Exploring conformational dynamics and equlibria of ABC transporters using EPR techniques

This is a web version of my PhD thesis. Some copyrighted publications have been omitted and replaced with link to the corresponding webpage. The thesis is published under GPL v2 license.
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Exploring conformational dynamics and equlibria of ABC transporters using EPR techniques
Doctoral Dissertation

0.0.1 Abstract (English)

ATP binding cassette (ABC) transporters form a significant super family of membrane proteins coupling the energy of ATP hydrolysis to substrate transport across the cell membrane. Unraveling transport and inhibition mechanisms is crucial to address several diseases caused by malfunction, over expression and mutation of ABC transporters. Several biochemical tools including electron microscopy and X-ray crystallography have aided the mechanistic characterization of many ABC transporters in static states of the transport cycle. While providing unprecedented insight into the mechanism, static states cannot explain the complete machinery. To achieve a full understanding, all the intermediate states as well as the collective behavior of transporters throughout the cycle need to be studied. Site-directed spin labeling and electron paramagnetic resonance (EPR) techniques provide a powerful set of tools to investigate macromolecules in general and can provide invaluable information on dynamics, structure and function of ABC transporters under physiological conditions.

ABC importers are restricted to bacteria, importing nutrients and other vital molecules into the cell. One of the main objectives of an import system is the uptake of finest carbohydrates available for optimizing energy in a competitive environment, which is vital for the survival of microorganisms. Therefore, bacteria developed a preferential carbohydrates import system to maximize the growth by removing the need for transporting and processing secondary carbon sources (e.g. maltose) when there is a preferred energy available (e.g. glucose). The maltose importer MalE-FGK\(_2\) studied in this work is a bacterial maltose importer from Escherichia coli which gets inhibited in presence of glucose by unphosphorylated EIIA\(^{Glc}\), a sugar-specific enzyme II. Phosphoenolpyruvate carbohydrate phosphotransferase system (PTS) is responsible for the change of phosphorylation state of EIIA\(^{Glc}\) and carbohydrate uptake regulation in many bacterial cells. The maltose importer MalE-FGK\(_2\) has undergone decades of investigation. Therefore, it is an optimal model to study the fundamental mechanism of action of ABC transporters and the modes of EIIA\(^{Glc}\) interaction and inhibition in PTS using EPR techniques. In this work we found that EIIA\(^{Glc}\) inhibits the transport by preventing the closure of MalK dimer in the cytoplasm. Additionally, we found that inhibition can happen regardless of the conformational state of the maltose importer while the available crystal structure suggested the mechanism of inhibition in only one conformational state.

ABC exporters on the other hand are found in both prokaryotes and eukaryotes and are responsible for the expulsion of toxins and drugs out of the cellular cytoplasm. ABC exporters are shown to be the source of several hereditary diseases in mammals. They are also known to be responsible for multiple-drug resistance (MDR) in tumor cells and antibiotic resistance in bacteria. TM287/288, an ABC exporter from Thermotoga maritima has shown to expel some drugs including the anti cancer drug daunomycin highlighting its analogy to the multiple drug resistance transporters in humans. In this thesis, the inward/outward facing mechanism at the basis of substrate translocation was studied by EPR and molecular dynamics simulations. Furthermore, a new crystal structure of the transporter was analyzed and confirmed using DEER distance measurements.

0.0.2 Abstract (German)

ATP-Bindungskassetten-(ABC)-Transporter bilden eine bedeutende Superfamilie von Membranproteinen, die Energie aus der Hydrolyse von ATP nutzen, um Substratmoleküle über die Zellmembran zu transportieren. Ein detailliertes Verständnis der Transportmechanismen, sowie ihrer Inhibition ist notwendig, um Krankheiten zu bekämpfen, die durch Fehlfunktionen, Mutationen oder Überexpression von ABC-Transportern verursacht werden. Verschiedene biochemische Werkzeuge wie Elektronenmikroskopie oder Röntgenkristallographie haben tiefe Einblicke in die Struktur und Funktion von verschiedenen ABC-Transportern gegeben, jedoch liefern sie nur statische Einsichten in den Transportzyklus. Diese statischen Bilder können jedoch nicht vollständig den Transportzyklus erklären. Dazu sind zusätzliche Methoden nötig, die die Dynamik und die Zwischenzustände des Systems beschreiben können. Elektronenspinresonanz (ESR/EPR)-Spektroskopie in Kombination mit ortsspezifischer Spinmarkierung bietet leistungsstarke Werkzeuge um genau diese Dynamiken zu untersuchen.

ABC-Importer kommen nur in Bakterien vor. Sie transportieren Nährstoffe und andere lebenswichtige Moleküle in die Zelle. Hauptsächlich werden spezifische Kohlenhydrate transportiert, um den Energiehaushalt der Bakterien zu optimieren, wodurch die Zellen in ihrer natürlichen Umgebung überleben können. Dabei erlaubt das System den Transport und die Verarbeitung von sekundären Kohlenstoffquellen (z.B. Maltose) abzuschalten, wenn die bevorzugte Energiequelle (z.B. Glukose) verfügbar ist. In dieser Arbeit wird der Maltose-Importer MalE-FGK\(_2\) aus Escherichia coli untersucht. In Gegenwart von Glukose wird MalE-FGK\(_2\) durch das Protein EIIA\(^{Glc}\) gehemmt, welches ein Teil des Phosphoenolpyruvat-Kohlenhydrat-Phosphotransferase-Systems (PTS) ist. EIIA\(^{Glc}\) selbst wird durch seinen Phosphorylierungszustand reguliert. MalE-FGK\(_2\) und seine Regulation über EIIA\(^{Glc}\) ist bereits gut in der Literatur beschrieben worden. Daher stellt es ein gutes Modellsystem dar, um die grundlegenden Wirkmechanismen von ABC-Transportern mittels EPR-Methoden zu untersuchen. Wir zeigen, dass EIIA\(^{Glc}\) den Zuckertransport durch MalE-FGK\(_2\) hemmt, indem es das Schlie\ss en des MalK-Dimers im Zytoplasma verhindert, was unabhängig vom Konformationszustand des Maltose-Importeurs erfolgt.

ABC-Exporter kommen sowohl in Prokaryonten als auch in Eukaryonten vor und sind für die Ausscheidung von Toxinen und Medikamenten aus der Zelle in den extrazellulären Raum verantwortlich. Mehrere genetisch vererbbare Krankheiten haben ihre Ursache in genetischen Mutationen von ABC-Exportern. Au\ss erdem können ABC-Exporter für Arzneimittelresistenzen von Tumorzellen und Antibiotikaresistenzen von Bakterien verantwortlich sein. Der ABC-Transporter TM287/288 von Thermotoga maritima kann z.B. das Krebsmedikament Daunomycin über Membranen transportieren und hat somit eine analoge Funktion zu menschlichen ABC-Exportern. In dieser Arbeit wurde der Substrat-Transportmechanismus von TM287/288 mittels EPR und Molekulardynamik-Simulationen untersucht. Darüber hinaus konnte mittels DEER-Distanzmessungen eine neue Kristallstruktur des Transporters verifiziert werden.

Table of Contents

  • 1. Introduction
  • 2. Results
  • 3. Conclusion and outlook
  • 4. Appendix
  • 1 Introduction

    Cell membrane is an essential barrier safeguarding cell contents from the environment. All of the cell interaction with the surroundings including signaling, uptake of nutrients and efflux of waste and toxins from inside the cell are regulated through membrane-integrated proteins among which ATP Binding Cassette (ABC) transporters form a very important class. ABC transporters are found in all three domains of life. Their function is to couple the energy of ATP hydrolysis to the import and export of substrates across the membrane by a transport process called alternating-access" in which the transporter switches between two important states, an inward and an outward facing conformation.

    1.1 ABC transporters

    ABC transporters transport several types of substrates including lipids, heavy metal ions, inorganic acids, glutathione conjugates, sugars, amino acids, peptides, secondary metabolites, and xenomolecules, used as drugs across various membranes by cycling between two main conformations driven and powered by adenosine triphosphate (ATP) binding and hydrolysis Davidson-2008. ABC transporters are functionally classified into two main families: importers and exporters Kerr-2002. Each family is further divided into types according to their structural similarity, evolutionary path or type of transported substrates. Adopting the classification based on structural and fold similarities, ABC importers are grouped into three types: type I importers which follow an alternating access mechanism driven by the presence of the substrate (e.g. maltose importer MalE-FGK\(_2\), Figure fig:abc-transporters A), type II importers which accept substrates in a nucleotide-free state, with ATP hydrolysis driving them to the inward facing conformation Clifton-2014 (e.g. vitamin B12 importer BtuCD-F, Figure fig:abc-transporters B) and energy-coupling factor (ECF, or type III) importers with a modular architecture working independently of solute-binding proteins (e.g. folate-specific transporter ECF–FolT, Figure fig:abc-transporters C). ABC exporters on the other hand include two main types: type I encompasses most of the known exporters (e.g. mouse P-gp Figure fig:abc-transporters D) and type II (ABCG1 proteins) with a unique fold (CRYOEM structure of ABCG2, an example of this type, solved recently taylor-2017-struc-human is shown in Figure fig:abc-transporters E).

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    Figure 1: ABC transporters comprise two families: ABC importers and ABC exporters. ABC importers (top row) are in turn divided into three types based on structural and fold similarities. This figure shows an example member of each type. A maltose importer MalE-FGK\(_2\) from E. coli, a type I ABC importer oldham-2011-cryst-struc (PDB: 3PV0), B vitamin B12 importer BtuCD-F from E. coli, a type II ABC importer hvorup-2007-asymm-struc (PDB: 2QI9) and C folate importer from L. delbrueckii swier-2016-struc-insig (PDB: 5JSZ). ABC exporters (bottom row) are divided into two types. D mouse P-glycoprotein (P-gp) is a type I exporter esser-2016-struc-multid, E ABCG2 human multidrug exporter is a type II exporter taylor-2017-struc-human. Renders created with VMD version 1.9.3.

    ABC transporters minimally consist of four core domains: two nucleotide-binding domains (NBD) which are highly conserved in all ABC transporters and two trans-membrane domains (TMDs) which carry many hydrophobic residues for integration into the cell membrane. The energy of ATP hydrolysis is harnessed in the NBDs and transferred to TMDs, where substrates are accommodated and transferred. The NBD sequence is in most of the cases more than 25% identical and has a typical 3D fold Kerr-2002. The specificity of transported substrates for each transporter is dictated by the sequence of the TMD region. Transporters can have a different number of polypeptide chains, going from four polypeptides in many bacteria (e.g. BtuCD locher-2002-e) to one full domain polypeptide chain (the most prominent example is the human multi-drug resistance exporter P-gp aller-2009-struc-p). ABC exporter proteins exist also with two main polypeptide chains, which can be homodimers (e.g. Sav1866 dawson-2006-struc-bacter) or heterodimers (e.g. BmrCD torres-2009-yhei-heter). Another common feature of ABC transporters is the cytoplasmic coupling helix which binds each NBD to one TMD. This helix lies approximately parallel to the membrane bilayer and is responsible for communicating the conformational state of the NBDs to the TMDs.

    Among this super family of proteins, ABC exporters have drawn more attention as more than 40 years of research in this field has shown that they are responsible for many hereditary diseases such as cystic fibrosis (related to mutations in the ABC chloride channel CFTR gadsby-2006-abc-protein) and multiple-drug resistance (MDR) in tumor cells (related to over expression of ABC exporters P-gp and MRP1 pajic-2009-moder-increas). Antibiotic resistance in bacteria is also related to the ABC exporters PatAB Garvey-2010, LmrCD Zaidi-2008 and EfrCD H-rlimann-2016.

    ABC importers are also relevant for bacteria to adjust to available energy sources for survival. Therefore, a deep mechanistic understanding of those proteins can aid the development of specific methods to expand the antibiotic tools available. The uptake of nutrients which occurs in bacteria is dependent on substrate binding proteins (SBP) which are tailored for high affinity towards the substrate and, once in the liganded form, towards the the periplasmic gate of the importer. The energy is efficiently harvested in bacteria by regulating importers activity in the presence of different nutrients promoting more ready-to-use carbon sources. This regulation is done through the carbohydrate phosphotransferase system (PTS). PTS has several functions among which phosphorylation and unphosphorylation (i.e. accepting a phosphoryl group from a donor and donation to an acceptor) of enzyme I (EI) and enzyme II (EII) play the main role in this regulation. It is shown that the carbohydrate specificity of the importers in bacteria is controlled by EII which is in turn classified into four families with distinct evolutionary origins: glucose-fructose-lactose, ascorbate-galactitol, mannose and dihydroxyacetone families. EIIA\(^{Glc}\) is listed under the glucose family of enzyme II, which inhibits maltose importers in the presence of glucose deutscher-2006-how-phosp.

    1.1.1 TM287/288, a heterodimeric ABC exporter

    TM287/288 is an ABC exporter from an anaerobic, gram-negative, hyperthermophilic bacterium called Thermotoga maritima. In contrast to many bacterial ABC exporters which are homodimers (e.g. LmrA, MsbA), most of the eukaryotic ABC exporters are heterodimers or contain a single polypeptide chain. TM287/288 is a heterodimer with two monomeric polypeptides called TM287 and TM288. TM287/288 shares 36% sequence similarity with LmrCD from Lactococcus lactis, and both were shown to be able to export the anti cancer drug daunomycin, highlighting important analogies between bacterial transporters and multiple drug resistance transporters in humans Hohl-2012.

    1.1.1.1 Structure

    The TM287/288 NBD is characterized by two distinct ATP binding and hydrolysis sites. The consensus site has all the canonical residues needed for ATP hydrolysis in the Walker B and switch motifs while the degenerate site lacks some residues that are important for ATP hydrolysis (e.g. aspartate instead of glutamate in the Walker B and glutamine instead of histidine in the switch motif). This asymmetry between the two sites is also seen in some other eukaryotic transporters like CFTR Liu-2017 and TAP1/2 Oldham-2016. When I started my doctorate research, there were two crystal structures of TM287/288 available (Figure fig:crystals) both of which were corroborated by EPR distance measurements: one in the presence of an AMPPNP molecule, an ATP analog that has been widely used in many ABC transporters (PDB: 3QF4 Hohl-2012) and one in the absence of nucleotide and substrate (PDB 4Q4H Hohl-2014). Schematics of the ATP molecule along with two frequently used analogues, AMPPNP and ATPγS molecules are shown in Figure fig:atp-and-analogs. Binding of the AMPPNP molecule to only one of the NBD sites (the degenerate site, Figure fig:crystals) denotes the asymmetry of the NBD sites in TM278/288. From the two available crystal structures, it can be seen that the 12 transmembrane helices of TM287/288 TMD create a large cavity for substrates. This cavity is accessible from the cytoplasm and also from the membrane bilayer through a lateral opening in the inward-facing state. In contrast to many other exporters which show a total disengagement of NBDs in the absence of nucleotide and substrate, the apo state of TM287/288 shows a partial contact of NBDs. This was later observed in a cryoelectron microscopy (CRYOEM) kim-2014-subnan-resol and a crystal structure N-ll-2017 study of TmrAB, another heterodimeric exporter. Additionally, the EPR experiments confirmed that in the presence of AMPPNP the transporter remains in an inward facing state, in contrast to other homodimeric exporters (e.g. MsbA Ward-2007).

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    Figure 2: Inward facing conformation of TM287/288 in absence of nucleotide and substrate (apo, PDB: 4Q4H) and in presence of an AMPPNP molecule in the degenerate NBD site (PDB: 3QF4). The TM287 chain is colored cyan and the TM288 pink. The membrane boundaries are depicted in scale with the protein as gray rectangle. Created with VMD version 1.9.3.

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    Figure 3: Schematics of A adenosine-tiphosphate (ATP), B adenylyl-imidodiphosphate (AMPPNP) and C [γ-S35]adenosine 5'-thiotriphosphate (ATPγS) molecules. AMPPNP and ATPγS molecules are widely used ATP analogs to induce pre-hydrolytic states in transporters.

    1.1.1.2 Transport cycle

    The degenerate site of the NBDs in TM287/288 accommodates one ATP molecule with high affinity, but it is impaired in hydrolyzing it. The structural rearrangement of the degenerate site due to ATP binding is transferred by means of two D-loops (loops featuring a highly conserved aspartate) to the consensus site, where a second ATP molecule binds. Prior to our study on TM287/288, there were two export mechanisms suggested for heterodimeric exporters in the literature. The export mechanism suggested by Hohl et al. Hohl-2014 assumes that ATP binding to both sites leads to a dimerization of the NBDs. A structural change is then transferred to the TMDs via coupling helices and subsequently, the substrate efflux happens. Consequently, hydrolysis of ATP in the consensus site leads to resetting of the exporter to the inward facing conformation. This mechanism of transport was later challenged by Mishra et al. mishra-2014-confor-dynam: based on EPR data on BmrCD (a heterodimeric exporter), the authors suggested a mechanism different from that of homodimeric transporters. In the homodimeric transporters both NBD sites are active in ATPase and therefore ATP is hydrolyzed and replaced in both sites. ATP binding is the "power stroke" for the conformational change from the inward to the outward facing conformation and the transporter resets to the inward facing state after ATP hydrolysis occurs. Mishra et al., suggested that the power stroke is the ATP hydrolysis, based on the fact that AMPPNP (ATP analog) does not induce the conversion to the outward facing state of the transporter but ADP vanadate does. During my research I reached the following milestones using site-directed spin labeling EPR:

    1. revealing the conformational switch trigger (power stroke) in a heterodimeric exporter (TM287/288),
    2. studying the energy landscape of the transporter,
    3. finding which nucleotides and nucleotide analogs switch the conformation of a heterodimeric exporter and
    4. understanding the effect of temperature on the conformational equilibrium of TM287/288.

    1.1.2 MalE-FGK\(_2\), the maltose importer

    1.1.2.1 Structure

    MalE-FGK\(_2\) belongs to type I ABC importers which include six TMD helices in each subunit. There are several crystal structures solved for MalE-FGK\(_2\), among which four are very important in the whole mechanism: resting state in the absence of maltose and ATP khare-2009-alter-acces (PDB: 3FH6), outward-facing conformation in the presence of MalE, one maltose and two ATP molecules oldham-2007-cryst-struc (PDB: 2R6G), pre-translocation complex in the presence of MalE and two maltose molecules but in the absence of nucleotides oldham-2011-cryst-struc (PDB: 3PV0) and in the presence of regulatory enzyme II EIIA\(^{Glc}\) chen-2013-carbon-catab (PDB: 4JBW). Relevant structures are presented in Figure fig:MalFGK-crystals. MalE-FGK\(_2\) encompasses two TMD subunits MalF and MalG and two copies of MalK as NBD subunits. Since ATPase activity is stimulated upon addition of the maltose binding protein (MBP or MalE), it is well established that translocation of maltose needs MalE at the periplasmic side of the importer chen-2001-trapp-trans. MalE itself adopts an equilibrium of a closed (liganded) and open (unliganded) states in the absence of maltose. This equilibrium shifts towards the closed state when maltose is present hall-1997-two-modes.

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    Figure 4: MalFGK\(_2\) crystal structures. A resting state in the absence of maltose and ATP khare-2009-alter-acces (PDB: 3FH6). B pre-translocation complex in the presence of MalE but in the absence of nucleotides oldham-2011-cryst-struc (PDB: 3PV0). C outward-facing conformation in the presence of MalE and ATP oldham-2007-cryst-struc (PDB: 2R6G). \(\textbf{D,~E}\) in the presence of regulatory enzyme EIIAGlc chen-2013-carbon-catab (PDB: 4JBW). ATP and maltose molecules are represented in van der Waals radius spheres. Created with VMD version 1.9.3.

    1.1.2.2 Translocation cycle

    This transporter is very well studied and the number of available structural snapshots unveil the whole translocation machinery and provide indications towards the regulation mechanism mediated by EIIA\(^{Glc}\) when class A sugars like glucose are accessible. Upon ATP and liganded MalE (MalE+maltose) binding, the Malk subunits dimerize to a closed state letting the TMD subunits MalF and MalG open to accomodate maltose. MalE switches to an open state by releasing the substrate into the cavity formed by the TMD subunits. This whole procedure restarts with hydrolysis of the two ATP molecules and releasing maltose into the cytosol and MalE into the periplasm. The affinity of the transporter to liganded MalE in the closed state is very high when the transporter is in the resting state allowing easy binding to the periplasmic region. When the liganded MalE binds to the trasporter, the complex is ready to sandwich two ATP molecules in the NBDs, release maltose and undergo ATP hydrolysis orelle-2008-both-maltos. The regulation mechanism mediated by EIIA\(^{Glc}\) is not fully understood since there is only one crystal structure of the transporter with EIIA\(^{Glc}\) (Figure fig:MalFGK-crystals D and E). This structure shows the transporter in its resting state, inhibited by two EIIA\(^{Glc}\) enzymes but does not exclude the possibility of inhibition in other states of the transporter. During my research I addressed the following points via EPR spectroscopy:

    1. binding of EIIA\(^{Glc}\) to the MalK subunit in solution and its agreement with current crystal structures,
    2. state and conformational selectivity of EIIA\(^{Glc}\) binding and
    3. the inhibition mechanism of EIIA\(^{Glc}\).

    1.2 Electron Paramagnetic Resonance

    Electron paramagnetic resonance (EPR) also called electron magnetic resonance (EMR) and electron spin resonance (ESR) spectroscopy is a powerful tool to detect paramagnetic centers and coupled magnetic nuclei. Inherent to the fact that the formation of chemical bonds results in electrons pairing to an overall zero spin (\(S=0\)), most macromolecules that do not posses any free radicals or metal centers are invisible to EPR. However, by introducing spin labels at the points of interest, EPR provides site-specific information about dynamics, water accessibility and inter-spin distances. Here the basics of electron paramagnetic resonance are covered and the biological caveats of spin labeling will be addressed.

    1.2.1 Free electron

    Most elementary particles carry an intrinsic angular momentum called spin. The spin gives rise to a magnetic moment which is formulated in equation eq:e-mag-moment for an electron.

    \begin{equation} \vec{\mu} = \hbar \gamma_e \vec{S} = -g \beta_e \vec{S} \label{eq:e-mag-moment} \end{equation}

    where \(\beta_e=\frac{e\hbar}{2m_e}\) is the Bohr magneton, g is the electron's g-factor which accounts for the deviation of the electron's behavior from that of classical charged particle with the value of \(g=-2.00231930436182(52)\) mohr-2016-codat-recom and \(\gamma_e\) is the gyromagnetic ratio of the electron. In an unperturbed system, spin energy levels are degenerate. In the presence of an external magnetic field (e.g. \(\vec{B}^T_0= (0,0,B_0)\) in the direction of \(z\) axis), a lift of degeneracy in spin energy levels occurs due to different eigenvalues of the perturbed Hamiltonian. This effect is called the electron Zeeman interaction. Energy levels of the perturbed Hamiltonian corresponding to two spin z-projection numbers \(m_s=\pm \frac{1}{2}\) are:

    \begin{equation} E = \pm \frac{1}{2} g \beta_e B_0. \label{eq:e-spin-energy} \end{equation}

    EPR transitions between the two levels can be induced by incident microwave radiation

    \begin{equation} \Delta E = g \beta_e B_0 = \hbar \omega_0 \label{eq:e-energy-abs} \end{equation}

    where \(\omega_0 = - \gamma_e B_0\) is the Larmor frequency of the electron. Detecting the microwave absorption between energy levels with different electron spin quantum number (selection rule: \(S=\pm 1\)) is the fundamental principle of EPR spectroscopy. The energy difference and corresponding frequencies are illustrated in Figure fig:MWabsorption.

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    Figure 5: Energy levels of a free electron in an external magnetic field with different strength and corresponding resonance frequencies. Conventionally, different microwave frequency bands are named by letters (X, Q and W are the most commonly used bands in EPR).

    1.2.2 Time evolution of spin system

    1.2.2.1 Bloch equations

    The exerted torque on a single electron with spin \(\vec{S}\) in an external magnetic field is given by

    \begin{equation} \tau = \frac{\Delta \vec{S}}{\Delta t} = \vec{\mu} \times \vec{B}. \end{equation}

    However, EPR experiments are done on ensembles of electrons with total magnetization \(\vec{M}= \frac{1}{V} \Sigma \vec{\mu}\) which is proportional to the difference in the number of spins aligned parallel and anti-parallel to the external magnetic field. Thus, the torque of equation eq:e-energy-abs can be written as

    \begin{equation} \tau = \frac{d \vec{M}}{d t} = \vec{M} \times \gamma_e \vec{B}. \end{equation}

    Any displacement of the magnetization from the equilibrium state leads to a precession around the magnetic field axis (\(z\) axis by convention) with Larmor frequency \(\omega_0\). In EPR another external magnetic field is applied which is circularly polarized in the \(x-y\) plane to manipulate the spin system:

    \begin{equation} \vec{B}_1^T = (B_1\cos(\omega_{MW}t), B_1 \sin(\omega_{MW}t),0). \end{equation}

    For the ease of calculation, a rotating frame with the frequency of incident microwave \(\omega_{MW}\) in the plane perpendicular to \(z\) axis is defined. In this frame the precession frequency obeys \(\Omega=\omega_0-\omega_{MW}\) called resonance offset. For an on-resonant irradiation \(\Omega=0\) an effective nutation frequency is given by \(\omega_{eff}=\omega_1=\frac{g \beta_e B_1}{\hbar}\). To accurately describe the behavior of the system of spins, relaxation mechanisms \(T_1\) and \(T_2\) should be taken into account. Longitudinal relaxation (spin-lattice) \(T_1\) describes the process in which the \(z\) axis projection of the magnetization vector returns to its thermal equilibrium state. \(T_2\) is the transverse (spin-spin) relaxation time which describes the loss of coherence of the spins in the \(x-y\) plane. Relaxation mechanisms will be described in more detail in section 1.2.2.2 Relaxation mechanisms. The equation of motion describing the time evolution of the magnetization was first suggested by Felix Bloch bloch-1951-nuclear-induc. In the rotating frame the equation reads

    \begin{equation} \frac{d\vec{M}}{dt} = \vec{M}(t) \times \gamma_e \vec{B_{eff}} - \underline{\mathcal{R}}(\vec{M}(t)-\vec{M}_0)= \left( \begin{array}{c} -\Omega M_y - \frac{M_x}{T_2} \\ \Omega M_x - \omega_1 M_z - \frac{M_y}{T_2} \\ \omega_1 M_y - \frac{(M_z-M_0)}{T_1} \end{array} \right) \label{eq:bloch} \end{equation}

    with the effective field \(\vec{B_{eff}}\) including the oscillating magnetic field which is stationary along the \(x\) axis and static magnetic field which is \(\Delta B_0 = B_0 - B_{MW} = \frac{-\Omega}{\gamma_e} = \frac{-\omega_0}{\gamma_e} + \frac{\omega_{MW}}{\gamma_e}\) in the rotating frame

    \begin{equation} \vec{B_{eff}}= \left( \begin{array}{c} B_1 \\ 0 \\ \Delta B_0 \end{array} \right) \label{eq:bloch_mag_field} \end{equation}

    and \(\underline{\mathcal{R}}\) the relaxation tensor

    \begin{equation} \underline{\mathcal{R}}= \left( \begin{array}{ccc} \frac{1}{T_2} & 0 & 0\\ 0 & \frac{1}{T_2} & 0 \\ 0 & 0 & \frac{1}{T_1} \end{array} \right). \label{eq:bloch_rel_ten} \end{equation}
    1.2.2.2 Relaxation mechanisms

    Understanding relaxation mechanisms is decisive for setting up a proper EPR experiment. For the pulsed EPR techniques which are utilized in this work, the length of a pulse sequence is limited by the phase memory time \(T_m\) of the observed spin ensemble. Instead, the longitudinal relaxation time \(T_1\) mostly governs the rate at which the sequence can be repeated. Since these mechanisms are also highly temperature dependent, both the maximal length of a sequence and the temperature at which the experiment is performed should therefore be adjusted to yield the best results (for example the optimization of the DEER sequence is detailed in section 1.3.5 Double Electron-Electron Resonance (DEER)).

    1. Spin-lattice (longitudinal) relaxation (\(T_1\))

      Spin-lattice relaxation forces the magnetization to align back to the direction parallel to the external magnetic field restoring the preferred equilibrium value \(M_0\). Longitudinal relaxation is a first-order process in which spins flip back to the ground state due to coupling to phonons bloch-1951-nuclear-induc. In the early days of magnetic resonance studies in solids, the external environment in which the spins were placed was mostly a crystalline lattice of atoms, giving origin to the name spin-lattice relaxation. Complete formulation of \(T_1\) relaxation needs a pure quantum mechanical derivation since it deals with single spins which are quantum-mechanical entities. This description can be separated into direct transitions dominant at low temperatures and Raman transitions dominant at higher temperatures both of which are exponential functions of temperature. Hence, a simpler exponential relation was set forth by Bloch which describes this mechanism qualitatively

      \begin{equation} \frac{dM_z}{dt}=\frac{-(M_z-M_0)}{T_1} \end{equation}

      and therefore \(M_z=M_0(1-e^{\frac{-t}{T_1}})\) and \(T_1\) would be the time needed for \(M_z\) to restore to \(1-\frac{1}{e}\) of the equilibrium magnetization \(M_0\).

    2. Spin-spin (transversal) relaxation (\(T_2\))

      The decay of spin system's coherence in the \(x-y\) plane is described by the transversal relaxation mechanism with two main explanations. The local field felt by each spin is affected by the surrounding spins slightly changing the Larmor frequency which leads to a coherent dephasing of the spin ensemble. Moreover, two spins with the same Larmor frequency can undergo a flip-flop process and exchange their spin states. Transversal relaxation is also a first order temperature dependent exponential process. \(T_2\) is therefore defined as the time needed for the magnetization in the \(x-y\) plane to decrease to \(\frac{1}{e}\) of its initial value

      \begin{equation} \frac{dM_{x,y}}{dt}=\frac{-(M_{x,y})}{T_2} \end{equation}
    3. Phase memory time (\(T_m\))

      Pulsed EPR methods rely heavily on the coherent phase of the spin ensemble. Under realistic experimental conditions, apart from spin-spin relaxation mechanism there are other effects that cause dephasing in the spin ensemble. These effects include, but are not limited to \(B_0\) inhomogeneity and fluctuations, spectral, spin and instantaneous diffusion. The name phase memory time \(T_m\) is used to distinguish these effect from pure relaxation mechanisms which are the only mechanisms in an ideal spin system. Longitudinal relaxation also contributes to coherence loss and therefore to \(T_m\). Thus, \(T_m\) in the upper regime is limited by \(T_1\).

    1.2.3 Spin Hamiltonian

    Spin Hamiltonian describes the energy of states within the ground state of a paramagnetic center. It is derived from the Hamiltonian of the wave function of a bound electron abragam-1961-princ-nuclear-magnet.

    \begin{equation} \hat{\mathcal H_0}(S_1) = \underbrace{\hat{\mathcal H}_{EZ}}_\text{electron Zeeman} + \underbrace{\hat{\mathcal H}_{ZFS}}_\text{zero-field splitting}+ \underbrace{\hat{\mathcal H}_{HF}}_\text{hyperfine coupling}+\underbrace{\hat{\mathcal H}_{NZ}}_\text{nuclear Zeeman}+\underbrace{\hat{\mathcal H}_{NQ}}_\text{nuclear quadrupole}+\underbrace{\hat{\mathcal H}_{NN}}_\text{nuclear-nuclear spin} \label{eq:spinHam} \end{equation}

    This Hamiltonian only includes spin coordinates described by vector operators \(\hat{S}\) for electrons and \(\hat{I_k}\) for nuclei. Spatial degrees of freedom are encoded in second rank tensors \(\underline{g}\), \(\underline{D}\), \(\underline{A}\), \(\underline{P}\) and \(\underline{d}\) detailed later.

    1.2.3.1 Electron Zeeman interaction

    In most of the cases, at the applied static external magnetic field, the dominant term is the interaction between the electron spin and the external magnetic field which is defined by the so called electron Zeeman Hamiltonian

    \begin{equation} \hat{\mathcal H}_{EZ}= \frac{\beta_e}{\hbar} \vec{B^T_0} \underline{g} \hat{S}. \label{eq:ez_ham} \end{equation}

    The general form of the \(\underline{g}\) tensor reads

    \begin{equation} \underline{g} = \left( \begin{array}{ccc} g_{xx} & g_{xy} & g_{xz}\\ g_{yx} & g_{yy} & g_{yz} \\ g_{zx} & g_{zy} & g_{zz} \end{array} \right). \label{eq:g_tensor} \end{equation}

    In a molecular coordinate system, the principal axis is defined as an axis around which a rotation by \(\frac{2\pi}{n}\) results in the same molecule and \(n\) is the highest possible natural number that fulfills this condition. The \(\underine{g}\) matrix can be simplified by expressing it in the principal axis system (PAS)

    \begin{equation} \underline{g}_{PAS} = \left( \begin{array}{ccc} g_{xx} & 0 & 0\\ 0 & g_{yy} & 0 \\ 0 & 0 & g_{zz} \end{array} \right). \label{eq:g_tensor_sim} \end{equation}

    For different molecular symmetries, this can be further simplified since diagonal elements can be written as \(g_{xx}=g_{yy}=g_{zz}\) (for cubic symmetry) and \(g_{xx}=g_{yy}=g_\perp\), \(g_{zz}=g_\parallel\) (for axial symmetry)2. The diagonal \(g\) value deviates from that of the free electron because of spin-orbit coupling. Due to the fact that only the interaction between ground and excited state leads to an admixture of orbital and spin angular momentum, for most organic radicals this deviation is rather small thanks to their high energy excited states. For transition metal complexes this deviation is higher. In this case, the ion mass also affects spin-orbit coupling as a relativistic effect.

    1.2.3.2 Nuclear Zeeman interaction

    The nuclear Zeeman interaction is analogous to the electron Zeeman interaction. This Hamiltonian contribution is described by

    \begin{equation} \hat{\mathcal H}_{NZ}= -\frac{\beta_n}{\hbar} \sum\limits_{k} g_{n,k}\vec{B^T_0} \hat{I}_k, \label{eq:nz_ham} \end{equation}

    where \(\hat{I}_k\) and \(g_{n,k}\) are the \(k^{th}\) nuclear spin vector operator and g-factor. \(\beta_n\) is nuclear magneton defined as \(\beta_n=\frac{e\hbar}{2m_p}\) with \(m_p\) being the mass of the proton. In EPR experiments without considering the chemical shielding tensor, this part of the Hamiltonian can be assumed to be isotropic with a negligible influence (except for the cases in which it is of the same order as hyperfine interaction).

    1.2.3.3 Hyperfine interaction

    The hyperfine interaction is a very important aspect in EPR spectroscopy because it provides accurate information about the magnetic environment of the spin. It derives from the interaction between the electron spin and the nuclear spins in its vicinity and consists of an isotropic \(\hat{\mathcal H}_{HF}\) (Fermi contact) and an anisotropic part \(\hat{\mathcal H}_{DD}\) from electron-nuclear dipole-dipole coupling. The Hamiltonian reads

    \begin{equation} \hat{\mathcal H}_{HF}= \sum\limits_{k} \hat{S} \underline{{A_k}} \hat{I}_k = \hat{\mathcal H}_{F} + \hat{\mathcal H}_{DD} = \sum\limits_{k} a_{iso,k}\hat{S^T} \hat{I_k} + \sum\limits_{k} \hat{S^T} \underline{{T_k}} \hat{I_k}, \label{eq:hf_ham} \end{equation}

    where \(\underline{A}\) is the hyperfine coupling tensor, \(\underline{T}\) the dipolar coupling tensor and \(a_{iso}\) the isotropic coupling constant. \(\underline{T}\) can be calculated using the general term for two interacting magnetic dipoles in the hyperfine principal axes system

    \begin{equation} \underline{T} = \frac{\mu_0}{4\pi}\frac{g_eg_n\beta_e\beta_n}{R^3}\left( \begin{array}{ccc} -1 & 0 & 0\\ 0 & -1 & 0 \\ 0 & 0 & 2 \end{array} \right) = \left( \begin{array}{ccc} -T & 0 & 0\\ 0 & -T & 0 \\ 0 & 0 & 2T \end{array} \right). \label{eq:T_tensor} \end{equation}

    R is the distance between two dipoles. \(g\) anisotropies and spin-orbit coupling are neglected in this term. This holds true as long as their contributions are small. Since the \(\underline{T}\) tensor is traceless, in the fast motion regime of an isotropic rotation only the isotropic part of the Hamiltonian contributes. The isotropic coupling constant \(a_{iso}\) can be calculated by

    \begin{equation} a_{iso}= \frac{2}{3}\frac{\mu_0}{\hbar}g_eg_n\beta_e\beta_n |\psi_0(0)|^2, \label{eq:a_iso} \end{equation}

    in which \(\mu_0\) is the permeability of the vacuum and \(|\psi_0(0)|^2\) is the probability to find the electron inside of the nucleus in the ground state which is most significant when electron is in the s orbital. An X-band EPR spectrum of an electron coupled via hyperfine interaction to a nucleus with spin \(I=1\) is shown in Figure fig:hyperfineCW.

    1.2.3.4 Nuclear quadrupole interaction

    The non-spherical charge distribution in nuclei with nuclear spins higher than \(\frac{1}{2}\) leads to a quadrupole moment which interacts with the electric field gradient created by electrons and other nuclei in its vicinity. This interaction is described by the Hamiltonian

    \begin{equation} \hat{\mathcal H}_{NQ}= \sum\limits_{I_k>1/2} \hat{I_k^T} \underline{{P}_k} \hat{I_k}, \label{eq:NQ_ham} \end{equation}

    where \(\underline{P}\) is the traceless nuclear quadrupole tensor in its principal axes system. In hyperfine EPR spectroscopy, first-order splitting can be seen due to nuclear quadrupole interaction. In a normal EPR spectrum, this interaction is a very small second-order effect which is hard to observe.

    1.2.3.5 Nuclear spin-spin interaction

    The nuclear spin-spin interaction can be written as

    \begin{equation} \hat{\mathcal H}_{NN}= \sum\limits_{k} \hat{I_i^T} \underline{d^{(i,k)}} \hat{I_k}, \label{eq:NN_ham} \end{equation}

    where \(\underline{d^{(i,k)}}\) is the nuclear dipole coupling tensor. Even though this part of the Hamiltonian is the key in solid state NMR spectroscopy, it is negligible when analyzing EPR spectra, even in hyperfine spectroscopy.

    1.2.3.6 Zero field splitting

    Even in the absence of an external magnetic field, dipole-dipole couplings between electron spins in spin systems with \(S>\frac{1}{2}\) and non-cubic symmetry lead to a lift of the degeneracy of the ground state energy levels. The interaction is described by

    \begin{equation} \hat{\mathcal H}_{ZFS}= \hat{S^T} \underline{D} \hat{S}, \label{eq:ZFS_ham} \end{equation}

    where \(\underline{D}\) is the symmetric and traceless zero-field tensor and \(\hat{S}=\sum\limits_{k} \hat{S}_k\) . This term manifests itself only in high spin systems (e.g. in Gd\(^{3+}\) with spin \(\frac{7}{2}\)) therefore it is not present in \(S=\frac{1}{2}\) radicals (e.g. nitroxides).

    1.2.3.7 Heisenberg exchange coupling

    Exchange coupling occurs when two spins are very close to each other (R < 1.5 \(nm\)) so that their orbitals overlap and the two electrons can be exchanged. Exchange coupling encompasses isotropic and anisotropic parts and can be characterized using the exchange coupling tensor \(\underline{J}\). The interaction is given by

    \begin{equation} \hat{\mathcal H}_{exch}= \hat{S^T_1} \underline{J} \hat{S}_2. \label{eq:exch-ham} \end{equation}

    For organic radicals, since the anisotropic part of \(\underline{J}\) can be neglected, equation eq:exch-ham simplifies to

    \begin{equation} \hat{\mathcal H}_{exch}= J\hat{S^T_1} \hat{S}_2. \label{eq:exch_ham_2} \end{equation}
    1.2.3.8 Electron spin-spin dipolar interaction

    This interaction is very important in the methods used throughout this work and provides a very powerful way to extract distance information between interacting spins. Similar to the electron-nucleus and nucleus-nucleus dipolar interactions, the electron-electron dipolar interaction can be obtained from the classical description of two magnetic dipoles interacting with each other

    \begin{equation} E = \frac{\mu_0}{4\pi \hbar}\frac{ g_1 g_2\beta_e^2}{ r_{12}^{3}}(2\cos\theta_1 \cos \theta_2 - \sin \theta_1\sin\theta_2 \cos\phi) \label{eq:dd_ham_class} \end{equation}

    The \(\theta_1\), \(\theta_2\) and \(\phi\) angles are depicted in Figure fig:dipolar-Hamiltonian A. For the special case of organic radicals with spin \(S=\frac{1}{2}\) and when the external magnetic field is strong, the dipoles align parallel to external magnetic field (along \(z\)) and the relative orientation of the connecting vector vanishes. In this regime, called high field approximation (weak coupling3), we have

    \begin{equation} E = \frac{\mu_0}{4\pi \hbar}\frac{ g_1 g_2\beta_e^2}{ r_{12}^{3}}(1-3\cos^2\theta), \label{eq:dd-ham-class-simp} \end{equation}

    where \(r_{12}\) is the interspin distance. The orientation in the magnetic field and the corresponding angles in the high field approximation are shown in Figure fig:dipolar-Hamiltonian B. Thus, the interaction Hamiltonian can be written as

    \begin{equation} \hat{\mathcal H}_{dd} = \hat{S}^T \underline{D} \hat{S} = \frac{\mu_0}{4\pi \hbar}\frac{ g_1 g_2 \beta_e^2}{ r_{12}^{3}}\Big[\hat{S_1^T} \hat{S}_2-\frac{3}{r_{12}^2}(\hat{S_1^T} \vec{r}_{12})(\hat{S_2^T} \vec{r}_{12})\Big]. \label{eq:dd_ham_class_simp} \end{equation}

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    Figure 6: Two interacting dipoles inside an external magnetic field \(B_0\). A strong coupling regime leading to non-parallel orientation of magnetizations. B weak coupling regime (high magnetic field) causing parallel orientation of magnetizations.

    In the principal axes system of the dipolar tensor and with negligible \(\underline{g}\) anisotropy, \(\underline{D}\) can be expressed as

    \begin{equation} \underline{D} = \frac{\mu_0}{4\pi \hbar}\frac{ g_1 g_2 \beta_e^2}{ r_{12}^{3}}\left( \begin{array}{ccc} -1 & 0 & 0\\ 0 & -1 & 0 \\ 0 & 0 & 2 \end{array} \right) = \left( \begin{array}{ccc} -\omega_{dd} & 0 & 0\\ 0 & -\omega_{dd} & 0 \\ 0 & 0 & 2\omega_{dd} \end{array} \right). \label{eq:dd-ham-D-tensor} \end{equation}

    Corresponding to eq:dd-ham-class-simp, the Hamiltonian in high field approximation simplifies to

    \begin{equation} \hat{\mathcal H}_{dd} = \frac{\mu_0}{4\pi \hbar}\frac{ g_1 g_2 \beta_e^2}{ r_{12}^{3}}\hat{S_1^T} \hat{S}_2 = \omega_{dd} \hat{S_1^T} \hat{S}_2 \label{eq:dd-ham-class-high-field} \end{equation}

    in which \(\omega_{dd}\) is proportional to \(r_{12}^{-3}\) and thus the distance between two spins can be measured by the electron-electron dipolar interaction. When considering all orientations present in a frozen or powder sample, equation eq:dd-ham-class-high-field leads to a distribution of frequencies called Pake pattern. The Pake pattern is shown in Figure fig:pake-pattern.

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    Figure 7: The Pake pattern as a result of randomly distributed orientations of the inter-spin vector in a sphere within the high field approximation. Horns in the Pake pattern are due to the spins in a perpendicular orientation which is the most favoured orientation. The \(\omega_{dd}\) is proportional to the distance between the spins and can be readily extracted from the Pake pattern. However, this is not practically used as the Gaussian normal distribution of even a single distance peak would lead to a broadening of Pake pattern. Other more reliable methods for distance extraction will be described in section 1.3.5 Double Electron-Electron Resonance (DEER).

    1.3 EPR techniques

    1.3.1 EPR experimental setup

    As detailed in section 1.2.3 Spin Hamiltonian, any EPR setup needs a static external magnetic field \(B_0\) and an oscillatory magnetic field \(B_1\). In EPR spectrometers, \(B_0\) is provided by a water-cooled electromagnet or a helium-cooled superconducting magnet (for fields \(>3\,T\)) with a relatively big opening to accommodate the components in which the sample is placed. \(B_1\) is provided by a microwave source which is then phase- and amplitude-controlled in the microwave bridge. The amplitude can be shape-modulated by a pulse shaping device and sent through several channels for pulse experiments and is later transmitted to a resonator in which the sample is placed. The reflection of the incident microwave from the sample is measured using microwave detectors. Resonators differ in the type of dielectric which adjusts the resonance frequency (ring, split-ring) and the cavity shape in which the sample is placed (rectangular, cylindrical). The quality (Q) factor of the resonator is defined as

    \begin{equation} Q = 2\pi\frac{\text{Energy stored in resonator}}{\text{Energy dissipated per cycle}}=\frac{\nu_{res}}{\nu_{FWHM}}, \label{eq:q-factor} \end{equation}

    where \(\nu_{res}\) is the resonance frequency of the resonator and \(\nu_{FWHM}\) is the full-width-at-half-maximum of the reflection coefficient (\(S\)) linear spectrum. The reflection coefficient is defined as the ratio of the reflected (\(b_1\)) to the incident (\(a_1\)) signal \(S=\frac{b_1}{a_1}\).

    In a continuous wave (CW) setup a very small number of spins are excited due to critically coupled and thus high Q factor of the resonator. Therefore, the noise suppression becomes important. This is achieved using a lock-in amplifier which adds an oscillation to the detection. The lock-in frequency is in a kHz range and its amplitude is optimized to prevent broadening of the signal along with smallest possible noise intensity.

    The microwave is seperated into a reference and a CW arm using a splitter. The reference signal is combined with the signal from the resonator in a type of constructive interference and detected by the diode. The amplitude of the reference arm is adjusted in a range that keeps the detection diode in the linear regime.

    In the pulse setup, the cavity's Q factor is usually kept low (see section 1.3.3 Pulse experiments). Thus a defense blanking is necessary to protect the detector during the pulses which introduces a dead time (usually about \(100\,ns\)) after and before the pulses without any detection possible. Therefore, free induction decay (FID) detection is not possible with most of the pulse EPR setups and most spin labels. The carrier frequency is removed using the phased signal from the reference arm and detected by utilizing an analog-to-digital converter (an oscilloscope in the simplest case). The schematics of an EPR spectrometer with combined CW and pulse functionality is shown in Figure fig:spectrometer. There are spectrometers in which only CW or pulse experiments can be performed. Modern spectrometers replace microwave sources (Figure fig:spectrometer red dashed region) with arbitrary waveform generators (AWG) which can handle phase, amplitude and frequency modulation of microwave pulses independently.

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    Figure 8: Simplified schematics of a hybrid CW/pulse EPR spectrometer. A microwave source (red) is used to produce a single frequency microwave which is then split into a CW/reference arm (pink lines) or pulsed/reference arm (cyan lines). Pulse setup (cyan pathway): The synthesized microwave can be split into several channels (most common types are stripline pulse forming unit (SPFU) and manual pulse forming unit (MPFU) channels) to control relative phase and attenuation seperately for different pulses. A second microwave source (blue) can be used for multi-frequency pulse-EPR techniques. The microwaves are then recombined in a mixer, amplified using a traveling-wave tube (TWT) amplifier and sent to the sample contained in an EPR cavity through a directional circulator. The reflected signal from the cavity is mixed with the reference signal and sent to an analog-to-digital-converter (ADC) through the circulator. CW setup (magenta pathway): The synthesized microwave is sent to the EPR cavity through a power attenuator and a circulator. The reflected signal is mixed with the reference signal and detected in the detection diode. A lock-in amplifier increases the signal-to-noise ratio by adding a modulation in kHz range to the B\(_0\) magnetic field which is sensed by the sample. The signal is then sent to the computer. Up to Q band (\(1.2\,T/34\,GHz\)), \(B_0\) is produced by electromagnets and can be swept in a range limited by magnetic fields corresponding to spectrometer working frequency. EPR cavity: An EPR cavity is built to provide maximum magnetic and minimum electric field from incident microwave at the sample position. Most EPR cavities privide a mechanism to adjust the coupling and match the frequency after the insertion of the sample.

    1.3.2 Continuous wave experiments

    CW EPR spectroscopy is based on the detection of microwave absorption by the sample inside a resonant cavity. The resonator should be critically coupled to the incident microwave (maximum possible Q factor) to ensure that the microwave reflection from the resonator is at its minimum. This allows any absorption of the incident microwave, which detunes the resonator and consequently causes microwave reflection, to be detected by the detector.

    1.3.2.1 Field swept spectrum

    Due to technical issues involved in sweeping the microwave frequency, a CW EPR spectrum is obtained by sweeping the static external magnetic field B\(_0\). In the frequency sweep, the linewidth of the absorption spectrum is \(\Gamma=\frac{2}{T_2}\) (Figure fig:lock-in) and centered at zero resonant offset \(\Omega\). In the magnetic field swept spectrum, the linewidth is \(\Gamma=\frac{2\hbar}{g_e\mu_BT_2}\) and the spectrum is centered at \(\frac{h\nu_{MW}}{g_e\mu_B}\). A lock-in amplifier is used to suppress the noise level by adding a modulation frequency (e.g. \(100\,kHz\)) to the external static magnetic field. Therefore, a derivative of the absorption spectrum is recorded. The modulation amplitude, \(\Delta B_0\) and the correlated signal amplitude \(\Delta V\) (Figure fig:lock-in) should be adjusted to avoid distortion of the spectral line shape while optimizing the signal-to-noise of the spectrum. To reach this, a small \(\Delta B_0\) is used and stepwise increased until a maximum is reached at which the spectral line is not yet broadened.

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    Figure 9: A absorption spectrum in frequency swept detection. B same spectrum in static field B\(_0\) sweep centered at \(\frac{h\nu_{MW}}{g_e\mu_B}\). C detected derivative spectrum as the output of lock-in amplifier.

    The energy levels of an electron coupled to a nucleus with nuclear spin \(I=1\) are depicted in Figure fig:hyperfineCW. MTSL, which is mainly used in this work as spin label (\(S_{nitroxide}=\frac{1}{2}\) and \(I_{^{14}N}=1\)), yields a CW spectrum at X-band with distinct features going from liquid state (Figure fig:hyperfineCW A) to solid state (Figure fig:hyperfineCW B). Anisotropy of \(\underline{A}\), along with orientation dependence of g value cause the spectral line shape to be interconnected to the motional freedom of the spin label. Hence, in solution, the CW spectrum provides information about the rotational correlation time of the probe and the protein domain it is tethered to. The rotational correlation time is a measure of the spin label rotation speed and it determines whether it can average out the spectral anisotropy. It includes contributions corresponding to the correlation times of side chain internal motions, fast backbone fluctuations and the overall protein rotational diffusion for small proteins.

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    Figure 10: Electron \(S=\frac{1}{2}\) coupled to nucleus with spin \(I=1\). Hyperfine coupling leads to further splitting of energy levels. A in liquid state the hyperfine tensor simplifies to \(A = \frac{1}{3}(A_{xx}+A_{yy}+A_{zz}) = a_{iso}\) which leads to three equal absorption intensities at X-band. B in solid state, the orientation dependence of the hyperfine tensor leads to broader lines for each nuclear spin projection.

    The area under the absorption spectrum is also dependent on the number of spins and can be used to determine the spin labeling efficiency in a sample with known protein concentration when compared to a standard with defined spin concentration.

    1.3.3 Pulse experiments

    On the contrary to CW experiments, in which the resonator is utilized in a critically coupled regime, pulse EPR uses an over-coupled resonator (lower Q factor) to increase the overall accessible bandwidth to accommodate broader excitation pulses along with second frequency pulses when necessary and to reduce the ring-down time and thus the time it takes for a microwave pulse to dissipate within the resonator. In pulse EPR techniques, spin packets that are quantized along the constant external magnetic field are flipped using a resonant oscillating magnetic field to an angle of interest (e.g. \(\frac{\pi}{2}\) pulse, \(\pi\) pulse, etc.) in a sequence. The spectra obtained from the experiment provides useful information about interactions of spin packets with surrounding nuclei and/or with each otherو dependent on the used pulse sequence. Since in pulse EPR the width of the excitation profile in the frequency domain increases with decreasing pulse length in the time domain, more spin packets can be flipped by using shorter pulses. The simplest pulse EPR sequence was first suggested by Erwin Hahn in 1950 hahn-1950-spin-echoes and was optimized later on. This sequence comprises a \(\frac{\pi}{2}\) pulse followed by a delay time (\(\tau\)) and a \(\pi\) pulse creating two back-to-back FIDs in a form of a refocused echo at the time \(2\tau\) (\(\frac{\pi}{2}-\tau-\pi-\tau-echo\)). This sequence allows indirect detection of the FID in EPR. The echo sequence is depicted in Figure fig:hahnSequence A. By using the AWG in the setup, more complex pulse shapes than simple rectangular pulses can be used. The criteria for an optimum pulse shape include having a tailored excitation bandwidth with smaller side wings to prevent overlap in multi frequency sequences. A rectangular pulse in time domain translates to a sinc function in the frequency domain which is not ideal. Therefore, Gaussian pulse shapes are used when an AWG is at hand4 minimizing the pulse overlap in the frequency domain. Since the maximum length of a sequence is limited by the phase memory time \(T_m\) and the pulse lengths should be optimized for maximum echo intensity, slight modifications in the echo sequence allow detection of both \(T_m\)5 and optimum \(\pi\) pulse lengths, as shown in fig:hahnSequence B and C, respectively.

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    Figure 11: A an echo sequence. A \(\frac{\pi}{2}\) pulse flips the magnetization from equlibrium orientation along \(z\) to the \(x-y\) plane. The flipped spin packet starts to dephase over time. A \(\pi\) pulse rephases the spin packets to an echo. B the echo scheme can be used to measure phase memory time \(T_m\) by incrementing the \(\pi\) pulse by \(\tau\). The echo will be incremented by \(2\tau\) and decreases exponentially with longer \(\tau_1\). C A nutation sequence can be used to measure the optimal \(\pi\) pulse length by introducing a pulse in the beginning of sequence which increases the length by \(\tau\). Next \(\frac{\pi}{2}\) and \(\pi\) pulses and echo position shift by the \(\tau\) as well. The echo intensity oscillates at the Rabi frequency, and the first minimum will yield the optimal length of a \(\pi\) pulse.

    The most famous pulse methods are pulsed electron-nuclear double resonance (ENDOR), pulsed electron-electron double resonance (PELDOR), with the most commonly used sequence being the double electron-electron resonance (DEER), electron spin echo envelope modulation (ESEEM) and hyperfine sublevel correlation (HYSCORE). To the interest of the current work, the DEER technique will be described in detail here, which yields inter-spin distances with high accuracy and it is widely used in structural biology in combination with site-directed spin labeling methods.

    1.3.4 Spin labels and obtainable information on proteins

    The specificity of EPR spectroscopy to paramagnetic species makes it very selective to paramagnetic sites in the sample. Site-directed spin labeling EPR is a technique which uses native or mutated cysteine residues at the sites of interest in proteins (or other type of labels in other macromolecules) for attaching molecules carrying permanent electron spins (spin labels) hubbell_investigation_1994. The most widely used labels are nitroxides bordignon-2017-epr-spect, which were first introduced by McConnell in the 1960s stone_spin-labeled_1965. The chemical structure unit is \(R_2NO\). The stability is high thanks to delocalized spin density (\(\sim\) 40% on nitrogen and \(\sim\) 60% on oxygen atom) and methyl substitution in the \(\beta\) position. The (1-Oxyl-2,2,5,5-tetramethylpyrroline-3- methyl) methanethiosulfonate (MTSL, also called MTSSL) label which is used in this thesis is depicted in Figure fig:MTSL.

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    Figure 12: MTSL ((1-Oxyl-2,2,5,5-tetramethylpyrroline-3-methyl) methanethiosulfonate) spin labeling mechanism. A a cysteine and an MTSL molecule reaction exploiting standard reactivity of thiosulfate esters. B formation of disulfide bond leading to a robust attachment of the label to the cysteine and release of sulfinic acid (\(HCH_3SO_2\)). EPR experiments reflect the interactions at the position of spin which differs from that of Cα (arrows depict the degrees of freedom for the attached label). Additionally, the effect is averaged by an array of rotamers ensemble since EPR is performed on many molecules. These factors should be considered in data evaluation and interpretation. For DEER distance measurements, MMM simulation code package is used that utilizes a precalculated rotamer library attached to the structure under study to predict the distance distribution expectations. Comparison between experiment and simulated distances yields a \(0.3-0.4\,nm\) standard deviation between the mean distances jeschke-2012-deer-distan.

    Other radicals, like the carbon-centered trityl, as well as chelated paramagnetic metal ions like copper Cu\(^{2+}\), gadolinium Gd\(^{3+}\) and manganese Mn\(^{2+}\) can also be used as alternative spin labels for distance measurements. The combination of site-directed spin labeling and EPR provides a powerful tool to study dynamics, accessibility and conformational changes of proteins in their native environment.

    1.3.4.1 Dynamics

    As mentioned in section 1.3.2.1 Field swept spectrum, CW EPR spectra of a spin-labeled proteins depend on the local dynamics of the spin label, internal motions of the side chain and the global rotational diffusion (GRD) of the protein it is attached to. To eliminate the contribution from spin label dynamics, other more restricted labeling strategies like bifunctional spin labels (BSL) can be used sahu-2017-charac-bifun. However, BSL labels need a pair of cysteines at \(i,i+3\) or \(i,i+4\) positions for \(\alpha\) helices and \(i,i+1\) or \(i,i+2\) for \(\beta\) strands which requires more modifications to the protein. When the quantitative separation of three contributions which affect the CW spectrum is not of high importance, the CW spectra can be used for a rough estimation of the mixed system dynamics. The fraction of free spin labels, as well as the ratio of mobile/immobile components can also be estimated since the recorded spectrum represents the sum of the contributions of all spin labels in the system. Figure fig:easyspin shows simulations of nitroxide radicals in different motion regimes.

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    Figure 13: Simulated spectra of nitroxide radical in different mobility regimes. A short rotational correlation time corresponds to a fast nitroxide motion which averages out spectral anisotropies, while a long correlation time corresponds to a slower motion with spectral anisotropies which become visible, yielding a broader spectrum. The simulation is done with the MATLAB code package EasySpin stoll-2006-easys-compr.

    1.3.4.2 Water accessibility

    Protein residues can be accessible to the solvent or be buried inside the protein with lower accessibility. This can also change with conformational changes/dynamics and folding. Accessibility of the spin-labeled residues can be measured and tracked using several EPR methods including conventional techniques of measuring the maximum hyperfine splitting and progressive power saturation in continuous-wave EPR, line shape analysis of electron-spin-echo-detected EPR spectra, electron spin echo envelope modulation (ESEEM) spectroscopy and Ovehauser dynamic nuclear polarization (ODNP). Overhauser DNP has gained an extensive momentum in recent years as it has the ability to enhance the nuclear magnetic resonance (NMR) signal6 by transferring electron polarization to the surrounding nuclei, as well as providing information on the mode of interaction between the protons of the water molecules and the nearby electron spins, within a range of \(0.5-1\,nm\). The latter allows quantifying surface water dynamics and therefore provides insights into water accessibility of spin labels attached to a specified site of a macromolecule doll-2012-liquid-state,segawa-2016-water-acces. Preliminary ODNP results on TM287/288 during my research period will be shown in chapter 3 section 3.4 Overhauser dynamic nuclear polarization (ODNP).

    1.3.5 Double Electron-Electron Resonance (DEER)

    While distance measurements using CW EPR at low temperature can reveal dipolar interactions via line broadening convolution for distances in the range of \(1.4-2.0\,nm\) in biomolecules, the DEER experiment martin-1998-deter-end,pannier-2000-dead-time is able to provide distance information up to \(6.0\,nm\) for membrane proteins and \(16\,nm\) for deuterated soluble proteins jeschke-2012-deer-distan,schmidt-2016-long-distan. DEER which is the most used technique in the current work is detailed in this section.

    1.3.5.1 Selection of spin-labeling sites

    The selection of positions to be spin labeled depends on the geometry of the target protein and viability of the mutation. The more pairs are measured, the more information about the changes in the protein in different static trappable states can be obtained. However, procedures to create the desired mutants, to purify and spin label the protein and address their functionality are very time consuming. Thus, a wise compromise is needed to efficiently select the pairs which allow sampling of different regions of the protein. Simulations can help in the selection procedure if a PDB file of the protein under investigation is available. The site to be used for spin labeling should be selected according to the type of amino acid and its accessibility for the spin label after the protein is folded. Additionally, the distance between two spin-labeled sites should be in the measurable distance range of DEER. The best range of mean distances for membrane proteins to optimize signal-to-noise is in the \(2-5\,nm\) range. The optimum way to prevent any folding misbehavior of the protein during protein preparation is to select natural cysteines of the sequence if they meet all other criteria. Otherwise, taking into account the polarity of the cysteine, threonine or serine amino acids are preferable to be mutated to cysteines. Non-polar amino acids such as alanine, valine, leucine, isoleucine and methionine can also be mutated to cysteines if other more feasible amino acids with high accessibility cannot be found in the region of interest.

    1.3.5.2 Distance simulations

    In addition to spin labeling success estimation, the expected distance from each spin pair should be simulated on existing structures to be compared with the experimetal data taking the conformational flexibility of spin label linker into account (see Figure fig:MTSL). There are several approaches from direct modeling of the protein with attached spin label using molecular dynamics or Monte Carlo approaches, to software suites with precalculated spin labels rotamer libraries like mtsslWizard sahu-2017-charac-bifun, PRONOX hatmal-2011-comput-model and MMM MMM. For the purpose of the current work, the MATLAB package MMM is used for both purposes. Among other functionalities, MMM is able to predict the inter-spin distances between spin labels such as MTSL, Gd-DOTA maleimide, etc.. To simulate the interspin distance distributions of the selected pairs using available structures, MMM attaches spin labels to the protein using a precalculated rotamer library approach. The rotamer library approach is used to predict favorable attachment sites by scanning the whole or a part of a protein. Furthermore, accessibility of a site is calculated in terms of the number of spin label rotamers which can be populated without backbone clash. An example of an MMM simulation and its agreement with experimental DEER distance data is shown in Figure fig:MMM.

    Sorry, your browser does not support SVG.

    Figure 14: MMM simulation of \(460^{TM287}-363^{TM288}\) pair labeled with MTSL. A visualization of MMM labeling simulation on the apo state crystal structure of TM287/288 (PDB: 4Q4H). The cloud of sticks show spin label rotamers which can be populated. Size of the red balls in the zoomed image denote the probability of finding the N-O bond midpoint carrying an unpaired electron at each position. Sum of all contributions from different spin label rotamers at each labeling position gives a prediction of the distance distribution. B comparison of the experimental data (colored lines) to the MMM simulations (colored histograms) for \(460^{TM287}-363^{TM288}\). ATP-VO trapped state has shown to maximally switch the conformation to the OF state with a small fraction of transporters remaining in the IF state (see chapter 2 section 2.3 The extracellular gate shapes the energy profile of an ABC exporter for more details).

    1.3.5.3 Strategy

    Two spin labels are introduced to the protein in positions of interest. A \(\pi\) pump pulse at the frequency \(\nu_2=\frac{\omega_2}{2\pi}\) is applied to spin 2 (also called pump spin). The pulse inverts the magnetization vector of spin 2 and thus the local magnetic field imposed on spin 1 (Figure fig:deerSequence). A spin echo is created at frequency \(\nu_1=\frac{\omega_1}{2\pi}\) for spin 1 and refocused using a \(\frac{\pi}{2}\xrightarrow{\tau_1}\pi\xrightarrow{\tau_1+\tau_2} \pi\) sequence with fixed interpulse delays. The pump \(\pi\) pulse is positioned before the refocused echo of the observer spin and its position is incremented in the dipolar evolution time window from \(-\tau_1\) to a maximum which is defined by \(\tau_2\) with dead time subtracted. In a 4-pulse DEER experiment, most of the inhomogeneous EPR broadenings (i.e. g-value dipersion, hyperfine coupling and other couplings of the excited fraction of spin 1 to other unexcited electron spins) are refocused in the echo using the observer sequence. However, the time-dependent echo intensity of the observer spin 1 (\(V(t)\)) gets dampened by an exponential factor rising from the transverse relaxation time \(T_2\) of the 1 spins and coupling to other excited 1 spins according to

    \begin{equation} V(t)=V(0)e^{-2k(\tau_1+\tau_2)} \label{eq:echo-damp} \end{equation}

    with

    \begin{equation} k=\frac{1}{T_{2,1}}+k_{ID}, \label{eq:echo-k} \end{equation}

    where \(T_{2,1}\) is the transverse relaxation time of the observer 1 spins and \(k_{ID}\) is the instantaneous diffusion decay rate

    \begin{equation} k_{ID}=c_1K_1 \label{eq:echo-kid}, \end{equation}

    which is proportional to spin concentration \(c_1\). \(K_1\) is inversely proportional to the observer \(\pi\) pulse length. Signal loss increases with increasing the interpulse delays \(\tau_1\) and \(\tau_2\) in the observer sequence as well as increasing the sample concentration. Additionally, if a fraction \(\lambda\) of the pump spin 2 is inverted by using the pump pulse, the frequency change in the observer spin 1 by dipolar electron-electron frequency \(\omega_{dd}\) leads to a phase gain \(\phi_i=\omega_{dd}t\) of a fraction \(\lambda_i\) of observer spins 1. The echo amplitude as a function of dipolar evolution time \(t\) can be calculated by

    \begin{equation} V(t)=\prod\limits_{i}\Big[1-\lambda_i[1-\cos(\omega_{dd}t)]\Big], \label{eq:echo_amp} \end{equation}

    where \(i\) includes all spin 2 which are coupled to observer spin 1 and

    \begin{equation} \omega_{dd}= \frac{\mu_0g_1g_2\mu^2_2}{4\pi\hbar}\frac{1}{r_3}(1-3\cos^2\theta), \label{eq:echo_dip_freq} \end{equation}

    where \(\theta\) is the angle between the external magnetic field vector and the interspin vector. By assuming that:

    1. The system is in the weak coupling regime meaning that both spins are quantized along the external magnetic field, the \(\omega_{dd}\) is small compared to the frequency difference \(|\omega_1-\omega_2|\) and exchange interaction can be neglected (see section 1.2.3.8 Electron spin-spin dipolar interaction).
    2. For a spin 1 only one spin 2 in the same protein is within the range of DEER.
    3. There is a negligible dependence between \(\lambda_i\) and \(\omega_{dd}\), meaning that the orientation (\(\theta\)) is averaged.

    In DEER, the time-dependent echo intensity takes the form

    \begin{equation} V(t)=F(t)B(t), \label{eq:echo-sig} \end{equation}

    where B(t) is the background function contributed by dipolar interactions from all other spins in the sample which in the case of a homogeneous distribution of molecules with \(d\) dimension reads

    \begin{equation} B(t)=\exp(-kt^{d/3}) \label{eq:echo-BG} \end{equation}

    and \(F(t)\) is the form factor with relation

    \begin{equation} F(t)=1-\lambda_i[1-\cos(\omega_{dd}t)]. \label{eq:echo-amp} \end{equation}

    In the case of more than two spins interacting in the sample (e.g. a system labeled with more than two spin labels), the form factor is a product of all possible pair contributions. This can give rise to additional peaks in the distance distribution. In such cases there is a need for the suppression of these so called ghost peaks. To achieve that, the pump pulse intensity can be decreased leading to a smaller intensity of the ghost peaks when normalized to the modulation depth hagens-2013-suppr-ghost.

    Sorry, your browser does not support SVG.

    Figure 15: A 4-pulse DEER sequence. Top and bottom sequence show the observer and pump sequence on spin 1 and 2 with frequencies \(\nu_1\) and \(\nu_2\), respectively. The detection window is the integral over the FWHM of the refocused observer echo. The sequence at the observer frequency has a fixed interpulse delay and creates a refocused echo of the spin group 1 (observer). Since spins 1 and 2 are coupled via dipolar interaction, inverting the spin group 2 using a \(\pi\) pulse in the pump frequency leads to a change in the resonance frequency of spins 1 which consequently prevents the echo to be refocused with the same pulse sequence. This leads to a phase accumulation which appears as an echo intensity modulation when pump pulse moves. This frequency of the modulation allows distance information to be extracted. B Flipping one spin packet using the pump pulse leads to a change in frequency of the dipolar-coupled spin packet by altering the local magnetic field that the other spin packet feels.

    The positioning of the pump and observer pulses is such that the overlap is minimized while the number of spins excited in the spectrum are maximized. A microwave amplifier (traveling wave tube, TWT) helps to decrease pulse time length providing broader excitation profiles in the frequency domain. The typical DEER pulse setup used in this work when interspin distances between two nitroxide probes are detected at Q band is shown in Figure fig:deerBW. Observer and pump Gaussian pulses have a length of 30-32 \(ns\) (this is the value of the pulse gate used to accomodate a Gaussian pulse with FWHM of 12-14 \(ns\) which is analogous to 12-14 \(ns\) rectangular \(\pi\) pulse). The pump pulse is positioned at a higher frequency in the resonator bandwidth, corresponding to a lower magnetic field in the Q-band spectrum of a nitroxide (Figure fig:deerBW).

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    Figure 16: A resonator profile of our custom built pulse Q-band resonator obtained by a series of nutation experiments at different microwave frequencies (detailed in section Pulse experiments). This resonators has a 6 \(dB\) (power) bandwidth of \(\sim\) 350 \(MHz\) and allows different frequency separations. Pump and observer pulses are positioned symmetrically with respect to the resonator profile to produce \(\pi\) pulses of similar length. B echo-detected field swept spectrum of a sample carrying two MTSL labels per protein. A 100 \(MHz\) separation in the frequency domain corresponds to \(\sim 35\,G\) separation in the magnetic field, with a Gaussian \(\pi\) pulse length of \(\sim 30-32\,ns\) for both observer and pump spins.

    1.3.5.4 Data analysis

    The background fit and removal is done on primary DEER traces according to equations eq:echo-sig and eq:echo-BG to extract the form factor (\(F(t)\)). The obtained form factor can be subsequently transformed into the Pake pattern by using a Fourier transformation. The interspin distance can be evaluated by extracting \(\omega_{dd}\) directly. However, the distance distribution calculation from a dipolar evolution function is an ill-posed problem meaning that very similar DEER traces may lead to very different distance distributions due to noise fitting and mixture of distances in a realistic multiple-distance sample which leads to a smearing of the Pake pattern. In data analysis, the ill-posedness should be taken into account to produce a reliable distance distribution. A good model-free strategy to solve this problem is Tikhonov regularization which provides a good compromise between resolution and smoothness of the fit and uses the distance non-negativity condition \(P(r)>0\) to stabilize the result. When the distance distribution's shape information is available, several model-based calculations are available as well. For instance two Gaussian model fit has been used in this work for two distinct conformational population of some TM287/288 mutants (see chapter 2 results). However, the range of applicability of model-based fitting is limited to well characterized samples. There are several code packages for DEER data analysis out of which the software package DeerAnalysis jeschke-2006-deeran-compr is used in this work.

    1.3.5.5 Tikhonov regularization

    Tikhonov regularization is a computational method with a library of simulated time domain signals \(S(t)\) generated from different assumed distance distributions \(P(r)\) using a kernel function \(K(t,r)\) which is well known for DEER with ideal pulses in the weak coupling regime.

    \begin{equation} S(t) = K(t,r) P(r), \label{eq:tikh-main} \end{equation}

    in which the kernel function reads

    \begin{equation} K(t,r)=\int_{0}^{1}\cos[(3x^2-1)\omega_{dd}t]dx \label{eq:tikh-kernel} \end{equation}

    with

    \begin{equation} \omega_{dd}=\frac{2\pi\times52.04 (\text{MHz}\cdot \text{nm}^{-3})}{r^3}. \label{eq:tikh-freq} \end{equation}

    A regularization parameter \(\alpha\) is defined to reconcile resolution and smoothness. To reach the best distance distribution, the function

    \begin{equation} G_\alpha(P)= \left|\left|S(t)-D(t)\right|\right|^2+\alpha\left|\left|\frac{d^2}{dr^2}P(r)\right|\right|^2 \label{eq:tikh-func} \end{equation}

    should be minimized. In the equation eq:tikh-func, the term \(\left|\left|S(t)-D(t)\right|\right|^2\) shows the squared of deviation between the simulated (\(S(t)\)) and (background corrected) experimental (\(D(t)\)) time domain signal while the term \(\alpha\left|\left|\frac{d^2}{dr^2}P(r)\right|\right|^2\) shows the smoothness of the distance distribution function (\(P(t)\)) weighted with the regularization parameter \(\alpha\). Larger \(\alpha\) yield a smoother distribution by reducing the sharpness which can ultimately lead to a broadening of the distance peaks. For a sample with a well-defined distance, smaller regularization factors \(\alpha\) are normally chosen to prevent this. For samples with broad distance distribution, larger regularization factor \(\alpha\) has shown to yield the best result. However, in most cases the shape of the distribution is not known in advance and the regularization factor \(\alpha\) should be optimized based on an extra step in the evaluation called L curve calculation. The L curve is a logarithmic plot of \(\rho(\alpha)\) versus \(\eta(\alpha)\) with

    \begin{equation} \rho(\alpha)=\left|\left|S(t)-D(t)\right|\right|^2_\alpha, \label{eq:tikh-rho} \end{equation} \begin{equation} \eta(\alpha)=\left|\left|\frac{d^2}{dr^2}P(r)\right|\right|^2_\alpha. \label{eq:tikh-eta} \end{equation}

    For good signal to noise data the plot shows an L shaped curve. The L curve and distance outcome for a sample dataset are shown Figure fig:deerEval. The best regularization parameter, placed near the edge of the L curve plot and the corresponding distance distribution are shown in green while two other extremes resulting in under-fitting or over-fitting of the data are shown in orange and blue, respectively.

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    Figure 17: DEER data evaluation for a doubly-labeled protein. A primary DEER data with fitted stretched exponential background (equation eq:echo-BG). B background corrected form factor (equation eq:echo-amp) in black and distance distribution function fit with different Tikhonov regularization factors in color. C The L curve for DEER data. \(\alpha=10\) is the best regularization parameter in this case. Small and large regularization parameters produce overfitted distance distribution with pronounced noise level and underfitted data with unrealistically broad distance distributions, respectively. D the distance distributions corresponding to different regularization parameters.

    1.3.5.6 Temperature, Concentration, Environment: Sensitivity Issues in DEER

    The length of a DEER trace and consequently the higher limit of the determinable distances is dictated by the transverse relaxation time of spin 1 (observer). Therefore, it is advantageous to lengthen the \(T_2\) time of spin-labeled proteins for DEER measurements. \(T_2\) relaxation can be further slowed by lowering the sample temperature to \(40-60\,K\) where the defining mechanism of \(T_2\) is solely proton spin diffusion. This can further be slowed down by deuterating the buffer and using a deuterated cryoprotectant (e.g. glycerol-d\(_8\)).

    Reconstitution of proteins in liposomes provide a physiological environment for membrane proteins. However, this procedure reduces the transverse relaxation time due to non-homogeneous confinement of labeled protein to liposomes and increased local proton concentration due to the lipid bilayer.

    2 Results

    In this chapter, the results are included as three published papers and one ready-to-submit manuscript. The supplementary material can be found in chapter 4 section 4.3 Supplementary materials.

    2.1 Exploring conformational equilibria of a heterodimeric ABC transporter

    The power stroke leading to conformational switch and consequent substrate transport in heterodimeric transporters has been a matter of disagreement in the field. This publication has dedicated the effort to shed light on the true conformational triggering mechanism along with the energy landscape of the transporter. The following is the output of a research work on the TM287/288 ABC transporter from 2015 to 2017 including more than 150 DEER distance measurements to sample all possible states and conformations as well as the effect of nucleotides to address this question. The importance of this work is the complete mapping of the cycle using EPR methods timachi-2017-explor-confor. This work was done in collaboration with the group of Prof. M. Seeger, University of Zurich. Supplementary materials are included in chapter 4 section 4.3.1 Exploring conformational equilibria of a heterodimeric ABC transporter - figures and supplementary materials.

    2.1.1 Contribution

    • More than 95% of the DEER distance measurements and all simulations/data evaluation.
    • Assistance in many protein purification activities at Free University Berlin.
    • DEER sample preparation at room or high temperatures.
    • Optimization of concentration, incubation time and mixing orders/ratios of different nucleotides.
    • Ranking of nucleotides in terms of their ability to switch the conformation.
    • Discussion of the data and writing of the manuscript.

    NOTE: Due to copyright considerations, this publication is not available in the online version, please refer to timachi-2017-explor-confor.

    2.2 Atomistic Mechanism of Large-Scale Conformational Transition in a Heterodimeric ABC Exporter

    Characterization of transporters using molecular dynamics simulations is of high interest in the field, as crystallography and other experimental techniques provide insight on frozen snapshot of static states of the transporter while MD simulations monitor intermediate states as well as energetic pathways of a conformational switch. However, MD simulations can sample a limited practical timescale and rely heavily on the initial conditions. EPR techniques can check for the reliability of these factors. This work is an example of such effort to reconcile two techniques for observing a transporter behavior in the environment relevant for functioning Goddeke-2018. This work was done in collaboration with the group of Prof. L. Schaefer, Ruhr University Bochum and Prof. M. Seeger, University of Zurich. The supplementary information of this work can be found in chapter 4 section Atomistic Mechanism of Large-Scale Conformational Transition in a Heterodimeric ABC Exporter - supplementary information.

    2.2.1 Contribution

    • MMM simulations, preparation, detection and evaluation of all DEER experiments.
    • Assistance in reconstitution of the transporter into liposomes.
    • Discussion of the data and writing of the manuscript.

    NOTE: Due to copyright considerations, this publication is not available in the online version, please refer to Goddeke-2018.

    2.3 The extracellular gate shapes the energy profile of an ABC exporter

    In this work, we probed the recently resolved crystal structure of TM287/288 using DEER distance measurements. Since the crystal was obtained in presence of a synthetic nanobody (Sybody) bound in the extracellular region, its effect on conformations and dynamics of the transporter is addressed as well. This manuscript is not published yet and the most recent revision follows crystal2017. This work was done in collaboration with the group of Prof. M. Seeger, University of Zurich. The supplementary information can be found in chapter 4 section The extracellular gate shapes the energy profile of an ABC exporter - supplementary information.

    2.3.1 Contribution

    This project builds upon previous unpublished work from 2015 probing the extracellular gate in the presence of some new D-to-A mutations as well as different E-to-Q and E-to-A mutations in the NBD region of the transporter to enable crystallographers to trap the outward-facing conformation of the transporter. Other contributions include:

    • Shaping the overall exposition by compiling and maintaining a report on the effect of all possible combinations of nucleotide, nanobody and mutations updated in a weekly basis through the 10-month time span of the project.
    • All EPR activities including simulations, sample preparation, experiments and evaluation.
    • Assessment and elimination of some artifacts in DEER distance measurements due to orthogonal labeling.
    • Discussion of the data and preparation of the EPR figures of the manuscript.

    NOTE: Due to copyright considerations, this publication is not available in the online version, please refer to crystal2017.

    2.4 Mode of Interaction of the Signal-Transducing Protein EIIA\(^{Glc}\) with the Maltose ABC Transporter in the Process of Inducer Exclusion

    In this work the interaction of the maltose E. coli transporter MalE-FGK\(_2\) with regulatory enzyme II EIIA\(^{Glc}\) is studied using a blend of biological and EPR techniques wuttge-2016-mode-inter. This work was done in collaboration with the group of Prof. E. Schneider, Humboldt University Berlin. The supplementary information can be found in chapter 4 section Mode of Interaction of the Signal-Transducing Protein EIIA\(^{Glc}\) with the Maltose ABC Transporter in the Process of Inducer Exclusion - supplementary information.

    2.4.1 Contribution

    • Simulation, experiments and evaluation of all EPR work.
    • Discussion of the data and preparation of the EPR figures of the manuscript.

    NOTE: Due to copyright considerations, this publication is not available in the online version, please refer to wuttge-2016-mode-inter.

    3 Conclusion and outlook

    Site-directed spin labeling EPR has proved to be an ideal tool to corroborate, substantiate and complement the results of other biophysical techniques. Studies detailed here further strengthened this notion especially in the field of ABC transporters. Here a short summary of the work on each ABC transporter studied as well as new techniques developed in the time span of my doctorate work and a reckoned outlook of those projects will be given.

    3.1 TM287/288

    In this work several crystal, homology models and MD structures of static states of TM287/288 have been validated and the energy landscape of the transporter has been unveiled. The propensity to sample energetically favored minima by the transporter in different conditions in the presence and absence of nucleotides or nucleotide analogs has been carefully evaluated. Thanks to the collaborative research between different groups and the work performed during my doctorate thesis, TM287/288 is currently one of the best characterized ABC exporters, the substrate translocation mechanism is established and the direct and allosteric effects of mutations in key residues of the sequence were discovered. Synthetic nanobodies, a currently popular field aimed at pharmaceutics, are examined and their effect on the energetics and dynamics of this transporter is investigated as an example of this type of interaction. The inhibitory, specificity and high affinity properties discovered here give hints towards the possibility of using nanobodies as specific drugs targeting each ABC transporter. Interesting future possibilities related to this projects are: 1. the use of orthogonal labeling strategies to study the interaction between nanobodies and transporters; 2. the use of spin-labeled drugs to monitor the substrate translocation mechanism; 3. the use of ODNP to focus on the changes in the water cavities during the IF/OF transition. I have already started working on Gd-labeled nanobodies as well as investigation of cavity water change on this ABC exporter using the ODNP setup in the lab, which will be briefly addressed in this chapter. First unpublished results are promising and will be followed up in the future lab work.

    3.2 MalE-FGK\(_2\)

    In our study on the maltose transporter MalE-FGK\(_2\), we have shown that unphosphorylated EIIAGlc is able to inhibit the maltose importer in any conformational state. Our data on the binding of EIIAGlc to the MalK dimer corroborated previous crystal structure on MalE-FGK\(_2\) in the presence of EIIAGlc chen-2013-carbon-catab. We showed that mutations in the EIIAGlc can alter the binding and thus hinder the inhibition. We also revealed the complete process of inhibition in the presence of glucose in agreement with the previous crystal structures and filled the gaps in the mode of EIIAGlc interaction in this context.

    3.3 Orthogonal site-directed spin labeling

    In orthogonal labeling, two or more different labels with different EPR spectra but having dipolar overlap are used on the same protein to enable tracking of several sites at the same time. This can be achieved using two different type of amino acid residues gmeiner-2017-orthog-tyros or using a different spin label (e.g. \(Gd^{+3}-DOTA\)) on binding proteins (extracellular nanobody for TM287/288 and maltose binding protein MalE for MalE-FGK\(_2\) complex) and mixing them with nitroxide-labeled protein under distinct conditions and concentration ratios. Orthogonal labeling also offers the possibility to perform in-cell dipolar EPR spectroscopy using reduction resistant nitroxides and gadolinium probes FEINTUCH2015415,qi-2014-gd-iii. An example of orthogonal labeling strategy on TM287/288 is shown in Figure fig:orthogonal. Gd-NO and NO-NO distances can be measured for any doubly- or triply-labeled positions.

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    Figure 18: Orthogonal spin labling strategy applied on TM287/288 with synthetic nanobody sybody#35 and first Gd-nitroxide DEER results. The available pairs of nitroxide spin labels were also used to probe the change in conformational equilibrium in the presence and absence of sybody. Gd-NO distances can be measured in different states to confirm binding of the sybody as well as the binding site. A spin labeled positions on TM287/288 using MTSL and on sybody#35 using maleimide-Gd-DOTA label. Lines connecting each two labels show the possible Gd-NO and NO-NO distance measurements (the sybody-transporter structure is still unpublished, see chapter 2 section 2.3 The extracellular gate shapes the energy profile of an ABC exporter ) B Gd-NO DEER distance measurements. \(54^{TM287}-271^{TM287}-71^{sybody}\) in the apo state shows no distance meaning that the sybody binds to the transporter only in the OF state. Distributions from all pairs agree with MMM simulations performed on the sybody-transporter crystal structure. Distances obtained on \(54^{TM287}-71^{sybody}\) and \(271^{TM287}-71^{sybody}\) provide the contribution from each nitroxide label to the Gd-NO distribution of \(54^{TM287}-271^{TM287}-71^{sybody}\) in the OF state of the transporter. NO-NO DEER distance measurements of this set of mutants are shown in section The extracellular gate shapes the energy profile of an ABC exporter. Renders created with VMD version 1.9.3, simulations done with MMM.

    3.4 Overhauser dynamic nuclear polarization (ODNP)

    As mentioned in chapter 1 section 1.3.4.2 Water accessibility, Overhauser dynamic nuclear polarization (ODNP) is a powerful tool to reveal information about the water accessibility of the spin label. In parallel to the work presented in this thesis, I optimized the hardware of the ODNP setup in the lab and developed control and evaluation software7. The reliability and reproducibility of the ODNP setup has now reached an acceptable level showing promising preliminary results on TM287/288 (shown in Figure fig:ODNP-TM200). The enhancement of the NMR signal is a qualitative sign of water accessibility of the labeled position if other experimental conditions are kept the same (e.g. EPR resonator Q factor, concentration of protein and spin labeling efficiency) and temperature effects are either compensated or avoided by using a cooling system. DNPy is a python code package which was developed during this work with the mentioned criteria in mind. A series of T\(_1\) experiments can be carried along with ODNP experiments at different powers of the input microwave to compensate for any unwanted sample heating effects. Additionally, TopDNP was developed to automate the complete ODNP experiment. These code packages provide a complete set of ODNP tools, maximizing reproducibility and minimizing the effort while maintaining complete control over the experiment and evaluation of the results.

    Sorry, your browser does not support SVG.

    Figure 19: Preliminary ODNP results obtained with the MTSL bound to \(200^{TM287}\). Visualization of the residue contact with the cavity water in the A apo state (PDB: 4Q4H) and B OF state (new crystal structure, see chapter 2 section 2.3 The extracellular gate shapes the energy profile of an ABC exporter). The residue \(200^{TM287}\) is shown in yellow van der Waals radius spheres. Cavity water is rendered as red and white surface. Upon conformational switch, the substrate cavity shifts towards periplasm to release the substrate decreasing the water accessibility of \(200^{TM287}\) residue. C ODNP results from two sets of states, apo and ATP-VO with three repetitions shown. As expected from the position of the spin-labeled residue, ATP-VO state shows less ODNP enhancement than the apo state, corresponding to less water accessibility. Renders created with VMD version 1.9.3.

    Bibliography

    4 Appendix

    4.1 Acknowledgements

    First and foremost, I would like to thank Prof. Enrica Bordignon for the tremendous amount of time and energy she invested to help and support me during my time in her group. I also thank all my colleagues in the group for instructive discussions and help they provided me: Markus Teucher, Tufa Assafa, Stephanie Bleicken, Sukhendu Nandi, Laura Galazzo and Svetlana Kucher. Especially, I appreciate the feedback and help on my thesis offered by Markus Teucher and Stephanie Bleicken.

    I would also like to thank all the scientific collaborators: Prof. E. Schneider and A. Licht from Humboldt University Berlin, Prof. M. Seeger and C. Hutter from University of Zurich and Prof. L. Schäfer and H. Göddeke from Ruhr University Bochum.

    I owe my deepest gratitude to my family members, particularly my parents who always stood by my side and supported me in all aspects of life.

    This work was realized by the financial support from the DFG grant 3000/1-2. Most of the experimental work was performed in the EPR RESOLV laboratories at Ruhr University Bochum.

    4.2 Software used for this thesis

    This thesis was written in GNU Emacs Org-mode provided by the scimax package. Protein renders were done with VMD version 1.9.3 and illustrations with Inkscape. MMM and EasySpin MATLAB code packages were used for DEER distance distributions and CW spectra simulations, respectively. DeerAnalysis MATLAB code package and DEER plot python script were used for extracting and plotting of experimental DEER distance distributions, respectively. TopDNP and DNPy python scripts were used to acquire and evaluate ODNP data, respectively.

    4.3 Supplementary materials

    4.3.1 Exploring conformational equilibria of a heterodimeric ABC transporter - figures and supplementary materials

    NOTE: Due to copyright considerations, this publication is not available in the online version, please refer to timachi-2017-explor-confor.

    4.3.2 Atomistic Mechanism of Large-Scale Conformational Transition in a Heterodimeric ABC Exporter - supplementary information

    NOTE: Due to copyright considerations, this publication is not available in the online version, please refer to Goddeke-2018.

    4.3.3 The extracellular gate shapes the energy profile of an ABC exporter - supplementary information

    NOTE: Due to copyright considerations, this publication is not available in the online version, please refer to crystal2017.

    4.3.4 Mode of Interaction of the Signal-Transducing Protein EIIA\(^{Glc}\) with the Maltose ABC Transporter in the Process of Inducer Exclusion - supplementary information

    NOTE: Due to copyright considerations, this publication is not available in the online version, please refer to wuttge-2016-mode-inter.

    Footnotes:

    1

    Name ABCG comes from another classification of ABC exporters in which 48 human exporters are grouped into 7 types ABCA to ABCG according to the range of substrate they transport.

    2

    However, in orthorhombic symmetry \(g_{xx}\ne g_{yy}\ne g_{zz}\).

    3

    Two spins are considered weakly coupled when their Larmor frequency difference (\(\Delta \omega = \omega_1-\omega_2\)) is considerably bigger than the dipolar coupling frequency (i.e. \(\Delta\omega \gg \left|\frac{\omega_{dd}}{4}\right|\) with \(\omega_{dd}\) calculated from eq:dd-ham-D-tensor). Since both \(\omega_1\) and \(\omega_2\) are magnetic-filed-dependent, this is also called high field approximation.

    4

    Pulses are shown as Gaussian in figures of this work as most of the pulse experiments were performed using an AWG setup with Gaussian pulses.

    5

    There are other sequences which are faster and measure phase memory time more accurately (e.g. Carr-Purcell-Meiboom-Gill (CPMG) sequence). Those techniques are not covered here.

    6

    Small thermal polarization of nuclear spins in NMR spectroscopy which are governed by Boltzmann distribution leads to a general lack of sensitivity.

    7

    The complete software suite for this setup has been developed by me and is openly available on SpinToolbox.com.

    Date: 2018-04-19 Thu 00:00

    Author: M. Hadi Timachi

    Created: 2018-10-08 Mon 14:59

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