fractions we use ³¹P NMR. The spectra obtained for the different fractions is displayed in figure 6.7b. On this figure we can also observe the resonances related to ATP, ADP and even AMP 6.7 along with the phosphate

<table><caption>**Table 6.2:** Quantification in 10⁻³ moles of G6P and ATP/ADP for the different fractions.</caption><thead><tr><th>Fractions</th><th>16</th><th>17</th><th>18</th><th>19</th><th>20</th><th>Total</th></tr></thead><tbody><tr><td>G6P-C<sub>1</sub></td><td>0.015</td><td>0.2</td><td>0.49</td><td>0.31</td><td>0.12</td><td>1.13</td></tr><tr><td>G6P-C<sub>2</sub> - 5</td><td>0.015</td><td>0.2</td><td>0.49</td><td>0.27</td><td>0.11</td><td>1.08</td></tr><tr><td>G6P-C<sub>6</sub></td><td>0.013</td><td>0.22</td><td>0.58</td><td>0.34</td><td>0.13</td><td>1.28</td></tr><tr><td>ATP/ADP</td><td>0.01</td><td>0.01</td><td>0.11</td><td>0.61</td><td>0.80</td><td>1.54</td></tr></tbody></table>
<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>

<figure><img src="image_49.png" /></figure>

<figure><img src="image_50.png" /></figure>

**Figure 6.7:** ³¹P NMR spectra with peak attribution. a) Spectrum obtained for fraction 18 complete spectra, with in c) a zoom over -4 -20 ppm region and in d) a zoom over -4 -11 ppm region. In b) are displayed the spectrum obtained for fractions 17-20. Assignments of phosphate groups have been deduced from the integration of the signals and the observed manifolds : 1 α-G6P, 2 β-G6P, 3 Phosphate buffer, 4 P₂ ATP, 5 P₃ ATP, 6 AMP, 7 P₂ ADP, 8 P₁ ADP, 9 P₁ ATP.

resonance of G6P. In the spectra given in 6.7 we can see that for fraction 17, no resonances different to G6P can be observed. This fraction is ~93% pure (measured with the relative signal intensities of all peaks in ³¹P spectrum). For fraction 18, G6P is still the predominant compound with higher concentration, however the concentration of Phosphate buffer, ATP and ADP cannot be neglected. For the other fractions G6P concentration is not predominant anymore. After quantification, the final production of [U¹³C, U²H]G6P was of 60 mg in fraction 17, and 158 mg in fraction 18. If both fractions are conserved 218 mg of [U¹³C, U²H]G6P were produced. Since fractions were collected every 5 min, collecting 25 fractions
imply a final duration of 2 h 5 min for the complete purification process. Compared to the FPLC purification method developed in [229] where 94.5 mg of [U<sup>13</sup>C, U<sup>2</sup>H]G6P were purified in a process that took ~ 11 h.

For future purifications, we plan to make successive passages through the column. Hence, the fractions that were not highly pure (>80%) and not conserved after the first passage could be filtered again, to retain the almost completely pure fraction, increasing rendered [U<sup>13</sup>C, U<sup>2</sup>H]G6P. However, the amount of purified G6P was half of the expected amount. The profile displayed in figure 6.2 suggest that most of G6P should be present in the fractions analysed, (16-20). The latter implies that half of the G6P was lost during the production/purification process. In this scope, it would be interesting to identify the main origins of G6P losses.

## 6.2 Kinetic analysis

The first experiments performed with the produced and purified [U<sup>-13</sup>C; U<sup>-2</sup>H] G6P focused on both confirming the anomeric specificity of G6PDH by DDNP as a proof of concept, and on determining the kinetics of the spontaneous anomerization of G6P. A simplified representation reaction pathway relative to the system under study is depicted in figure 6.8, where the approximations that were used for this study are indicated. The first approximation is to assume that, as shown in [74], G6PDH has a specific activity towards the β anomer of G6P. Secondly, since for the different experiments the cofactors are present in excess (~ 10-fold with respect to the substrate), their concentration is assumed constant and is discarded from the kinetic analysis. Both of these approximations were already used in the previous chapter.

The first DNP sample used in this round of experiments was prepared with nearly pure [U<sup>-13</sup>C, U<sup>-2</sup>H]G6P (according to the quantification procedure described previously - purification fraction #17). The DNP sample was a mixture of 10%:40%:50% H<sub>2</sub>O:D<sub>2</sub>O:Glycerol-d8 in volume. The final G6P concentration of the sample was 500 mM and the radical chosen was TEMPOL (4-hydroxy-TEMPO). The concentration of radical chosen for the experiment
<figure><img src="image_51.png" /><figcaption>**Figure 6.8:** Simplified scheme of the observed system for the series of experiments using G6P as the substrate. There are two kinetic parameters determining the anomerization of the substrate and one kinetic parameter related to the G6PDH activity on the β-G6P anomer. The dotted arrow represents the discarded transformation due to the enzyme specificity [33]. Gray arrows represent non studied reactions related to the spontaneous hydrolysis and isomerization of the δ-PGL.</figcaption></figure>

was 50 mM, concentration optimized for the static magnetic field (9.4 T, cryo-free polarizer) and the CP sequence used during the hyperpolarization of the substrate, subsubsection 4.2.3.2. 75 µL of the formerly presented sample were introduced in the polarizer for a total of 37.5 µmol of G6P. Two experiments were performed. Experiment A served as a reference to observe the conventional decay of G6P signal without any enzyme activity, and experiment B was performed with a high enzyme G6PDH activity (400 u). The G6PDH used (Merck), was extracted from *Saccharomyces cerevisiae* and packaged with a specific activity of 319 u.mg⁻¹

Both experiments were performed on our 9.4 T polarizer and followed the usual steps of DDNP. Maximum polarization was reached after ~6 CP steps (~one hour) at 1.2 K and under µ-wave irradiation. The µ-wave power was set to 75 mW and irradiation was performed at 263±1 GHz, modulated with a saw-tooth function over a range of 100 MHz. The DNP sample was dissolved in 5 mL of D₂O heated at 403 k and pressurized at 10.5 bar, and transferred to the NMR spectrometer, into a 10 mm NMR tube containing the solution with cofactors and, depending on the experiment, enzymes. The total transfer lasted 3 s although the G6P arrive to the NMR tube from the first scan, 1 s after the dissolution.

In experiment A, no enzymes were added to the solution sitting in the NMR tube. On the other hand, the cofactor, NADP⁺, was added so that the density and viscosity conditions would match as closely as possible in both experiments. The NADP⁺ concentration was a tenfold larger than substrate concentration in order to neglect its variation during the course of the experiment, and consider it constant for the reaction kinetics. Thus, 375 µmol
of NADP⁺ were added to a solution of HEPES buffer 200 mM, pH = 7.4. After mixing with the dissolved sample, the final sample volume was ~ 3 mL.

For experiment B, the same procedure was used, where 400 u of *glucose-6-phosphate dehydrogenase* yeast enzyme were added. After mixing with the dissolved sample, the final sample volume was ~3 mL.

Both experiments were acquired in the same 400 MHz bruker spectrometer, in a 10 mm BBO dual channel probe tuned to ¹³C and ¹H. Both ¹H and ²H decoupling were preformed using a Waltz-16 sequence during the acquisitions. The excitation pulses consisted on a series of subsequent squared pulses of 10° with a 1 s interval between each other.

### 6.2.1 Characterizing G6PDH activity and G6P anomerization rate

The summed spectra obtained for both cases (experiments A and B) are shown in figure 6.9. In experiment B, the production of δ-PGL (label 2) shows that the dehydrogenation reaction of G6P actually took place and that the enzyme was therefore active. In addition, a small resonance signal in the vicinity of δ-PGL, in the carbonyl region of the ¹³C spectrum can be assigned to γ-PGL, the isomerisation product of δ-PGL [226]. The spectra displayed in figure 6.9 is actually the superposition of 256 scan, hence 256 seconds. The large peak intensity ratio between the two isomers δ-PGL/γ-PGL suggests that the spontaneous isomerization process is slow compared to the production of the δ-PGL by the enzyme. Note also that, in the absence of glucose in the sample, no peak deconvolution is needed to analyze the anomeric signals, and the signal intensities of each metabolite were simply obtained by direct peak integration.

Both experiments were performed in the same pH and temperature conditions in order to avoid variations of the T₁ relaxation times. Hence, the differences in the signal decays of the two anomers only depended on the activity of the enzyme. In figure 6.10a, the anomeric ¹³C₁ signal intensities over time of the two anomers in experiments A (red) and B (blue) are depicted. For both experiments the α- and β-G6P signals are respectively represented by
<figure><img src="image_52.png" /><figcaption>**Figure 6.9:** Superposition of 256 scans for the two different experiments. For the peak attribution we have for the relevant molecules: **1 γ-PGL C₁**, **2 δ-PGL C₁**, **3 furanos C₁**, **4 furanos C₁**, **5 β-G6P C₁**, **6 α-G6P C₁**, **7\*** resonances overlay containing G6P C₁–5, PGL C₁–5, and glycerol C₂, **8 G6P C₆**, and **9 glycerol-d8 C₁.₃**. We can see in experiment B that the enzyme is active and producing δ-PGL. Additionally, a difference in the signal intensity ratio of both anomers (in the C₁ of α and β anomers) in the different experiments. Induction decay signals were processed using the NMRPipe software[231] and the Python library NMRglue[232] in the following way. A 2 Hz exponential apodization was used, and zero filling was applied prior to Fourier transformation.</figcaption></figure>

<figure><img src="image_53.png" /><figcaption>**Figure 6.10:** 6.10a Signal evolution of both G6P anomers for the different experiments. In this experiment A is in red and experiment B is in blue and we have ♦ and • that represent respectively the α-G6P and β-G6P signals. 6.10b 1D spectra of the two experiments at different times. We see that for the experiment with enzymes the signal of the β anomer disappear much faster.</figcaption></figure>
filled diamonds and circles. A simple inspection of this graph shows qualitative information about the differential kinetics of both anomers in both experiments. First, it appears that the β-G6P to α-G6P intensity ratios are larger in the reference experiment A than in experiment B. Moreover, α-G6P in both experiments and β-G6P for experiment A have apparent similar decay curves, in contrast to the β-G6P signal intensities that decay faster and disappear roughly 5 times faster in experiment B, see figure 6.10b. This seems to indicate an accelerated decay, therefore kinetics, of the β-anomer signal due to the selective consumption of the anomer in the enzymatic reaction.

The decay curve of each signal was fitted to an exponential decay to extract the rate at which the molecule relax and transforms. For experiment A, assuming that the G6P is initially at anomeric equilibrium, the concentration ratio should be constant over the duration of the experiment, and the signal should decay exponentially with $T_1$. For the first $n = 20$ scans, where the signal to noise ratio (SNR) is high enough), we computed the signal ratio between the two anomers of experiment A and obtain an average:

$$ \sum_{t=i}^{n} \frac{S_{\alpha i}^{A}/S_{\beta i}^{A}}{n} = 1.48 \pm 0.047 \qquad (6.2) $$

where the error was given by computing the associated standard deviation. The ratios at each time point of the anomeric signals are practically constant in time for experiment A. This confirmed the assumption that the experiment started at anomeric equilibrium. The intensities of both anomers versus time in experiment A are displayed in figure 6.11. Curves were fitted to a mono-exponential function to extract the relaxation rates of both anomers.

Thus, the following equation was used for the independent fit of both anomers in experiment A:

$$ S_{\alpha,\beta}^{A}(t) = S_{0}e^{-r_{\alpha,\beta} t} \times \cos(\theta)^{n} \qquad (6.3) $$

Where $\theta$ is the flip angle of the detection pulses (10°), n is the scan number at time t and $S_0$ represent initial signal. The extracted relaxation parameters were nearly equivalent, $r_{\alpha}^A = 0.1330$ and $r_{\beta}^A = 0.1338$,
<figure><img src="image_54.png" /><figcaption>**Figure 6.11:** Fit of the exponential decay (equation 6.3) for both anomers of G6P in experiment A. The extracted relaxation parameters seem to be almost equivalent $r_{\alpha}^{A} = 0.1330$ and $r_{\beta}^{A} = 0.1338$</figcaption></figure>

In a recent paper G6P anomeric ratio was measured at 309 K in pure D₂O, and was found to be ~ 1.7 [226]. To confirm the anomeric rate equilibrium value, obtained before and displayed in equation 6.2, we perform a new measurement of the anomeric ratio in the same experimental conditions.

To do so, a reference NMR spectrum was recorded with the sample recovered long after (~ day) experiment A, in the same temperature conditions. The reference spectrum was obtained by averaging 1024 scans, with squared excitation pulses of 30° at 20 s interval for a total duration of more than 5 hours. The resonance peaks of β-G6P and α-G6P ¹³C₁ were integrated and the ratio of the signals gave:

$$ \frac{S_{\alpha}^{ref}}{S_{\beta}^{ref}} = \frac{k_{\alpha\beta}}{k_{\beta\alpha}} = 1.44 \qquad (6.4) $$

which is consistent with the result obtained in eq. 6.2.

### 6.2.2 Pseudo-first order, complete reaction scheme

A more detailed and quantitative analysis of both the G6P anomerization and enzyme kinetics was performed by combining the observations of both experiments A and B, and by
taking into account the kinetics of the chemical reactions and the longitudinal relaxation rates $r_i = \frac{1}{T_i}$ of the different nuclei. The model used thus included relaxation times of the $^{13}$C 1 of both anomers of G6P, together with the anomerization rate constants $k_{\alpha\beta}$ and $k_{\beta\alpha}$. As explained above, owing to identical experimental conditions, these parameters were consid- ered identical in both experiments A and B. Moreover, in experiment B, and because of the large excess of NADP$^+$ cofactors, the kinetics of the enzymatic reaction was simplified and assumed a pseudo-first order reaction in [G6P]. Finally, the evolution of the $\delta$-PGL signal was represented by a leakage term $d_L$ that encompasses relaxation and consumption of the latter into 6PGA and isomerization with $\gamma$-PGL. Both experiments were fitted together in order to better constraint the definition of the output parameters by the fit.

$$ \frac{d}{dt} \begin{pmatrix} M_{G\alpha}^B \\ M_{G\beta}^B \\ M_L \end{pmatrix} = \begin{pmatrix} -k_{\alpha\beta} - r_G & k_{\beta\alpha} & 0 \\ k_{\alpha\beta} & -k_{dh} - r_G - k_{\beta\alpha} & 0 \\ 0 & k_{dh} & -d_L \end{pmatrix} \begin{pmatrix} M_{G\alpha}^B \\ M_{G\beta}^B \\ M_L \end{pmatrix} \quad (6.5) $$

Obviously, for experiment A, since no enzyme was present in the sample, no oxidation of G6P occurred so that only the parameters related to the anomerization (in blue in equations 6.6 and 6.5) and to the relaxation of G6P were considered. Therefore, the model simplified to:

$$ \frac{d}{dt} \begin{pmatrix} M_{G\alpha}^A \\ M_{G\beta}^A \end{pmatrix} = \begin{pmatrix} -k_{\alpha\beta} - r_G & k_{\beta\alpha} \\ k_{\alpha\beta} & -r_G - k_{\beta\alpha} \end{pmatrix} \begin{pmatrix} M_{G\alpha}^A \\ M_{G\beta}^A \end{pmatrix} \quad (6.6) $$

Fitting of the model parameters to the data was achieved through the Differential Evolu- tion (DE) algorithm[228], which adjusted a set of 10 different parameters including 3 kinetic parameters ($k_{\alpha\beta}$, $k_{\beta\alpha}$, $k_{dh}$), 1 relaxation parameters ($r_G$) and $d_L$ which has both a relaxation component and a kinetic component, and 5 parameters related to the initial values of the monitored signals ($S_i$ at time $t = 0$) in both experiments.
<figure><img src="image_55.png" /><figcaption>**Figure 6.12:** Data of experiments A and B simultaneously fitted with the model introduced in equations 6.6 and 6.5.</figcaption></figure>

<table><caption>**Table 6.3:** Output parameters of the simultaneous fit of experiments A and B. This parameters were injected to the model previously introduced in this paragraph to reproduce the signal evolution displayed in figure 6.12.</caption><thead><tr><td>Parameters</td><td>Value (s<sup>-1</sup>)</td></tr></thead><tbody><tr><td>k<sub>dh</sub></td><td>0.460</td></tr><tr><td>k<sub>αβ</sub></td><td>0.02</td></tr><tr><td>k<sub>βα</sub></td><td>0.015</td></tr><tr><td>r<sub>G</sub></td><td>0.132</td></tr><tr><td>d<sub>L</sub></td><td>0.092</td></tr></tbody></table>

In figure 6.12, the resulting fitted signals are displayed, which reproduce well the experimental observations. The obtained parameter values are displayed in table 6.3. The relaxation value for β-G6P and α-G6P is $r_G = 0.1338$, hence $T_1 = 7.47$ s found similar to the values documented in bibliography [226, 225], which can be explained by the resembling temperature conditions. The kinetic constant of the G6P oxidation has the value $k_{dh} = 0.46 s^{-1}$. In a first order kinetics, this is the initial slope of the G6P exponential decay curve. It also represents the maximum transformation rate of β-G6P, from which the enzyme activity can in principle be determined. Enzymes activities are given in units *unit* (*u*), $1 \text{ unit} = 1 \mu\text{mol.min}^{-1}$, and defined as the amount of transformed substrate (in $\mu$moles) per minute (note that the enzyme specific activity is in units and per mg of enzyme, $\mu\text{mol.min}^{-1}\text{mg}^{-1}$). Thus, the maximum enzyme activity can be calculated from the kinetic rate $k_{dh}$, using the amount of G6P $N_{G6P}^0$ (in $\mu$moles) and a time period of 60 s:

$$A_{dh}^{max} = k_{dh} \times N_{G6P}^{0} \times 60 \quad (6.7)$$

Assuming that the complete hyperpolrized G6P is transferred from the polarizer to the NMR spectrometer, so that $N_{G6P}^0 = 37.5\mu\text{mol}$, the maximum activity is then: $A_{dh}^{max} = 0.46 \times 37.5 \times 60 = 1024u$.
<figure><img src="image_56.png" /></figure>

<table><caption>**Table 6.4:** 6.4a Distribution of values obtained with a MC algorithm (100 iterations) for the different kinetic parameters in the model. 6.4b Average values and standard deviations resulting from the distributions obtained with the MC.</caption><thead><tr><th>Parameters</th><th>k<sub>dh</sub></th><th>k<sub>αβ</sub></th><th>k<sub>βα</sub></th><th>r<sub>G</sub></th><th>d<sub>L</sub></th></tr></thead><tbody><tr><td>Average</td><td>0.461</td><td>0.022</td><td>0.015</td><td>0.132</td><td>0.092</td></tr><tr><td>St. Deviation</td><td>1.10<sup>-4</sup></td><td>1.210<sup>-5</sup></td><td>1.310<sup>-5</sup></td><td>7.10<sup>-6</sup></td><td>5.310<sup>-7</sup></td></tr></tbody></table>

The latter estimate is ~2.5 times larger than the expected value, based on the specific activity of the enzyme and the amount used in the experiment (400 u). However, it should be noted that the determination of the activity depends in the amount of G6P transferred during the dissolution (see subsection 4.2.2). Considering that 3 mL out of the 5 mL dissolution sample typically reaches the NMR tube in our experiments, this value of $A_{dh}^{max}$ can be significantly overestimated. Besides, the specific enzyme activity indicated by the supplier is measured at 20 °C, whereas our DDNP experiment were performed at 37 °C, which may increase enzyme activity [233]. For these reasons, despite an apparent discrepancy, the obtained enzyme activity seems to be consistent with the experimental conditions. The analysis of the above experiments led to values of the G6P anomerization rates. These show that the $k_{αβ}$ rate is faster than the $k_{βα}$ rate, which is consistent with the knowledge that at equilibrium, there is a population excess of the G6P $β$ over the $α$ anomer. The associated equilibrium constant $K$ is given by: $K = \frac{k_{αβ}}{k_{βα}} = \frac{p_β}{p_α}$, the populations of both anomers. The experiments give the resulting value $K = \frac{k_{αβ}}{k_{βα}} = 1.42$, which is consistent with the ratio
extracted in a direct manner from the reference NMR experiment, using equation 6.4. Addi-
tionally, the constant is in agreement with documented values of the anomeric equilibrium
[75, 226].

The impact of the detection noise on the resulting values was estimated with a MC al-
gorithm. Experimental noise was again estimated for each experiment by computing the
standard deviation of the signal in a region without resonances. The averages and standard
deviations of the resulting distributions are presented in table 6.4b. As we can see, all pa-
rameters are well defined with errors inferior to 0.1% of the resulting values.

In conclusion, when we assess the validity of the fit results by analyzing the pertinence
of the different parameters we found that:

* Both measures of the relaxation parameters, which are equivalent as expected, are consistent with values in literature.

* Anomerization parameters tend to an equilibrium value that is consistent with the one found in a separate measurement and document in bibliography.

* The obtained G6PDH activity is consistent with the preparation of the experiment.

* The noise did not affect the values obtained for the extracted parameters.

Hence the methodology seems to provide a reliable approach to characterize the kinetics of
such complex system of reactions.
<figure><img src="image_57.png" /></figure>
# Part IV

## In cell fluxomic studies by DDNP
Chapter 7

Glucose metabolism in *E.coli* K12

**7.1 A brief background overview**

DDNP-NMR has been used as a targeted method to monitor the fate of (hyperpolarized)
substrates and their metabolites, giving access to the kinetic study of selected metabolic
pathways under various circumstances. Both *in vivo* [43, 234, 234, 42, 235] and in-cell studies
of metabolism [53, 236, 237, 238, 51, 239] have benefited from the high sensitivity, therefore
temporal resolution, afforded by DDNP. The combination of DDNP and MRI have enabled
the observation of metabolism in isolated tissues [240, 241], living animals [235, 242] and in
humans[234, 42, 243]. DDNP has been applied to various cell types , such as bacteria[236,
244, 245], yeast[180, 236, 246] and eukaryotic cells, including macrophages or parasites [51,
239, 247]. A number of studies have focused on cancer metabolism by monitoring the uptake
of [1-¹³C]pyruvate and its transformation into [1-¹³C]lactate [234, 51, 238]. The particularly
long relaxation time of pyruvate C₁ and its role in metabolism make it a natural choice
as hyperpolarized substrate for such studies[238, 234]. Requested in particular for *in vivo*
spectroscopy and imaging in clinical trials [42, 234].

Although [1-¹³C] pyruvate has also been widely used for in-cell DDNP [248, 239, 246, 247, 244], several studies using ¹³C-labeled glucose [51, 236, 245], or alternative ¹³C labeled substrates have been proposed [249, 47]. DDNP has been used to monitor the evolution of [U¹³C, U²H]-glucose and of its metabolites in *E.coli* [236], for different growth conditions.
<figure><img src="image_58.png" /><figcaption>**Figure 7.1:** Figures taken from [236]. 7.1a Comparison of glucose metabolism of e.coli BL21 in different growth conditions. The production of 6PGL seems reduce with the growth phase. 7.1a Signal evolution of different detected metabolites.</figcaption></figure>

A qualitative assessment of the metabolic state at the different growth phases was made (figure 7.1 adapted from ref. [236]).

In a similar perspective, we tried and improved our DDNP methodology to make it a tool
able to assess the metabolic response of living cells prepared in various metabolic states to a
rapidly changing environment, in the present case, a sudden glucose injection into the cell
suspension. This involves performing and analyzing real-time kinetics of hyperpolarized
substrates, such as [U-¹³C, U-²H]-glucose and its metabolic products, in different cellular
systems. Experiments were mainly performed on E. coli cells grown to different states, in
order to study the adaptation of the metabolic response.
## 7.2 Materials and methods

### 7.2.1 Cell culture

*E.coli* K12 (DH10B) were stored in stock solutions of 30% glycerol at -80°C. When needed, frozen stock solutions were scrapped with sterile pipet cones to add bacteria to a 250 ml erlenmeyer flask containing 25 ml of rich lysogeny broth (LB) medium, they were grown over night at 37°C and 230 rpm shaker speed. Precultures were inoculated in 50 ml of LB medium contained in 500 ml erlenmeyer flasks to an optical density (OD) $OD_{600} < 0.4$, and grown at 37°C and 230 rpm shaker speed to the desired $OD_{600}$, which is proportional to the cell concentration in the culture, and is used to monitor the growth stage. For *E. coli*, $OD_{600}$ of 1.0 corresponds to $8 \times 10^8$ cells/mL. Cells were harvested at different stages of the growth phase, immediately (~ minutes) before the DDNP experiment is performed. The results presented in this chapter are from experiments performed on cell suspensions that were harvested at ODs ranging from 0.8 (early exponential growth phase, ≈ $6.4 \times 10^8$ cell/mL) to 2.8 (stationary phase, ≈ $2.24 \times 10^9$ cell/mL). Cells were harvested after centrifugation (3850 G-force for 5 minutes) and supernatants were discarded. Cell pellets were then washed in 2 mL of a 100 mM HEPES buffer pH 7.4, and resuspended in 0.5 mL of the same HEPES buffer and 35 µM EDTA. The cell suspension was then transferred into a 10 mm NMR tube moments before the DDNP experiment.

### 7.2.2 DNP setup and NMR

Glucose samples were prepared for DNP following a usual procedure [226]. A solution of H₂O:DMSO:D₂O with a 15%:35%:50% volume composition was prepared, in which the polar-izing agent TEMPOL (4-Hydroxy-TEMPO) was dissolved to reach a final concentration of 40 mM. [U-¹³C, U-²H]-glucose was added to the sample to attain near-saturation conditions at a concentration of 5 M. Doubly ²H, ¹³C, labelled glucose was used in order to avoid too fast relaxation following dissolution. A [U-¹³C, U-²H]-glucose stock solution with a concentra-
tion of 5 M was prepared for multiple DNP experiments. For each experiment a sample of 50 µL transferred to a PEEK sample holder was inserted in the cryostat, as described above (subsection 4.1.1 and ??), in contact with a bath of liquid helium where it solidifies as a glass.

DNP experiments were performed alternatively with two DNP polarizers operating at 6.7 T (Bruker prototype operating at 1.2 K and μ wave irradiation at 187.9 GHz, and 350mW W of power) and 9.4 T (cryogen-free system with μ wave frequency 263 ± 1 GHz and power=75 mW). The sample was hyperpolarized at ~ 1.27 K using a cross-polarization sequence to accelerate polarization buildup and to increase the steady-state polarization (see subsection 4.2.3.2). Steady-state polarization was typically reached in 50 min.

In both cases, μ wave irradiation was modulated with a saw-tooth function over a range of 100 MHz with a modulation frequency of 1-2 kHz, in order to increase the saturation region of the EPR spectrum of the radicals, and thereby enhance the DNP efficiency.[250] Dissolution was achieved by flushing 5 mL of D₂O previously heated to 403 K at 10.5 bar onto the frozen hyperpolarized sample. The hyperpolarized solutions were transferred from the polarizer to the 400 MHz spectrometer (distant by ~ 5-6 m from each other) upon Helium gas flow. Mixing of the hyperpolarized solution with the cell suspension takes place in a 10 mm NMR tube sitting inside the NMR spectrometer, typically began less then one second after dissolution and was complete after 3 seconds.

NMR spectra were recorded at *T* = 310 K on a 9.4 T Avance III Bruker spectrometer with a 10 mm BBO probe. Each DDNP experiment consisted in a series of 1D ¹³C spectra with 10⁰ read pulses. ²H decoupling was performed in all experiments. Alternatively, ¹H decoupling was not used during acquisition in the post-DDNP (thermalized), but only in the reference samples used for the identification of the metabolites. In both cases, decoupling was achieved using a WALTZ16 pulse sequence.[159]

NMR FIDs were apodized with an 10-Hz exponential window, and zero filling was applied prior to Fourier transformation. Processing of the NMR data was performed using the NMRPipe software,[231] and the obtained spectra were exported to ascii format for peak integration using the Python library NMRglue.[232]