Polarization Transfer Dynamics in Multi-Spin Systems Using the DREAM Scheme

Research Collection

Doctoral Thesis

Polarization transfer dynamics in multi-spin systems using the DREAM scheme

Author(s): Westfeld, Thomas

Publication Date: 2010

Permanent Link: https://doi.org/10.3929/ethz-a-006410379

Rights / License: In Copyright - Non-Commercial Use Permitted

This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use.

ETH Library DISS. ETH NO. 19196

Polarization Transfer Dynamics in Multi-Spin Systems Using the DREAM Scheme A dissertation submitted to ETH ZÜRICH

for the degree of Doctor of Sciences

presented by THOMAS WESTFELD

born September 9, 1979 citizen of the Federal Republic of Germany

accepted on the recommendation of Prof. Dr. Beat H. Meier, examiner Prof. Dr. Roland Riek, co-examiner

2010

Meiner Mutter

nanos gigantium humeris insidentes Bernardus Carnotensis

Contents

Abbreviations ix

Abstract xi

Zusammenfassung xiii

1. General Introduction 1 1.1. Quantum-mechanical Framework of NMR ...... 1 1.1.1. Hamiltonians in NMR ...... 1 1.1.2. Describing the Outcome of an NMR Experiment ...... 5 1.1.3. Average-Hamiltonian Theory ...... 6 1.1.4. Spherical-Tensor Representations and Rotations ...... 7 1.1.5. Magic-Angle Spinning ...... 9 1.1.6. Adiabatic Fast-Passage ...... 13 1.2. NMR on Biomolecules ...... 15 1.2.1. Liquid-State NMR ...... 15 1.2.2. Solid-State NMR ...... 17 1.3. The Assignment Problem ...... 21

I. Solid-State NMR Studies of the Prion Protein HET-s (156-289) 25

2. Introduction To Prion Proteins and Amyloids 27 2.1. Discovery of Prions ...... 27 2.2. Replication of Prions and Amyloid Fiber Formation ...... 28 2.3. Amyloid diseases ...... 30 2.4. Fungal Prions ...... 31

v vi Contents

2.5. The HET-s Prion ...... 32 2.5.1. Biological Background ...... 32 2.5.2. Solid-state NMR Studies on HET-s(218–289) ...... 33 2.5.3. The HET-s(156–289) Prion ...... 34

3. Experimental 37 3.1. Bacterial Strains ...... 37 3.2. Protein Expression and Puriﬁcation...... 37 3.2.1. Transformation of pET24-HET-s(156–289) Vector ...... 37 3.2.2. Expression of U-13C,15N HET-s (156-289) ...... 37 3.2.3. Expression of HET-s(156–289) Using Auto-Induction ...... 38 3.2.4. Cell Work-Up and Lysis ...... 38 3.2.5. Puriﬁcation...... 39 3.2.6. SDS–PAGE ...... 39 3.2.7. Fibrilization and Sample Preparation ...... 39 3.2.8. Preparation of Low Temperature Samples ...... 40 3.3. Electron Microscopy ...... 40 3.4. NMR Experiments ...... 40 3.4.1. Solid-State NMR Experiments ...... 40 3.4.2. Data Processing and Data Analysis ...... 43

4. Results 45 4.1. Expression of HET-s(156–289) ...... 45 4.1.1. Expression of U-13C,15N HET-s (156-289) ...... 45 4.1.2. Expression of HET-s(156–289) Using Auto-induction ...... 45 4.1.3. Refolding and Fibrilization of HET-s(156–289) ...... 47 4.2. Solid-State NMR studies ...... 47 4.2.1. Comparing HET-s(218–289) and HET-s(156–289) ...... 47 4.2.2. Chemical Shift Mapping ...... 56 4.2.3. Low-Temperature Measurements ...... 56 4.2.4. Using non Dipolar-Based Experiments ...... 62

5. Discussion 67 5.1. Solid-state NMR Spectra of HET-s(156–289) ...... 67 5.2. J-BasedSpectra...... 69 Contents vii

6. Conclusion 71

II. The DREAM Experiment in Multi-Spin Systems 73

7. Introduction to the DREAM Experiment 75 7.1. Theoretical Description ...... 76 7.1.1. The HORROR Experiment ...... 76 7.1.2. From HORROR to DREAM ...... 80 7.1.3. DREAM in Multi-Spin Systems ...... 83 7.2. Simulation Strategies ...... 85 7.3. DREAMing Away ...... 87

8. Experimental 91 8.1. Simulation of DREAM Transfer ...... 91 8.1.1. Simulating the Mixing Using Time-Slicing ...... 92 8.1.2. Simulating the Mixing Using Floquet Theory ...... 92 8.2. Experimental DREAM Spectra ...... 93 8.2.1. DREAM Spectra of Single Amino Acids ...... 93 8.2.2. DREAM Spectra of Ubiquitin ...... 94 8.2.3. Data Evaluation ...... 94

9. Results 97 9.1. Simulation Strategies ...... 97 9.2. Transfer Efﬁciency Dependence on Carrier Position and RF Field . . . 99 9.3. Cross Peak Patterns in Protein Spectra ...... 104 9.3.1. Experimental DREAM Spectra ...... 104 9.3.2. Simulated DREAM Spectra ...... 105 9.3.3. Comparing Simulated and Experimental DREAM Spectra . . . 105

10.Discussion 115 10.1. Simulation Strategies of DREAM Spectra ...... 115 10.2. Transfer Efﬁciency Dependence on Carrier Position and RF Field . . . 117 10.3. Cross Peak Patterns in Protein Spectra ...... 120 viii Contents

11.Conclusion 123

12.Outlook 125

Bibliography 129

Acknowledgements 143

Curriculum Vitae 145

Publications 147 Abbreviations

1D One dimensional 2D Two dimensional APHH CP Adiabatic-passage Hartmann-Hahn cross-polarization AHT Average Hamiltonian theory BSE Bovine spongiform encephalopathy CJD Creutzfeldt-Jakob disease CP Cross-polarization CSA Chemical shift anisotropy DARR Dipolar assisted rotational resonance DNA Deoxyribonucleic acid DREAM Dipolar recoupling enhanced by amplitude modulation FT Fourier transform GFP Green ﬂuorescent protein GSS Gerstmann-Sträussler syndrome HORROR Homonuclear rotary-resonance INEPT Insensitive nuclei enhanced by polarization transfer LAB Laboratory frame MAS Magic-angle spinning MiByte Mebibyte (1 Mebibyte = 10242 byte) MOL Molecular ﬁxed frame MRI Magnetic resonance imaging NMR Nuclear magnetic resonance NOE Nuclear Overhauser effect λ = OD600 Optical density at wavelength 600 nm PAS Principle axis frame ppm Parts per million Prion Proteinaceous infectious particle

ix x Contents

RF Radio frequency RNA Ribonucleic acid ROT Rotor ﬁxed frame SDS Sodium dodecyl sulfate STEM Scanning transmission electron microscopy TOBSY Through-bond spectroscopy TPPM Two pulse phase modulation WiW WURST–inverse–WURST WURST Wideband, uniform rate, and smooth truncation XiX x–inverse–x Abstract

In this thesis two projects are presented which demonstrate the application of solid- state NMR on prion proteins and the characteristics of a polarization transfer method in the context of biomolecular NMR. Prion proteins are linked with a number of neurodegenerative diseases such as bovine spongiform encephalopathy (BSE) in cattle or chronic wasting disease (CWD) in mule deer and elk. In humans known prion diseases are the Creutzfeldt-Jakob disease, the Gerstmann-Sträussler syndrome and kuru. The protein is therefore transformed from a soluble state into an infectious prion state in which it aggregates to amyloid plaques which consist of protein fibrils. The prion protein HET-s studied in this work is from the filamentous fungus Po- dospora anserina. In this organism the prion is involved in the recognition of the compatibility of other species before cell fusion. In this case the prion is not pathogenic, but has an important function for the fungus. Amyloids are not soluble and do not form crystals which make them inaccessible for standard protein structure determination techniques such as X-ray crystallography or liquid-state NMR. However solid-state NMR studies have been applied suc- cessfully to gain insight into the structure of prions. In the first project of this work a C-terminal fragment of HET-s from residue 156 to 289 is studied. This fragment can be divided into a prion forming domain from residue 218 to 289 and roughly the same number of residues which are located in the globular part of the protein from residue 156 to 217. It has been shown that the prion forming domain alone is able for form amyloid fibril which are infectious to the fungus but is not active with respect to its function to distinguish between compatible and non compatible cell fusion partners. In contrast the fragment studied here is in this respect biologically active. To characterize this fragment the protein was produced recombinantely by expression in E.coli. The uniformly 13C and 15N labeled sample was then used to collect

xi xii Abstract

different 2D correlation spectra at ambient and low temperature. This data was compared to the analogous spectra of the prion forming domain alone. It was possible to show that the prion forming domain has the same structure in HET-s(156–289) and HET-s(218–289) . The additional residues are visible in the spectrum at positions indicating that they are in a random coil. There are also resonances observed which indicate that some residues are in an alpha-helical conformation. The weak signal intensity and the observed random-coil chemical shift indicate that the part belonging to the globular domain of HET-s(156–289) is structurally disordered. The second project of this thesis demonstrates how a method for reintroducing the dipolar coupling in solid-state NMR under Magic Angle Spinning (MAS) can be tailored to facilitate the analysis of protein spectra. MAS is averaging the dipolar interaction between two spins. To use this dipolar coupling to promote polarization transfer it is reintroduced by applying radio frequency pulses. Such experiments are usually termed recoupling experiments. In this work the dipolar recoupling enhanced by amplitude modulation (DREAM) scheme is characterized when applied to multi-spin systems such as the proteinogenic amino acids. This scheme is used in the context of biomolecular NMR as an efﬁcient transfer step in multi-dimensional spectra which are recorded for the assignment of resonances in the spectrum to the nuclei in the molecule. It has been observed that different experimental parameters can lead to spectra in which signals of different amino acids are missing. To investigate this effect the DREAM scheme was simulated numerically on single amino acids. It is demonstrated that the irradiation frequency during the mixing sequence is the experimental parameter inﬂuencing the presence of cross peaks the most. By comparing the cross-peaks intensity between CA and CB in all proteogenic amino acids excluding tryptophane it is shown that there are experimental conditions under which cross-peaks of certain amino acids are attenuated. The simulations are compared to DREAM spectra recorded on ubiquitin. It is shown that the quantum- mechanical simulation of single amino acids are a good measure to estimate the cross- peak intensity in a protein spectrum. Finally it is shown how the transfer patterns can be deduced from the different chemical shifts of the spins contributing to the dipolar coupling network and the irradiation frequency during mixing. Zusammenfassung

Diese Arbeit besteht aus zwei Teilen. Im ersten Teil wird eine Festkörper-NMR Un- tersuchung an einem Fragment eines Prionproteins vorgestellt. Der zweite Teil befaßt sich mit den Eigenschaften einer Methode zum Polarisationstransfer, welche in der biomolekularen NMR ihre Anwendung findet. Prionenproteine sind das Pathogen in mehreren neurodegenerativen Erkrankun- gen wie z.B. Bovine spongiforme Enzephalopathie (BSE) in Rindern und chronic wasting disease (CWD) in Maultierhirschen und Elche. Bei Menschen sind bekannte Prionenkrankheiten die Creutzfeldt-Jakob Krankheit, das Gerstmann-Sträussler Syn- drom und Kuru. Das Protein geht dabei von einer löslichen zu einer unlöslichen Form über. Diese aggregieren zu Amyloidablagerungen, welche wiederum aus Proteinfi- brillen bestehen und das eigentliche Pathogen bilden. Das Prionprotein HET-s, welches in dieser Arbeit untersucht wird, stammt aus dem filamentösen Pilz Podospora anserina. In diesem Organismus steht es im Zusammen- hang mit der Kompatibilitätserkennung anderes Spezies vor der Zellfusion. In diesem Fall hat das Prion keine pathogene Wirkung, sondern hat eine wichtige Function. Amyloide können nicht mit den beiden standard Proteinstrukturaufklärungsme- thoden wie flüssig NMR oder Röntgenstrukturanalyse untersucht werden, da sie we- der löslich sind noch Kristalle bilden. Strukturelle Informationen über Prionen konn- ten jedoch mit Hilfe der Festkörper-NMR erhalten werden. Der erste Teil dieser Arbeit untersucht ein C-terminales Fragment von HET-s von Aminsäure 156 bis 289. Dieses Fragment kann in eine Prionendomäne von Amino- säure 218 bis 289 und einen ungefähr gleich langen Teil von Aminosäure 156 bis 217 unterteilt werden, wobei sich der letztere Teil in der globulären Domäne befindet. Es wurde gezeigt, dass ein Fragment welches ausschließlich aus der Prionendomä- ne besteht Amyloide bildet, welche für den Pilz infektiös sind. Es ist jedoch nicht in dem Sinne aktiv, daß kompatible Spezies vor der Zellfusion erkannt werden. Dies hingegen ist der Fall für das hier untersuchte Fragment.

xiii xiv Zusammenfassung

Zur Charakterisierung dieses Konstrukts wurde es rekominant in E.Coli expri- miert. Von der uniform 13Cund15N isotopenangereicherten Probe wurden ver- schiedene 2D Korrelationsspektren bei Raumtemperatur und tiefer Temperatur aufgenommen. Diese wurde mit analogen Spektren eines separaten Konstrukts verglichen, welches ausschließlich aus der Prionendomäne besteht. Es wurde gezeigt, daß die Prionendomäne in HET-s(156–289) und HET-s(218–289) die gleiche Struktur hat. Die zusätzlichen Aminosäuren sind im Spektrum an Positionen sichtbar, die auf eine random-coil Struktur hindeuten. Allerdings gibt es auch Resonanzen, die eine alpha- helikale Konformation einiger Aminosäuren nahelegen. Die geringe Signalintensität und die beobachteten random-coil chemischen Verschiebungen weisen darauf hin, daß die globuläre Domäne von HET-s(218–289) strukturell ungeordnet ist. Im zweiten Projekt wird gezeigt, wie eine Methode zur Wiedereinführung der Di- polkopplung in Festkörper-NMR gemessen unter Probenrotation am magischen Win- kel magic angle spinning (MAS) angepasst werden kann, um die Analyse von Prote- inspektren zu vereinfachen. Durch MAS wird die dipolare Wechselwirkung zweier Spins ausgemittelt. Um diese trotzdem zum Polarisationstransfer benutzen zu kön- nen, muss sie mittels Radiofrequenzpulsen wieder eingeführt werden. In dieser Ar- beit wird die Anwendung der Wiedereinführung der dipolaren Wechselwirkung mittels Amplitudenmodulation, genannt dipolar recoupling enhanced by amplitude modulation (DREAM) in Vielspinsystemen wie Aminosäuren charakterisiert. Diese Methodik kommt im Kontext der biomolekularen NMR als efﬁzienter Trans- ferschritt in multi-dimensionalen Spektren zum Einsatz, welche zur Zuordnung der Resonanzen im Spektrum zu den Atomkernen im Molekül aufgenommen werden. Es wurde beobachtet, daß unterschiedliche experimentelle Parameter zu Spektren mit fehlenden Signalen bestimmter Aminosäuren führen können. Um dieses Phänomen zu untersuchen, wurde die DREAM Sequenz an einzelnen Aminosäuren numerisch simuliert. Die Einstrahlfrequenz während der Mischung beeinﬂußt an meisten das Auftreten von Kreuzsignalen. Durch einen Vergleich der Kreuzsignalintensitäten zwischen CA und CB in allen proteogen Aminosäuren außer Tryptophan wird gezeigt, daß unter bestimmten Bedingungen die Signale bestimmter Aminosäuren abgeschwächt werden. Diese Simulationen werden mit experimen- tellen DREAM Spektren von Ubiquitin verglichen. Abschließend wird gezeigt, wie die entstehenden Transfermuster aus den chemischen Verschiebungen der dipolar gekoppelten Spins und der Mischeinstrahlfrequenz hergeleitet werden können. 1. General Introduction

1.1. Quantum-mechanical Framework of NMR

Nuclear Magnetic Resonance spectroscopy (NMR) is based on the observation of spin. It is a quantum mechanical property which has no classical counterpart. How- ever Felix Bloch has introduced as early as 1946 a set of phenomenological equations which describe the evolution of the nuclear magnetization in a static magnetic field [1]. These equation describe in analogy to a spinning top precessing in the earth’s gravitation field the dynamics of the bulk magnetization of an NMR-active sample. Despite their elegant simplicity they are not able to describe phenomena which are based on the quantum-mechanical properties of the spin such as J-couplings. As a consequence a quantum-mechanical treatment of the various effects in NMR is necessary. In the following the Hamiltonians describing the interactions in an NMR experiment are briefly introduced. It is assumed that the system under investigation 1 consists of spins with the spin quantum number 2 only. The Liouville-von Neumann equation is outlined which is used to calculate the time evolution of a given system under given Hamiltonians. Solid-state NMR spectra are often recorded by using a technique called magic angle spinning which is introduced together with the methods that allow an analytical description of this process.

1.1.1. Hamiltonians in NMR

The Zeeman Hamiltonian

The Zeeman Hamiltonian describes the interaction of a spin with a magnetic ﬁeld:

H = − γ ˆZ ∑ i Iˆi B0 (1.1) i

1 2 1 General Introduction

γ = i is an isotopic specific constant of spin i and named gyromagnetic ratio, Iî ( ) Iîx, Iîy, Iîz is the vector operator of the spin angular-momentum and B0 the magnetic field vector. In NMR this field is generally assumed to be static and by convention the field vector is aligned with the z-axis. In this simplified picture the magnetic field =( ) ω = −γ vector is given by B0 0, 0, B0 . With the Larmor frequency 0 B0 equation (1.1) can be rewritten as

H = ω ˆZ ∑ 0,i Iˆiz. (1.2) i

The RF Field Hamiltonian

The interaction of the spins with a RF field can be understood easily if the RF field is regarded as a changing electro-magnetic field. In analogy to the Zeeman Hamiltonian (1.1) the RF field Hamiltonian is given by

H ( )=− γ ( ) ˆRF t ∑ i Iî B1 t . (1.3) i ( ) B1 t is the field vector of the magnetic component of the RF irradiation and can be time dependent and composed of several frequencies. In practice the RF field is circular polarized and can be described as

( )= ( (ω + ϕ) (ω + ϕ) ) B1 t B1 cos 1t ,sin 1t ,0 . (1.4)

The generation of such a circular polarized field needs two coils around the sample which have to be aligned orthogonally and their individual RF fields must be exactly equal. The technical implementation is difficult. Instead linearly polarized magnetic fields are used which can be decomposed into two counter-rotating circular polarized fields. The time-dependent field vector then simplifies to

( )= ( (ω + ϕ) ) B1 t 2 B1 cos 1t ,0,0 . (1.5)

Although the field strength B1 of the RF field is typically around three orders of magnitude smaller than the dominating static magnetic field B0,theRFfield is able to rotate the magnetization away from the z-axis. The reason for this behavior is that the RF irradiation is resonant with the Larmor frequency. 1.1 Quantum-mechanical Framework of NMR 3

The trajectory of the magnetization during RF irradiation in the static laboratory frame is complicated. It is convenient to describe this process in a coordinate system ω which rotates with the RF frequency 1 around the z-axis. This frame is called the rotating frame. The two rotating field components of the linearly polarized field ro- − ω tate in this frame with a frequency of 0 and 2 1 respectively. The counter-rotating component is far off-resonant with the Larmor frequency and is usually neglected. The RF field Hamiltonian in the rotating frame is time-independent and given by:

H = − γ ˆ RF ∑ i Iˆx,i B1. (1.6) i

The Chemical-Shift Hamiltonian

The Larmor frequency as used in equation (1.2) is correct for a bare nucleus. In general the nucleus is surrounded by electrons which can change the strength of the magnetic ﬁeld strength at the nucleus. This perturbation of magnetic ﬁeld generates a shift of the Larmor frequency which is called chemical shift and is described by the following Hamiltonian:

Hˆ = − γ ˆ σ CS ∑ i Ii i B0. (1.7) i σ The chemical-shielding-anisotropy tensor i describes how this shielding of the magnetic field by the electrons is dependent on the relative orientation of the molecule with respect to the external magnetic field. In high field approximation only the component parallel to the static magnetic field σ i,zz is retained, as the axial terms Iˆx and Iˆy average to zero

H = σ ω ˆCS ∑ i,zz 0i Iˆiz. (1.8) i σ In the case of liquid-state NMR the orientation dependence of i,zz is averaged by σ the isotropic tumbling of the molecules in solution. In this case i,zz in equation (1.8) σ is replaced by iso which is deﬁned as follows

1 σ = σ + σ + σ . (1.9) iso 3 i,xx i,yy i,zz In solid-state NMR this averaging of the chemical shift by isotropic tumbling can 4 1 General Introduction be mimicked by a technique termed “magic angle spinning” (MAS) which will be discussed in section 1.1.5.

The Dipolar-Coupling Hamiltonian

The dipolar coupling can be understood in a classical picture if one imagines two magnetic dipoles which are inﬂuencing each other. The interaction energy of these μ μ dipoles with their corresponding dipole moments 1 and 2, respectively is given by μ = 0 1 μ · μ − 3 (μ · )(μ · ) E π | | 3 1 2 2 1 r12 2 r12 (1.10) 4 r12 r12 The vector r12 is connecting the two dipole moments through space. Equation 1.10 results in the dipolar-coupling Hamiltonian for a multi-spin system as follows δ(i,j) Hˆ = ∑ − D ˆ ·ˆ − 3 (ˆ · )(ˆ · ) D Ii Ij 2 Ii rij Ij rij (1.11) ij,i

δ(i,j) With the dipolar constant D deﬁned as

( ) μ γ γ h¯ δ i,j = − 0 i j D 2 π 3 . (1.12) 4 rij In high magnetic ﬁelds, the dipolar-coupling Hamiltonian for a homonuclear spin system is given by

( ) δ i,j (3cos2 θ − 1) Hˆ = D ij ˆ ˆ − 1( ˆ+ ˆ− + ˆ− ˆ+) D ∑ 2IizIjz Ii Ij Ii Ij . (1.13) ij,i

( ) δ i,j (3cos2 θ − 1) H = D ij ˆD ∑ 2IˆizIˆjz. (1.14) ij,i

The dipolar interaction is quantiﬁed by the dipole-dipole coupling constant dij 1.1 Quantum-mechanical Framework of NMR 5

which is given by

(i,j) ( − 2 θ ) ( ) δ 1 3cos ij d i,j = D (1.15) 2 2 ( ) Besides known physical constants, d i,j depends on the orientation θ of the inter- − nuclear vector with respect to the magnetic ﬁeld and on the distance r 3. Due to its orientation dependency the dipolar coupling can not be observed in liquid-state NMR because it is trace-less and therefore averaged to zero by the molecular tumbling.

The J-Coupling Hamiltonian

In contrast to the dipolar coupling the J-coupling is not a direct interaction between the spins, but is mediated through electrons participating in a chemical bond between the atoms. This makes the J-coupling a valuable tool for the application of NMR spectroscopy in a chemical environment as the J-coupling network mirrors directly the constitution of the molecule. The corresponding Hamiltonian has the form

H = π ˆJ, aniso 2 ∑ Iˆi J ij Iˆj (1.16) ij,i

J ij is the J-coupling tensor. The remaining anisotropic parts of the J-coupling are small and often ignored. The isotropic part for a homonuclear two-spin system is given by

H = π ( ) ˆJ 2 Jij Iˆi Iˆj (1.17)

with Jij equal to the average of the diagonal elements of J ij

1 J = (Jij + Jij + Jij ). (1.18) ij 3 xx yy zz

1.1.2. Describing the Outcome of an NMR Experiment

In section 1.1.1 the interactions present in a NMR experiment are introduced. To make predictions on the result of a measurement the state of the spin system has to be described. Quantum-mechanically it can be expressed either by the wave function ψ(t) or by the density operator ρ(t) [2, 3]. 6 1 General Introduction

If relaxation is disregarded, the time evolution of the density operator under a given Hamiltonian Hˆ is described by the Liouville-von Neumann equation

d ρˆ(t)=−i Hˆ , ρˆ(t) . (1.19) dt The Hamiltonian Hˆ consists of the different interactions introduced in previous section 1.1.1. For time-independent Hamiltonians the solution of equation (1.19) is given by

ρˆ(t)=exp −iHˆ t ρˆ(0) exp +iHˆ t . (1.20)

From a more formal point of view this corresponds to a rotation of the density operator ρˆ around the Hamiltonian Hˆ . This is one of the main concepts of the product operator formalism, which is widely used in liquid-state NMR [4].

1.1.3. Average-Hamiltonian Theory

The presented solution (1.20) of the Liouville-von Neumann equation is valid for time-independent Hamiltonians only. In NMR this is not always the case. How- ever sometimes it is possible to approximate a time-dependent Hamiltonian by a time-independent one simply by neglecting all the time-dependent (“non-secular”) contributions. An example of this treatment is given by the derivation of the RF field Hamiltonian in the rotating frame in equation (1.6) as all counter-rotating time- dependent terms are neglected. In this example it is a good approximation because the size of the Zeeman Hamiltonian and with it the Larmor frequency is much larger than the the RF field strength. A more general approach is Average-Hamiltonian theory. To apply Average-Ham- iltonian theory two requirements must be fulfilled: first, the Hamiltonian must be τ H ( )= periodic. This means that it is possible to defineacycletime C for which ˆ t H ( + τ ) ˆ t C holds. Second, the observation is stroboscopic and synchronized with in- τ teger multiples of the cycle time C. Furthermore it is assumed that during this cycle H H time the Hamiltonian consists of two piece-wise constant Hamiltonians ˆ1 and ˆ2 τ τ withadurationof 1 and 2, respectively. It has been derived by Haeberlen and Waugh [5] that it is possible to expand the 1.1 Quantum-mechanical Framework of NMR 7 time-dependent Hamiltonian into an average Hamiltonian of the form

(0) (1) (2) Hˆ = Hˆ + Hˆ + Hˆ + ... (1.21) with

(0) Hˆ = 1 Hˆ τ + Hˆ τ τ 1 1 2 2 C (1) − Hˆ = i Hˆ τ Hˆ τ τ 2 2, 1 1 2 C (2) − Hˆ = i Hˆ τ Hˆ τ Hˆ τ + Hˆ τ Hˆ τ Hˆ τ τ 2 2, 2 2, 1 1 2 2, 1 1 , 2 2 (1.22) 12 C

This expansion of a time-dependent Hamiltonian into a series of time-independent ones can be generalized for an arbitrary number of piece-wise constant Hamiltonians and further to continuously time-dependent Hamiltonians. The derivation for this case will not be presented here, but can be found in the literature [5]. The different terms of the series expansion of a continuously time-dependent Hamiltonian is given by

τ C (0) Hˆ = 1 Hˆ ( ) τ dt1 t1 C 0 τ C t2 (1) − Hˆ = i Hˆ ( ) Hˆ ( ) τ dt2 dt1 t2 , t1 2 C 0 0 τ C t3 t2 (2) − Hˆ = 1 Hˆ ( ) Hˆ ( ) Hˆ ( ) + Hˆ ( ) Hˆ ( ) Hˆ ( ) τ dt3 dt2 dt1 t3 , t2 , t1 t3 , t2 , t1 . 6 C 0 0 0 (1.23)

1.1.4. Spherical-Tensor Representations and Rotations

In NMR rotation operations are common. Examples are the rotation of operators e.g. by RF pulses or the rotation of coordinate frames like in the case of the rotating frame. By using spherical tensors, these rotations are simpliﬁed. The full derivation of the 8 1 General Introduction

spherical tensors can be found in the book of Slichter [2] or Mehring [6]. In general the Hamiltonian is a scalar operator because it represents the energy of a quantum-mechanical system which is a scalar quantity. The Hamiltonian can be

decomposed into a scalar product of a spin tensor Tˆ,m and a space tensor A,m:

N H = (− )m · ˆ ∑ ∑ 1 A,m Tˆ,−m. (1.24) =0 m=− N is the rank of the interaction. In NMR there are interactions of rank one (Zeeman interaction and chemical shift) and of rank two (dipolar interaction and J interaction). Rotations of spherical tensors can be formally written as

new = oldD N (α β γ) A,m ∑ A,m m ,m , , . (1.25) m =− new A,m are the components of the tensor expressed in the new frame of reference. old A,m are the components in the old frame. The two frames are related by a three- dimensional rotation which is deﬁned by the Euler angles α, β and γ. The convention is made that the three Euler rotations are carried around the z, y and z axes, respec- D N (α β γ) tively. m ,m , , are elements of the Wigner rotation matrix for a tensor of rank N. These elements can be regarded as weighting factors as all the components of the same rank are mixed. The Wigner rotation matrix elements can be expressed in terms N (β) of the reduced Wigner elements dm ,m as follows:

D N (α β γ)= −iαm N (β) −iγm m ,m , , e dm ,m e . (1.26) In solid-state NMR multiple coordinate systems are play an important role in the theoretical framework used to describe experiments. Usually the spatial parts of the Hamiltonians are converted from their principle axis frame (PAS) of the interaction via several consecutive rotations to the laboratory frame of reference (LAB) (see ﬁg- ure 1.1). Four different frames of reference can be involved:

1. The principle axis frame (PAS) is the frame in which the axes of the coordinate system align with the principle axes of the tensor. When expressed in a cartesian representation this corresponds to a 3×3 matrix with only the diagonal popu- lated. The interaction can either be described by these three diagonal values or 1.1 Quantum-mechanical Framework of NMR 9

more commonly by the isotropic average a iso, the anisotropy δ and the asymmetry η. In spherical tensor notation the components or the spatial part are given by PAS = −√1 iso PAS = 3 δ PAS = 1δη A0,0 a A2,0 A2,±2 (1.27) 3 2 2

2. The molecular fixed frame (MOL): In a system with multiple interactions it can be useful to define a common frame of reference which is fixed in respect to the molecule. The orientation of the coordinate axes is arbitrary, e.g. for some application it could be beneficial to align one axis with one bond. This frame can also be useful if the sample is not consisting of molecules, for example a calcium fluoride powder. In this case the “molecular” frame can be aligned with the crystal axes.

3. The rotor fixed frame (ROT): In powdered samples a special technique to narrow the resonance called “Magic-Angle Spinning” (MAS) is often applied. It will be discussed in detail in section 1.1.5. The transformation into the rotor fixed frame relates each possible orientation of a single crystallite to a common coordinate system fixed to the rotor. In the case of an ideal powder all crystallite orientations are present.

4. The laboratory frame (LAB) is the ﬁnal frame of reference. By convention its z-axis is aligned with the static magnetic ﬁeld. In the case of MAS the transformation from the ROT to the LAB frame involves a time-dependent Euler angles

ω rt as the rotor is moving. In addition the rotation axis is inclined with respect to the static magnetic ﬁeld by the “magic angle” θ m. The value of this angle and its consequences to the spectrum will be discussed in section 1.1.5.

1.1.5. Magic-Angle Spinning

Solid-state NMR spectra of a static powdered sample are often broad and featureless. The powder includes all possible molecular orientations and so the spectrum is dom- inated by anisotropic contributions (e.g. the CSA or the dipolar coupling). In the case 10 1 General Introduction

LAB ROT

PAS MOL

Figure 1.1. Illustration of the four coordinate systems used in solid-state NMR on powdered samples under MAS. The four different frames are the laboratory frame (LAB), the rotor-ﬁxed frame (ROT), the molecular ﬁxed frame (MOL) and the principle axis frame (PAS) with respect to the interaction. The triplet of Euler angles needed to rotate one frame to the other are given in the arrows. 1.1 Quantum-mechanical Framework of NMR 11

of a non-decoupled static 13C spectrum the resonances are several kHz broad which leads to a complex spectrum with overlapping signals.

In the late 1950s a method for narrowing the lines of powdered spectra was developed independently by Andrew et al. and Lowe et al. [7, 8]. Both authors suggest that a rapid sample rotation around an inclined axis with respect to the main magnetic ﬁeld can lead to an averaging of the anisotropic contributions and thus lead to a line-narrowing effect. By the sample rotation the spatial part of the Hamiltonian is modulated with the rotation frequency ω r:

ω Hˆ ( )= im rt (θ ) ROT ˆ t ∑ e dm,0 r A,m T,0. (1.28) m=−

For this continuously changing Hamiltonian a cycle time of τr =(2π)/ω r can be deﬁned. The angle θ r is the angle between the static magnetic ﬁeld and the rotation axis. By applying the average Hamiltonian formalism presented in section 1.1.3 a zeroth-order Hamiltonian of the following form can be obtained:

τr (0) 1 Hˆ = Hˆ (t) dt τr 0 (1.29) 3cos2 θ − 1 = r AROTTˆ . 2 2,0 2,0

The average Hamiltonian in zeroth order vanishes if the inclination angle is set such ◦ that θ = arccos √1 ≈ 54.7 . This angle is called the “magic angle” and is indicated r 3 by the symbol θ m. Isotropic interactions which are represented as zeroth-rank tensors 0 (θ ) are unaffected by MAS because the corresponding Wigner matrix√ element d0,0 m evaluates to 1. First rank tensors on the other hand are scaled by 1/ 3.

As an example the effect of MAS on the chemical shift Hamiltonian of k spins will be discussed. The ﬁrst three orders of the average Hamiltonian are given by: 12 1 General Introduction

τr (0) ω Hˆ = − 0,k σ ˆ CS ∑ zz,k Ikz dt τr k 0 τ r √ ω − ω − ω ω ω − 0,k 2i rt ROT + i rt ROT − i rt ROT + 2i rt ROT ˆ ∑ e A2,−2 2 e A2,−1 e A2,1 e A2,2 Ikz dt 3τr k 0 = − ω σ ∑ 0,k k,zzIˆkz k τr t2 (1) Hˆ = − i Hˆ ( ) Hˆ ( ) = CS dt2 CS t2 , CS t1 dt1 0 2τr 0 0 ( ) Hˆ 2 = CS 0 (1.30)

In this case the zeroth order average Hamiltonian is the full average Hamiltonian and describes the system exactly if observation occurs only at integer multiples of the

cycle time τr as required in section 1.1.3. This result is independent of the spinning frequency which means that the anisotropic parts of the chemical shift are always averaged to zero. The restriction of the sampling also means that the spectral width of the spectrum equals the spinning frequency. In consequence all spinning side bands which are present at integer multiple of the spinning frequency are folded back onto the center band. In practice the sampling frequency is chosen based on the positions of the resonances in the spectrum and not based on the spinning frequency. In this case all spinning side bands can be observed experimentally. The intensity of these side bands can be determined analytically and is given by an infinite sum over Bessel functions. From the intensities of the side band manifold at a given spinning frequency tensor parameters like the anisotropy δ and the asymmetry η can be extracted [9]. In a publication by Maricq and Waugh [10] the effect of MAS on different Hamil- tonians is discussed in detail. One important point is the classification of interactions into inhomogeneous and homogeneous. An inhomogeneous interaction has a van- H ( ) H ( ) = ishing commutator of the form ˆ t2 , ˆ t1 0. For a homogeneous interaction this commutator does not vanish. In the above example in equation (1.30) the first 1.1 Quantum-mechanical Framework of NMR 13

and second order average Hamiltonian evaluate to zero because the chemical shift is an inhomogeneous interaction with respect to sample rotation. The opposite is true for the homonuclear dipolar coupling with is a homogeneous interaction and so the higher order average Hamiltonian terms do not vanish. A priori it is not known how many terms of this series expansion are needed to approximate the full average Hamiltonian.

1.1.6. Adiabatic Fast-Passage

Adiabatic methods have been used since the very early days of NMR [1], but are still used widespreadly in contemporary NMR [11–13]. The key feature of adiabatic experiments is that the density operator is manipulated while it stays aligned with the Hamiltonian. Due to their parallel alignment the density operator does not evolve under the Hamiltonian as shown by the Liouville-von Neumann equation (1.19). The Hamiltonian is slowly changed and thereby “dragging” the density operator. This behavior is shown graphically in ﬁgure 1.2(b). Alternatively a “sudden” inversion could be performed (ﬁgure 1.2(a)), in which the density operator does not commute with the Hamiltonian and evolves under this time-independent Hamilto- nian.

(a) A “sudden” inversion (b) An adiabatic inversion

Figure 1.2. Comparison of two inversion methods in NMR. In the case of a “sudden” inversion the density operator nutates around a time-independent Hamiltonian. In an adiabatic inversion the density operator stays aligned with a slowly changing Hamiltonian and “dragged” around. 14 1 General Introduction

In practice the Hamiltonian is often the RF Hamiltonian as it is under direct control by the spectroscopist. Among the most common application is an adiabatic inversion which is done by sweeping the frequency of an RF field through the spectrum from a large positive to a large negative offset. Every resonance in the spectrum independent ω of its frequency is inverted. In the case of a constant RF amplitude RF the spin-lock field changes as shown in figure 1.3. In the ideal case of the frequency offset going from Ω(0)=+∞ to Ω(τ)=−∞ the direction of the Hamiltonian is inverted over the duration of the sweep τ from the +z to the −z direction.

Figure 1.3. Field components of an RF frequency sweep with constant amplitude. The length of the ω ( )= Ω( )2 + ω2 effective ﬁeld is given by eff t t RF.

The Hamiltonian at an arbitrary time during the sweep is characterized by the ef- ω ( )= Ω( )2 + ω2 Θ( ) fective field strength eff t t RF and the angle t between the field vector and the positive z-axis . An efficient “dragging” of the density operator by the changing Hamiltonian is only possible if the Hamiltonian is changing slowly. This adiabatic condition is given in equation (1.31). dΘ(t) ω ω (t) with Θ(t)=arctan RF (1.31) dt eff Ω(t) It can be seen that the critical situation during the sweep is at the resonance condition when the length of the effective field is given by the RF field only. To describe the adiabatic condition of equation (1.31) quantitatively, the adiabaticity factor Q is introduced as follows: 1.2 NMR on Biomolecules 15

ω (t) Q(t)= eff (1.32) dΘ(t)/dt The adiabaticity factor Q is a measure how good the parallel alignment of the density operator and the Hamiltonian can be retained throughout the sweep. It has been shown by Haase et al. [14] and Schäfer et al. [15] that it is possible to derive an analytic expression which relates the minimal adiabaticity Q min at the center of a linear amplitude sweep to the inversion efficiency. In their publication they show that for a = ≈ minimal adiabaticity factor as low as Q min 1 still an inversion efficiency of 65% is achieved. The main advantage of adiabatic techniques is that they are robust with respect to offset effects. These methods are applied when large bandwidths have to be covered. This is the case in magnetic resonance imaging (MRI) when surface coils are used. They are directly attached to the patient and offer higher sensitivity but have the major drawback of generating inhomogeneous RF fields. In this setup the density operator can nevertheless be precisely manipulated using adiabatic methods [16]. In spectroscopy the inversion of a density operator by an RF field is a very common operation. Because of that adiabatic pulses and adiabatic passages have been used for many applications (e.g. for decoupling [17–19], heteronuclear polarization transfer [20–22] and also homonuclear polarization transfer [23–26]).

1.2. NMR on Biomolecules

1.2.1. Liquid-State NMR

For structural investigations on biomolecules two techniques are able to deliver information at the atomic level. First, X-ray diffraction techniques provide high resolution structures of proteins and represent the de facto “gold standard” of the structure elucidation techniques available today. The crucial step in obtaining these precise structures is the ability to produce a sample of the required quality. For X-ray methods three dimensional single-crystals of the sample have to be grown which diffract beyond 3 Å. This process can be time-consuming and cumbersome especially in the case of membrane proteins. Second, using nuclear magnetic resonance spectroscopy (NMR) it is also possible 16 1 General Introduction

to gain insight into the structure of biomolecules at atomic resolution. In contrast to X-ray, liquid-state NMR has other sample requirements: the molecule of interest must be soluble in a solvent in a sufﬁciently high concentration without aggregating. No crystallization is necessary. Furthermore the molecule has to be stable in this environment for the duration of the measurement which depends on the concentration of the molecule and can be as long as weeks. To maintain a steady environment during this time period, salt concentration, pH of the solvent and temperature are controlled. The underlying physical phenomena rendering liquid-state NMR a versatile and powerful method are the rapid molecular tumbling of the molecule of interest in solution and the long lifetime of the spin states. Molecular tumbling averages all anisotropic interaction to zero, which simpliﬁes the Hamiltonian to the form:

Hˆ = Hˆ + Hˆ + Hˆ iso + Hˆ Z RF CS J. (1.33) H ˆZ describes the dominant Zeeman interaction between the nuclear spin and the H static magnetic field B0, ˆRF is the interaction of the spins with the applied radio- Hˆ iso frequency (RF) field. CS represents the isotropic chemical shift of each spin which can be understood as a perturbation to the static magnetic field B0 by the electrons surrounding the nucleus. These Hamiltonians have been discussed in more detail in section 1.1.1. The only coherent mechanism to transfer magnetization between spins in liquid- H state NMR is the J-coupling which is given by the last term ˆJ in equation (1.33). Relaxation phenomena present in the system have been omitted in equation 1.33. One reason why relaxation occurs is because the anisotropic interactions are mod-

ulated by the isotropic tumbling leading to spin–lattice (T1) and spin–spin (T2)re- τ laxation. For proteins up to 40 kDa the correlation time C which describes the time a molecule needs to rotate around one radian, is in the order of nanoseconds. For larger proteins the longer correlation time does not lead to a full averaging of the

anisotropic interactions, which can be observed as faster T2 relaxation. This results in a faster decaying signal and increased line width of the resonances in the spectrum. This problem was tackled by using relaxation-optimized pulse sequences such as TROSY [27] enabling studies of larger proteins of up to 100 kDa. The Zeeman interaction of the spin with the magnetic is weak, which leads to a small splitting of the eigenstates. In consequence the population difference in ther- 1.2 NMR on Biomolecules 17

mal equilibrium as described by the Boltzmann distribution is small which results in weak signal. To make NMR applicable, technical advancements like the develop- ment of Fourier-transform (FT) NMR [28], high ﬁeld super-conducting magnets and the introduction of cryogenic probe heads [29] improved the sensitivity of NMR measurements tremendously. This progress was supplemented with new techniques like multi-dimensional NMR[30], selective pulses [31, 32], composite pulse decoupling [33–35] and in general more sophisticated pulse sequences [36]. Especially better polarization transfer techniques play a key role in the success of three-dimensional spectroscopy [37], which made the analysis of spectra with large number of resonances possible.

1.2.2. Solid-State NMR

Although first NMR measurements in the condensed phase were done both in liquid phase by Bloch et al. [1, 38] and in solid phase by Purcell et al. [39], the application of NMR spectroscopy for analytical purposes on organic molecules in the solid phase was difficult. The reason for this is that the molecules under investigation are static with respect to the applied magnetic field. This means that the assumption that all anisotropic interactions vanish no longer holds and thus the simplified Hamiltonian of equation (1.33) is no longer valid. The full anisotropic Hamiltonian for a system in the solid-state is of the form:

H = H + H + H + H + H ˆ ˆZ ˆRF ˆCS ˆD ˆJ. (1.34) H The main difference is that in addition to the new term ˆD which is the dipole- H dipole interaction between two nuclei, also the chemical shift term ˆCS is now anisotropic in nature. This can be easily understood by considering that the shielding electrons are not equally distributed around the nucleus, but instead polarized by the chemical bonds they are contributing to. A widely-used technique to obtain well-resolved spectra is to record them under magic-angle spinning (MAS). As shown in section 1.1.5 MAS can be used to average anisotropic contributions to the Hamiltonian. Experiments show that the averaging effect which leads to a line narrowing depends on the spinning frequency. In an average Hamiltonian picture this hints at the 18 1 General Introduction

presence of contributions to the Hamiltonian which are homogeneous with respect to sample rotation. As shown by Maricq and Waugh [10] the homonuclear dipole– dipole interaction is a homogeneous interaction which is reduced in magnitude and altered by the MAS but is not averaged out fully unless the spinning frequency is inﬁnitely large. Because of this large residual line width of the 1H resonances, modern biomolecular NMR focuses on low-γ nuclei like 13C,15N and additionally 31P in the case of nucleic acids. However in recent years special techniques have evolved which allow protons to be studied in the solid phase. In this case dilution of the strongly dipolar coupled spin bath is necessary, which can be achieved by deuteration [40]. Another approach is to conduct the NMR experiment at high MAS frequencies [41] as the residual line width of a homogeneously broadened line scales with the inverse of the MAS frequency [42]. It has been outlined in section 1.1.5 how the heteronuclear dipolar coupling is fully averaged out by MAS. In more complex spin systems in which a strong homonuclear dipolar coupling is present this averaging is not complete anymore. A spectrum with sharp resonances can in this case be obtained by applying an additional RF irradiation on protons. In a quantum-mechanical picture the Hamiltonian of the interaction becomes doubly modulated. The spatial part is modulated by the MAS and simultaneously the spin part is modulated by the RF irradiation. First decoupling was done using cw-irradiation. This very basic approach was replaced as late as 1995 by a broad-band multi-pulse decoupling scheme called TPPM [43]. For high spinning speeds the XiX decoupling sequence was introduced in 2002 [44]. An analytic description of these multi pulse decoupling sequences is complicated and often involves more complex treatments e.g. using Floquet theory [45]. Contrasting liquid-state NMR where all coherent polarization transfer is mediated by the weak J-coupling, in the solid-state the much stronger dipole–dipole interaction can be used. As pointed out earlier this interaction is averaged by MAS and has to be reintroduced by RF irradiation which interferes with the MAS. To create the initial polarization on 13C a cross-polarization (CP) step [46] is used to transfer polarization from protons to carbon. The reason for using CP is twofold: the magnetization on protons is larger on protons than carbons due to the about four times higher gyromagnetic ration γ. This leads to an increased initial polarization on carbons and ﬁnally to a higher signal to noise ratio. The second reason is that the protons relax 1.2 NMR on Biomolecules 19

much faster due to their strong homonuclear dipolar couplings. This means that the recycle delay of each scan needed to allow the spin system to return to equilibrium can be much shorter, leading to a higher signal to noise ratio per unit time. There is a broad variety of homo- and heteronuclear mixing steps to be employed in multi-dimensional spectroscopy. There are schemes which rely on cw-irradiation (e.g. DREAM [47]), discrete pulses (e.g. REDOR [48]), phase modulated irradiation (e.g. C and R sequences [49] or TOBSY [26]) or do not use any irradiation at all (e.g. PDSD). Two-dimensional experiments can be divided into four distinct parts: the ﬁrst part is a preparation step. In solid-state NMR this step often involves a cross-polarization transfer. The second part is the evolution of the spin system. The evolution period contains a variable time delay and is usually denoted t1. The third step is the mixing step in which the prepared density operator evolves under a Hamiltonian which promotes polarization transfer. The fourth part of the experiment is ﬁnally the de-

tection of the NMR signal in dependence of the variable delay t1. By recording a series of spectra with incrementing t1 a two-dimensional data set is obtained. A two- dimensional Fourier transform converts the recorded interferogram into a spectrum in which a polarization transfer is visible as cross peaks between the two transfer partners. In figure 1.4 two 2D pulse sequences are outlined. The DREAM transfer is an adiabatic method which makes the polarization transfer more efficient and more robust against misadjustments of the RF field used for mixing or offset effects caused by the chemical shift distribution. Although the TOBSY method is per se not an adiabatic 1 method, a single C-element used for the C924 sequence can be constructed out of two adiabatic inversions using WURST [25] pulses. As shown in section 1.1.6 adiabatic inversions are robust with respect to chemical shift offsets or RF inhomogeneity. In this case where many inversions are concatenated a high inversion efficiency is crucial as pulse imperfections would accumulate. The difference between these two experiments is that DREAM is a double-quantum mixing sequence which generates a characteristic inversion of the sign of the signal after each transfer step. The TOBSY experiment is special among the mixing sequences used in solid-state NMR as it uses the J-coupling to transfer magnetization. As this is the weakest interaction in the full Hamiltonian a mixing Hamiltonian is generated in 1 which all other contributions are suppressed by the C924 sequence. 20 1 General Introduction

decoupling CW decoupling CP 1H

t mixing CP 1 13C

dcc Jcc

1 DREAM TOBSY WiW924

Figure 1.4. Solid-state NMR pulse sequences used for homonuclear 13C–13C correlations experiments. After creation of initial 13C magnetization by an adiabatic cross-polarization step and frequency labeling during t1 two different mixing steps can be used. The main difference between these two schemes is that the TOBSY scheme is using the JCC coupling whereas the DREAM scheme is based on the dipolar coupling. In this case the C-elements of the TOBSY sequence are build by using adiabatic WURST pulses. 1.3 The Assignment Problem 21

The combination of fast MAS, elaborated multi-pulse sequences and high-ﬁeld magnets make solid-state NMR a valuable tool for answering biophysical questions [50, 51]. As solid-state NMR does not rely on molecular tumbling to generate highly- resolved spectra there is no intrinsic limit given by relaxation as in liquid-state NMR. The limits in solid-state NMR are currently given by the resolution in the spectrum. Even with multi-pulse decoupling and fast MAS the line width tends to be bigger than in the liquid phase.

1.3. The Assignment Problem

Although the phenomenon of nuclear magnetic resonance has been first studied by physicist it turns out to be a valuable tool for chemists, material scientists and biolo- gists. The acquired spectra which show the resonance frequency of the nuclei have to be translated from this physical property to the chemical or structural information of interest e.g. the chemical constitution. The first step is to identify which nuclear resonance frequency is caused by which spin in the molecule under investigation. In small molecules this assignment process can be straightforward since the chemical bonding topology of the atom determines the chemical shift of the nucleus. This task gets more demanding if more nuclei have a similar electronic environments thus a similar chemical shift. In this case resonance lines can overlap depending on their line widths and make the assignment more challenging. This situation is commonly found in the case of synthetic or biological poly- mers, consisting of similar repetitive units. A way of solving this problem is to acquire multi-dimensional spectra. This approach was pioneered by Jeener [52] and developed by Ernst [53]. The advantage of two-dimensional spectra is that the relationship of two atoms is shown instead of just the resonance frequency of each atom independently. The relationship between these atoms is defined by the experiment performed: e.g. in the case of the COSY experiment in liquids a cross peak between two resonances is visible if the two partners have an active J-coupling and are of the same isotope [54, 55]. A wide range of two-dimensional spectra are known employing different polarization transfer techniques. They are classified into spectra correlating atoms of the same isotopes which are called homonuclear and into spectra correlating different isotopes 22 1 General Introduction

which are called heteronuclear spectra. In liquid-state NMR polarization transfer steps which are mediated by the J-coupling and the Nuclear Overhauser Effect (NOE) are the most common [36]. Under special conditions these two mechanism can be used in solid-state NMR, too, although in this case most experiments use the stronger dipolar coupling for polarization transfer. In general a high polarization efficiency is crucial in multi-dimensional spectroscopy, especially when more than one polarization step is involved. The main advantage of multi-dimensional spectroscopy is that resonances which were indistinguishable before can now be separated. In the case of a two-dimensional COSY spectrum the neighboring spin of the two overlapping resonances in one dimension may have a different chemical shift in the second dimension, leading to a separation of the peaks. In protein NMR the assignment problem for larger systems is still unsolved. Stan- dard assignment procedures have been developed which are based on 3D spectra correlating 1H,13C and 15N [56]. In large proteins however signal overlap caused by a bigger number of resonances or increased line width limits the success of these methods. This problem of spectral crowding is tackled by three different approaches: firstly, technical advancements in the area of super-conducting NMR magnets allowed the acquisition of spectra at increasing static magnetic field strengths. The strongest commercially available magnet has a field strength of 23.49 T corresponding to a 1Hreso- nance frequency of 1 GHz. The larger magnetic field leads to bigger differences in the resonance frequency and also to a higher sensitivity as the magnetization increases with the field strength. Secondly there are methods which allow spectral editing. This means that it is possible to manipulate the spectrum such that only desired resonances are present. A widely-used example is the distorsionless enhancement of NMR signals by polarization transfer (DEPT) method [57], which is used for 13C -1D spectra for small organic molecules in the liquid phase. In the DEPT spectrum the dependency of the polarization transfer efficiency on the flip angle of a refocussing pulse is used to generate spectra in which for example methine groups are shown only. This simplification allows unambiguous assignment of the resonances more easily. In the case of proteins amino acids with a non-polar aliphatic side chain often have similar chemical shifts of the side-chain atoms. There have been methods proposed 1.3 The Assignment Problem 23

which allow separation of these side-chain resonance depending on the amino acid type [58, 59]. Common to all these method is the dependence of the presence of J- couplings as a selection criterion. This approach is not well suited for solid-state NMR, in which the dipolar coupling is the dominating spin-spin interaction. A spectral editing procedure which uses the homonuclear dipolar coupling in solids is the DREAM spin-pair filter [47]. This filter allows the recording of spectra of 13C–13C spin pairs in the presence of a large background of isolated 13Cspins. The last possibility to reduce spectral crowding also reduces the number of resonances visible in the measurement. Contrasting the spectral editing or filtering approaches described before, isotopic labels can be incorporated in the molecule under investigation at desired positions. In this way the distinction is made not on an spectroscopic but on a chemical or biochemical level usually requiring the synthesis of different isotopomers of the molecule. Prominent nuclei under investigation by NMR are 1H,13C and 15N . The natural abundance of 13C is 1.1% whereas only 0.4% of all natural nitrogen is the NMR-active nucleus 15N . To make investigation of biomolecules possible they are often produced with an enriched 13C and 15N content. The synthesis of small peptides is usually carried out using standard solid-phase synthesis techniques using Fmoc-protected building blocks [60]. The building blocks are often commercially available in various isotope compositions allowing easy synthesis of the molecule as the desired isotopomer. In contrast proteins are often produced recombinantely using organisms such as E.coli. In this case the growth medium is supplemented with U-13C -glucose and 15N ammonium chloride as the solely carbon and nitrogen source, respectively. From these educts proteins are synthesized in which all carbons are 13C and all nitrogen are 15N . Although this is beneficial from a signal to noise point of view, this labeling scheme can lead to spectral crowding especially for larger proteins. Alternatively several other labeling schemes have been discussed and are reviewed by Goto et al. [61]. In solid state NMR often 13C–13C correlation spectra are recorded. For samples which have a line width comparable with the homonuclear J-coupling, this coupling can limit the achievable resolution. In this case the labelling scheme developed by LeMaster [62] and apply by Oschkinat et al. [63] can be advantageous as it leads to an alternating 13C–12C–13C labeling pattern in which no direct 13C–13C pairs are present. The alternated labeling is achieved by using [2-13C ] or [1,3-13C ] glycerol 24 1 General Introduction

as carbon source in the recombinant expression. Another possibility is to reversely label the protein by using U-13C glucose as the carbon source and supplementing the amino acid of interest in its natural isotope composition [64]. In the product this amino acid type is not labeled. In all of the cases when isotope labeled protein is expressed recombinantely the metabolic pathways of the carbon source to the protein of interest have to be taken into account. There is the phenomenon of isotopic scrambling that means incorpora- tion of isotopes at positions which are not wanted, leading to an isotope distribution. In some cases scrambling can be minimized by choosing the appropriate starting ma- terials. For the study of large proteins or protein complexes only partial labeling can be advantageous. In this case the protein is cut in two with the cut placed in a flexible loop region. These two parts are then expressed separately each with its desired labeling pattern. The two parts are then concatenated using intein chemistry [61]. When using this approach the proper refolding of the product has to be verified. A resonance assignment is the basis for almost all other spectroscopic investigations. In the case of complicated systems made of similar repetitive units this assignment can be difficult because of spectral overlap of the resonances. The combination of technical advancements in the design of super-conducting magnets, sophisticated pulse sequences and isotope labeling has led to big advancements in the assignment of large proteins. Strategies and methods for assignment based on solid-state NMR data were outlined in detail by Detken et al. [65]. Using the example of the fully 13C,15N labeled decapeptide antamanide it is demonstrated how solid-state NMR can be used as an analytical method on biomolecules. Although the system under investigation may not seem to have a lot in common with the much larger proteins of more than 200 amino acids studied today (e.g. by Schütz et al. [66]), all the crucial aspects of a suc- cessful assignment are discussed. Part I.

Solid-State NMR Studies of the Prion Protein HET-s (156-289)

2. Introduction To Prion Proteins and Amyloids

2.1. Discovery of Prions

Prion diseases came into focus of the general public as the bovine spongiform encephalopathy (BSE) infected a large fraction of the British cattle in the 1990s. Prions itself were postulated as early as 1967 when Griffith framed the prion-only hypothesis, meaning that the infectious agent causing scrapie in sheep consists of proteins only [67]. Until then it was thought that pathogens like viruses and bacteria were always carrying nucleic acids as genetic material needed for replication. This hypothesis challenged the central dogma of molecular biology formulated by Crick in 1958 [68], in which he proposes that there are information pathways in living organisms as shown in figure 2.1. Nucleic acids (RNA and DNA) act as an information storage. In eukaryotic and prokaryotic cells information flows from DNA, which can be replicated by transcription to RNA and by translation to protein as depicted by the solid arrows. In viruses other pathways are possible like reverse transcription of RNA into DNA and RNA duplication (dashed arrows). This implies that on one hand nucleic acids are always involved in replication for storing information. On the other hand proteins are a “dead end” and cannot transfer information any further. Alper et al. [70] observed that after exposing the scrapie agent to high doses of ultra- violet irradiation the agent was still able to replicate itself. From this data nucleic acids could be excluded as the information carrier in scrapie. A strong evidence of the protein-only hypothesis was found by Prusiner [69] in 1982. By treating the scrapie agent with six different chemicals known for their ability to cut or denature proteins he showed that protein activity is required for infectivity. To distinguish this new pathogens from know bacteria, viruses and viroids, he coined

27 28 2 Introduction To Prion Proteins and Amyloids

DNA

RNA Protein

Figure 2.1. Flow direction of information adapted from Crick [68]. Solid arrows represent the general information flow in eukaryotic and prokaryotic systems. Dashed arrows represent special information flow in viruses. The dotted arrow represents information flow in prion systems as suggested by Griffith [67] and proven by Prusiner [69].

the word “prion” for proteinaceous infectious particle. The discovered prion protein was called PrP which is ubiquitous in the cell in its soluble α-helical form PrPC. It turned out that this very same protein can exist in a prion form called PrPSc, which is insoluble and β-sheet-rich. The existence of one protein in two folds contradicts Anfinsen’s hypothesis that “information dictating the native fold of protein domains is encoded in their amino acid sequence” [71]. The information flow diagram in figure 2.1 can now be extended by the self-replication of protein as depicted by the dotted arrow.

2.2. Replication of Prions and Amyloid Fiber Formation

It has been shown by Prusiner et al. [72] that PrPSc in its prion form aggregates to fibrous protein aggregates called amyloids. It turned out that prions often form these aggregates which share characteristics like a beta-sheet structure, green birefringence upon staining with congo-red and a fibrillar morphology [73]. The replication of a prion is based on the fact that the protein in its prion form can act as a catalyst for the conversion from the non-prion to the prion form. In figure 2.2 the conversion of a natively folded protein into a prion and the subsequent formation of an amyloid fiber is outlined. The first step is overcoming kinetic or thermodynamic barriers which inhibit the conversion. This can happen by changing the environment of the protein by altering temperature, pH or ionic strength. Another possibility is 2.2 Replication of Prions and Amyloid Fiber Formation 29 that a catalyst lowers the activation energy that the reaction can occur. Once formed, the ends of the amyloid fibers act as a catalyst for the conformer conversion and are thereby elongated. After a certain length of the polymer is reached, the fiber can break apart forming smaller fragments with more active ends. The amount of catalyst present is increased and the reaction is accelerated.

Native Prion conformers conformers

Initial prion induction by nucleation Fiber fragmentation Seed

Conformation conversion Amyloid fiber at fiber ends

Figure 2.2. Conversion of native conformers to prion conformers adapted from Shorter et al. [74]. The initial step of amyloid fiber formation is a spontaneous conversion of protein from its native to its prion form. This process is usually inhibited by kinetic or thermodynamic barriers. The ends of the short polymer act as a catalyst for the prion conversion and polymerization process thereby elongating the fiber. After several elongation steps the fiber can break apart forming more catalytically active ends and speeding up the reaction.

Formation of an amyloid does not necessarily mean that it is also transmissible. Infectivity and thus its prion characteristics can be inhibited by several reasons. For example there may be simply not enough convertible substrate for the fiber to grow. Also ingestion of amyloids alone is not sufficient, it has to be resistant to proteases that it survives the gut and can finally reach the central nervous system where substrate is present. There is also a kinetic aspect to be considered in the living cell. As the cell reaches mitosis stage in the cell cycle, enough amyloids have to be present to act as seeds in the next generation. If the fiber concentration drops below a certain threshold transmissibility is lost. Linked to this is the mechanical stability of the fiber. If the fiber is too stable to fragment there are too less catalytically active ends [74]. 30 2 Introduction To Prion Proteins and Amyloids

2.3. Amyloid diseases

Many amyloid diseases are neurodegenerative [75] but also other parts of the body can be affected like in the case of diabetes type-II [76, 77]. First observed and characterized was scrapie, a disease affecting sheep. The disease has been recognized in Europe for over 200 years and is widespread among other countries worldwide [78]. Other animals are also affected by chronic wasting disease in mule deer and elk [79], bovine spongiform encephalopathy (BSE) in cattle [80] and more recently feline spongiform encephalopathy in domestic cats [81]. In humans known prion diseases were divided into Creutzfeldt-Jakob disease (CJD), Gerstmann-Sträussler syndrome (GSS) and kuru.

Kuru is a neurodegenerative disease spread among the Fore tribe in Papua New Guinea. It was ﬁrst examined by western medicine in the 1950s [82]. The disease affected mainly women and children because boys older than 6–8 years participated little in ritual cannibalistic feasts of dead relatives. Especially ingestion of brain tissue in which amyloids are enriched caused a kuru epidemic in the late 1950s. After endocannibalistic rituals have been forbidden in 1954, the number of cases of kuru fell from over 200 per year in the late 1950s to one to two cases per year in the 1990s. Besides the unusual way of infection kuru exhibits typical characteristics of a prion disease such as enrichment of amyloid aggregates in the brain and long incubation times which can exceed 50 years.

Although this infection path among humans is extraordinary it is hypothesized that this was also the way BSE was able to spread so widely among British cattle. In this case cattle was rendered to produce cattle feed and by this recycling the infectious tissue of rare sporadic BSE cases were held in the food chain [78].

The ingestion of contaminated meat by humans could be a major threat to public health as it has been observed that variant Creutzfeldt-Jakob disease (vCJD) can be caused by dietary uptake of BSE prions through contaminated meat [83]. Because of the long incubation time of up to 40 years it remains unclear how many cases especially in the UK are in the asymptomatic phase of vCJD.

There are also human amyloid diseases which are not caused by prions such as Alzheimer’s disease, type-II diabetes and Parkinson’s disease. 2.4 Fungal Prions 31

2.4. Fungal Prions

The existence of prion proteins is not limited to mammals. There are also fungal prions for example [URE3], [PSI] and [PIN] from the yeast Saccharomyces cerevisiae and the here studied [HET-s] prion of Podospora anserina. These genes express the proteins Ure2p, Sup35p, Rnq1p and HET-s, respectively. The prion proteins consist of two different domains, the prion forming domain and the globular domain [84] (see ﬁgure 2.3). In the case of Sup35p and PrP there are parts of the sequence whose status is still unclear. It is proposed that these could be a linker between the two different domains. Characteristic for the prion forming domain is its high asparagine and glutamine content.

Ure2p 1 94 354

Sup35p 1114 254 685

Rnq1p 1 153 405

HET-s 1 218 289

PrP 1 ~91 ~125 231

Figure 2.3. Prion and globular domains of the prion proteins Ure2p, Sup35p, Rnq1p, HET-s and PrP. Prion domains are shown in light grey. Sup35p and PrP have a domain which is neither a prion or a globular domain and is shown in dark grey. Adapted from Baxa et al. [84].

The conversion of the soluble wild-type protein into its prion form can be understood as a molecular switch, which is able to alter the activity of the protein. Unlike other regulatory mechanisms in the cell a major change in secondary structure occurs. The soluble form of Ure2p and Sup35p have cellular functions that are lost on prion formation. In the case of Rnq1p and HET-s the prion form is recognized by the 32 2 Introduction To Prion Proteins and Amyloids

organism. Whereas the function of Rnq1p in its prion form is unknown, the prion form of HET-s plays a role as a marker for heterokaryon incompatibility.

2.5. The HET-s Prion

2.5.1. Biological Background

The protein under investigation is the HET-s prion protein of the filamentous fungus Podospora anserina. This fungus can fuse with the same and also different individu- als [85, 86]. After the fusion event occurred the two fungi share the same cytoplasm and form a single cell with different nuclei called heterokaryons. The viability of these heterokaryons is controlled by at least nine different het loci on the fungus’ genome. On one of these loci two different alleles can be present: First, het-s encodes the HET-s protein, which can itself be in the soluble or prion form denoted by the phenotypes [HET-s*] and [HET-s], respectively. Second, the het-S allele encodes the HET-S protein, which exists in a soluble form only and its corresponding phe- notype is called [HET-S]. The different combinations possible determine if the new heterokaryon formed is viable. A fusion of [HET-s*] and [HET-S] is viable, whereas the [HET-s] / [HET-S] combination is not. [HET-s*] strains can spontaneously con- vert to their prion counterpart [HET-s] and a fusion of [HET-s*] with [HET-s] leads to a quantitative reaction of [HET-s*] to the prion [HET-s] form [87]. In this case the two different isoforms of HET-s are used as an additional criterion in the compatibility check before fusion. The HET-s protein is 289 amino acids long. The prion domain consists of the C- terminal residues 218–289, which are resistant to digestion with protease K [85]. The HET-s(218–289) prion forms amyloid fibers in vitro and is sufficient to infect wild- type [HET-s*] strains. This short construct however lost its ability to trigger a [HET-S] / [HET-s] heterokaryon incompatibility reaction. It has been shown by Balguerie et al. that the construct containing roughly half of the globular domain and the prion domain HET-s(157–289) is able to interact with HET-S and forms fibrils as wild-type HET-s or HET-s(218–289) [88]. In addition different fibril morphology was observed by fluorescence assays carried out on the HET-s(157–289)/GFP fusion protein. Whereas wt HET-s and HET-s(218–289) form dot-like aggregates in their fibrillar form, HET-s(157–289) forms elongated fibrils of 2.5 The HET-s Prion 33

up to 150 μminlength.

2.5.2. Solid-state NMR Studies on HET-s(218–289)

Amyloid ﬁbrils although highly ordered on an atomic level cannot be crystallized and subjected to analysis by X-ray crystallography. As NMR is probing the local structure only, amyloid ﬁbrils have been extensively studied by solid-state NMR [89,

90]. In particular α-synuclein [91], β2-microglobulin [92], transthyretin TTR(105–115) [93] and Alzheimer Aβ [94, 95] have been studied in detail. In the case of the prion protein Ure2p there is a scientific controversy if this prion retains its alpha-helical conformation when protein fibrils are formed [96–99]. This would make Ure2p special as other prions typically form beta-sheet rich amyloids. Solid-state NMR is used in this case to yield experimental evidence [100–103]. The HET-s(218–289) construct shows beneficial properties. First as the prion protein is found in fungi it is not pathogenic to humans which makes handling easy compared to e.g. the Alzheimer protein Aβ. Furthermore HET-s(218–289) can be expressed recombinantely in E.coli in a routine fashion, which enables easy incorpo- ration of 13C,15N isotopes in different labeling schemes suitable for NMR. From a spectroscopic point of view there are several characteristics facilitating the studies. ◦ First the prion protein is very stable. Samples stored for several years at 4 C do not show any degradation. As in solid-state NMR typically the residual dipolar couplings determine the achievable line width strong decoupling is needed. Although technical improvements have been made in probe design, sample heating by RF irradiation and air friction of the MAS rotor is an issue for thermolabile proteins. HET-s(218–289) is thermostable allowing strong decoupling fields which led to highly resolved spectra. All these characteristics allowed to gain insight into the structure on an atomic level by solid-state NMR. The C-terminal part HET-s(218–289) shows the typical cross-β structure [104, 105]. There are also flexible parts in the fibrillar core of HET-s, which are not visible to dipolar-based solid-state NMR methods. They have been characterized by spectra which do not rely on the presence of dipolar couplings because these could be averaged out by motion [106]. There are however also residues which have not been detected by either method and are left unassigned. The HET-s(218–289) protein is the first amyloid protein, for which a structural model was proposed [107]. 34 2 Introduction To Prion Proteins and Amyloids

2.5.3. The HET-s(156–289) Prion

It has been reported by Balguerie et al. that the prion forming domain of HET-s (residues 218–289) shows only an attenuated incompatibility reaction with no visible barrage formation [108, 109]. It is suggested that in vivo proteolytic degradation of HET-s(218–289) is faster than fibril formation as in vitro HET-s(218–289) is able to promote fibril formation. It has been shown by the Dalstra et al. [109] that an artifi- cial construct which includes roughly half of the N-terminal globular domain ranging from residues 157–289 is a prion and that it is able to trigger the heterokaryon incompatibility reaction in vivo. In an essay using a green fluorescent protein (GFP) fusion with HETs(157–289) it was shown that the fiber morphology in vivo is different from HETs(218–289)/GFP. The shorter construct forms elongated fibrils whose length can exceeded 30 μm. In an study using electron microscopy the fibril morphology of HET-s(157–289) and HET-s(218–289) was investigated and compared. Sen et al. showed in their work [110] that fibrils formed by the longer construct are with 5.9 ± 0.4 nm significantly thicker than their shorter counterpart with 4.4 ± 0.3 nm. Using scanning transmission electron microscopy (STEM) the mass-per-unit-length was determined. This measurement gives insight into how many subunits form a repetitive unit in the fibril. Within the error they showed that these units consist of one protein in both HETs(157–289) and HET-s(218–289) . From these results they conclude that the additional N-terminal residues in HET-s(157–289) do not alter the amyloid backbone which is formed by HET-s(218–289) alone. In this work a similar construct is investigated ranging from residues 156–289. The sequence is given in figure 2.4. The comparison of the amino acid composition of HET-s(156–289)and the prion forming domain HET-s(218–289) is given in table 2.1. 2.5 The HET-s Prion 35

160. 170. 180. 190. 200. MLEKIVDQVARFVDELEKAFPIEAVCHKLAEIEIEEVEDEASLTILKDAA

†† 210. 220. 230. 240. 250. GGIDAAMSDAAAQKIDAIVGRNSAKDIRTEERARVQLGNVVTAAALHGGI

†† 260. 270. 280. 290. RISDQTTNSVETVVGKGESRVLIGNEYGGKGFWDNHHHHHH

Figure 2.4. Sequence of the HET-s(156–289)–His6 protein. The prion forming domain is shown in inverted colors. Amino acids marked with a dagger † are unassigned and are located in the loop region of HET-s(218–289) .

Table 2.1. Amino acid composition of HET-s(156–289) in the prion-forming domain 218–289 and the additional residues. Unassigned residues have not been detected by dipolar-based or J-based methods or show no chemical shift dispersion and. The His6-tag is not taken into account in this comparison.

Residue 156–289 156–218 218–289 unassigned in 218–289 Ala 18 12 6 1 Arg 7 1 6 1 Asn 5 0 5 1 Asp 10 6 4 3 Cys 1 1 0 0 Gln 4 2 2 0 Glu 15 10 5 0 Gly 12 2 10 2 His 3 1 2 1 Ile 12 6 6 3 Leu 8 5 3 0 Lys 8 4 4 1 Met 2 2 0 0 Phe 3 2 1 0 Pro 1 1 0 0 Ser 6 2 4 1 Thr 6 1 5 0 Trp 1 0 1 0 Tyr 1 0 1 0 Val 13 5 8 0

3. Experimental

3.1. Bacterial Strains

For cloning purposes and DNA work the E.coli strain DH5α [111] was used. For IPTG- induced and auto-induced overexpression of HET-s(156–289) the strain BL21(DE3) [112] was used.

3.2. Protein Expression and Puriﬁcation

3.2.1. Transformation of pET24-HET-s(156–289) Vector

µ A 100 l aliquot of CaCl2-competent BL21(DE3) cells was incubated on ice for 20 min with 2 µl of a plasmid mini-prep of pET24a-HET-s. The cells were heat shocked at ◦ 42 C in a water bath for 100 s, rescued with 1 ml of SOC medium and incubated for ◦ 1 min on ice. Then the cells were placed for 1 h at 37 C. 100 µl of this culture was plated on LB plates supplemented with 50 µg/ml kanamycin and incubated over- ◦ night at 37 C.

3.2.2. Expression of U-13C,15N HET-s(156–289)

For optimization of the expression protocol HET-s(156–289) protein was expressed in BL21(DE3) cells in LB medium. 5 ml of LB medium supplemented with 50 µg/ml kanamycin were inoculated with ◦ a single colony of the freshly transformed cells and incubated under shaking at 37 C overnight. 50 ml of LB medium containing kanamycin in the same concentration were inoculated with 5 ml of this freshly prepared overnight culture in a bafﬂed 250 ml ◦ Erlenmeyer ﬂask and incubated under shaking at 37 Cfor2h.

37 38 3 Experimental

2l of U-13C,15N M9 medium containing 50 µg/ml kanamycin were divided up into two 1 l portions in 5 l bafﬂed Erlenmeyer vessels and inoculated with 20 ml of ◦ the fresh overnight culture each. The cells were grown at 37 C under shaking to

an OD600 of 0.6 and then induced by addition of IPTG to a ﬁnal concentration of ◦ 1 mM. The temperature was lowered to 30 C and cells were harvested after 16 h by ◦ centrifugation (13000×g, 10 min, 4 C). Cells were worked up and lyzed as described in Section 3.2.4.

3.2.3. Expression of HET-s(156–289) Using Auto-Induction

The protocol for auto-induction was adapted from Studier et al. [113]. 5 ml of LB medium supplemented with 50 µg/ml kanamycin were inoculated with a single col- ◦ ony of the freshly transformed cells and incubated under shaking at 37 Cfor9h. 80 ml of ZYM-5052 auto-induction medium containing kanamycin in the same concentration were inoculated with 800 µl of this freshly prepared dense culture in a ◦ bafﬂed 500 ml Erlenmeyer ﬂask and incubated under shaking at 30 Covernight. ◦ Cells were harvested after 16 h by centrifugation (13000×g, 10 min, 4 C). Cells were worked up and lyzed as described in Section 3.2.4.

3.2.4. Cell Work-Up and Lysis

The separated cell pellet obtained by centrifugation was resuspended in 40 ml of an ice-cold 50 mM Tris-HCl (pH 8.0), 150 mM sodium chloride buffer. The suspension was supplemented with 1 mM Phenylmethylsulfonylfluorid (PMSF) and immedi- ately afterwards passed twice through a 110S microfluidizer (Microfluidics, Newton, ◦ MA, USA). The lysate was fractionated by centrifugation (50000×g, 1 h, 4 C). The supernatant was discarded and pellets were collected and resuspended in 10 ml 50 mM Tris-HCl (pH 8.0) buffer. Solid guanidinium-hydrochloride was added until satura- ◦ tion. To improve inclusion body solubilization the solution was incubated at 37 C under shaking overnight. Cell wall debris and the insoluble fraction were pelleted by ultra-centrifugation ◦ (125,000×g, 45 min, 4 C). The supernatant was transferred to a new tube and again ultra-centrifuged under the same conditions. The two-fold centrifugation is necessary to prevent clogging of the column. The supernatant was supplemented with solid 3.2 Protein Expression and Purification 39

imidazole to a ﬁnal concentration of 20 mM.

3.2.5. Puriﬁcation

+ The solution was divided up into two parts and puriﬁed by Ni2 -NTA chromatography, carried out on an Äkta Prime FPLC system using HisTrap FF 5 ml and 1 ml columns (Amersham) (running buffer: 6 M guanidinium hydrochloride, 150 mM sodium chloride, 20 mM imidazole, 50 mM Tris-HCl (pH 8.0); elution buffer: 6 M guanidinium hydrochloride, 150 mM sodium chloride, 500 mM imidazole, 50 mM Tris- HCl (pH 8.0)). Active fractions were pooled and concentrated using Amicon Ultra-15 concentrators (Millipore) with a molecular weight cutoff of 3 kDa. The sample was run over a HiLoad 16/60 Superdex 75 column (Amersham) using 6 M guanidinium chloride, 0.5 M sodium chloride, 20 mM imidazole, 50 mM Tris-HCl (pH 8.0), 10% (v/v) glycerol as running buffer.

3.2.6. SDS–PAGE

SDS–PAGE was used to monitor the protein overexpression and the puriﬁcation process. Samples obtained under denaturing conditions containing guanidinium hydrochloride were desalted by precipitation following the protocol of Wessel–Flügge [114]. This step is necessary as SDS forms with guanidinium hydrochloride a precipitate which prevents analysis by electrophoresis. The precipitate obtained in the last step of the Wessel–Flügge protocol was resolved in SDS–PAGE loading buffer and ◦ heated to 95 C for 10 min and loaded on the gel. Gradient gels with a concentration gradient of 12–4% acrylamide were used.

3.2.7. Fibrilization and Sample Preparation

The eluded fractions of the gel filtration were concentrated using Amicon Ultra-15 concentrators (Millipore) and dialyzed twice into fibrilization buffer (50 mM Tris- ◦ HCl (pH 8.0), 150 mM sodium chloride) at 4 C, for a minimum of 24 h each. To desalt the formed fibrils, the solution was finally dialyzed twice into nano-pure water under the same conditions. For dialysis SnakeSkin dialysis membrane (Pierce) with a molecular weight cutoff of 3.5 kDa was used. 40 3 Experimental

◦ Fibrils were pelleted by centrifugation (111,000×g, 1 h, 4 C), per 100 mg wet ﬁbril mass, 100 µl of a 100 mM DSS (4,4-dimethyl-4-silapentane-1-sulfonic acid) stock solution was added as an internal standard for NMR measurements. The pellet was dried in a SpeedVac (SPD 111V) operating at 50 mbar pressure, leading to an approximate evaporation rate of 60 µl per hour. Finally, the sample was centrifuged into a MAS rotor by ultra-centrifugation using ◦ home-build inserts in a Beckmann SW-41 rotor (111,000×g, 30,000 rpm, 1 h, 4 C).

3.2.8. Preparation of Low Temperature Samples

To study HET-s(156–289) at low temperatures the protein was fibrilized as described in section 3.2.7 but instead of drying the fibrils they were incubated under shaking over night in a water:glycerol (1:1) mixture. The fibrils were centrifuged into a 4 mm Varian/Chemagnetics pencil MAS rotor.

3.3. Electron Microscopy

For negative staining, sample aliquots of 5 µl were applied to a weakly glow-dis- charged carbon coated 400-mesh/inch copper grid. The sample was allowed to ad- sorb for 30 sec, washed twice with water, and negatively stained for 20 s with 2% (w/v) uranyl acetate. Specimens were examined in a FEI Morgagni 268 transmission electron microscope operated at 80 kV.

3.4. NMR Experiments

3.4.1. Solid-State NMR Experiments

General Remarks

All spectra were recorded on a Bruker AV600 spectrometer operating at a static ﬁeld of 14.09 T. For solid-state NMR experiments Chemagnetics/Varian 4 mm triple-resonance T3 probes equipped with a pencil MAS module and a 2.5 mm Bruker triple- resonance probe were used. The temperature of the samples was actively controlled. 1H chemical shifts were calibrated using DSS (4,4-dimethyl-4-silapentane-1-sulfonic 3.4 NMR Experiments 41

acid) as an internal reference [115, 116]. 13C and 15N shifts were calibrated indi- rectly to the proton signal of DSS with a 13Cto1H and 15Nto1H frequency ratio Ξ Ξ 15 of 13C = 0.25144953 and 15N = 0.10132912, respectively [117] leading to Nshifts relative to liquid ammonia. To characterize the HET-s(156–289) protein by solid-state NMR, several pulse sequences and polarization-transfer mechanisms were used. In general, the pulse sequences differ by the way initial 13C polarization is created and the mixing step involved. Typically an adiabatic passage through the Hartmann–Hahn condition (APPH) [20, 21, 118] was chosen as the initial step. This dipolar-based mechanism ◦ is contrasted by a NOE-presaturation followed by a 90 -Pulse, which is commonly used in liquid-state NMR. For proton-decoupling during free evolution periods at MAS frequencies above 20 kHz the XiX scheme [44] was conducted. At lower spinning speeds the Spinal64 scheme [19] was used. For broad-band homonuclear polarization transfer either the DREAM [47, 119], DARR [120, 121] or adiabatic TOBSY [26, 122] recoupling sequence were implemented. For sign discrimination in the indirect dimension TPPI [123] was employed. The experimental details for the solid-state pulse sequences used in this work have been collected in Tables 3.1, 3.2.

Double-Resonance Experiments

The experimental schemes used for recording 13C–13C correlation spectra are shown in Figure 1.4. Spectra based on the adiabatic DREAM scheme [47, 119] were recorded at 27 kHz MAS. This spectrum was optimized for 13C–13C transfer in the aliphatic region by setting the carrier position to 46.7 ppm. The field strength of the irradiated RF-field was optimized experimentally to give most negative signal intensity. Two experiments using a TOBSY transfer step were performed. As building block 1 for the C924 symmetry based pulse train an adiabatic WURST-5 pulse followed by the 1 inverse of this pulse was used leading to a WiW24 scheme, as described by Hardy et al. [26]. The sample was rotated around the magic angle at a rotation frequency of 27 kHz, leading to a WURST pulse length of 99 μs. The total mixing time was 10 ms. During the TOBSY mixing off-resonance cw decoupling was applied. The offset of the cw irradiation was determined experimentally. The first spectrum was recorded using an adiabatic cross-polarization step for the creation of the initial polarization 42 3 Experimental

Table 3.1. Experimental conditions of the 13C–13C correlation experiments.

Parameter DREAM TOBSY HETCOR DARR

pulse sequence Figure 1.4 ––

spectrum Figure 4.5 Figure 4.12(a) Figure 4.13 Figure 4.3 MAS frequency [kHz] 27 27 27 12

ω ω τ CP 1H, 13C [kHz], CP [ms] 117,80,2 – 84, 53, 2.5

mixing time [ms] 8 10 – 20 Δ ω DREAM: RF,dest, 1 [kHz] 5,7.5,14 – –– ω 1 TOBSY: 1H [kHz] – WiW924 –– ω 1,X=87 kHz τ τ HETCOR: ref,1, ref,2[ms] – – 1.9, 1.3 –

decoupling XiX XiX XiX Spinal64 ω τ μ 1H [kHz], 2 [ s] 140,68.5 150,70 121,84.1 100, 4.8

t1 increments 1024 1024 178 758

scans / t1 increment 64 64 256 48

SW t1 and t2 [kHz] 50 40 7.5/50 50

on 13C (parameters given in table 3.1). Second a TOBSY spectrum using a NOE presaturation followed by a 90 degree pulse was acquired (presaturation length: 2 s, 4 kHz RF ﬁeld strength). The homonuclear 13C–13C correlation spectra were Fourier transformed using a cosine-squared window function with zero ﬁlling to 2048 data points in both dimensions. Contrasting the dipolar-based experiments above, a J-based INEPT-HETCOR was recorded. The INEPT delays were optimized experimentally to trade off the build- up of the anti-phase magnetization against T2 relaxation. For processing the indirect dimension was linearly predicted to 256 points. 3.4 NMR Experiments 43

Table 3.2. Experimental conditions of low-temperature experiments.

Parameter 1D–13C CP DARR

spectrum Figure 4.8 Figure 4.9 MAS frequency [kHz] 12 12

ω ω τ CP 1H, 13C [kHz], CP [ms] 76, 50, 2.5 70, 55, 2.5

mixing time [ms] – 50 ω PDSD: 1H [kHz] – 5.6

decoupling scheme Spinal64 ω τ μ 1H [kHz], 2 [ s] 100, 4.8

SW t1 and t2 [kHz] 50 50

Temperature range [K] 153–263 223–279

Low-Temperature Experiments

Low-temperature experiments were done using a Varian/Chemagnetics T3 4 mm pencil probe. The sample was cooled with nitrogen gas, which was passed through a home-built heat exchanger in a liquid nitrogen reservoir. A gas inlet temperature into the probe as low as 100 K was achieved using this setup. The temperature was actively stabilized with a Varian/Chemagnetics VT stack. To avoid freezing, nitrogen was used as purge-, drive- and bearing gas.

3.4.2. Data Processing and Data Analysis

Spectra were processed using either the Topspin software package (Bruker–Biospin) or the NMRpipe processing suite [124]. Resonance assignment was carried out using the program SPARKY [125]. 44 3 Experimental

Chemical-Shift Analysis

To compare the chemical shifts of HET-s(156–289) to HET-s(218–289) a peak picking on the DREAM (figure 4.5), TOBSY (figure 4.12(a)) and DARR (figure 4.3) was performed using SPARKY, followed by an automated assignment by looking for peak maxima in the HET-s(156–289) spectra, which are closer than 0.6 ppm from the value found in HET-s(218–289) (BMRB #11064)[126]. The differences in 13C chemical shifts were plotted against the sequence using a custom Perl [127] script (figure 4.7); For chemical shift mapping studies chemical shift values of HET-s(156–289) were compared to the assignment of HET-s(218–289). 4. Results

4.1. Expression of HET-s(156–289)

4.1.1. Expression of U-13C,15N HET-s(156–289)

The over expression of HET-s(156–289) in E.coli was carried out using an adapted protocol presented in section 3.2. It turned out that the crucial step in the protein production is the resolubilization of the inclusion bodies after cell lysis. Incubation at room temperature with a 6 M guanidinium hydrochloride buffer led to a clear solu- ◦ tion. Even after extensive centrifugation (50’000×g, 1 h, 4 C) the supernatant loaded + on a HisTrap FF Ni2 -NTA affinity column blocked the column in several runs. This problem was solved by incubating the insoluble fraction of the cell lysis with satu- ◦ rated Guanidinium hydrochloride solution at 37 C overnight. Also the centrifugation step was repeated after transferring the supernatant into a clean centrifugation tube. + Chromatographic purification under denaturing conditions consisted of a Ni2 - NTA affinity chromatography in which quantitative binding was observed, as no

HET-s(156–289)-His6 could be observed by SDS-PAGE in the flow-through. In the eluted fraction the target protein was detected by SDS–PAGE in high concentration as shown in figure 4.1(a). To further remove residual impurities a Superdex gel filtration under denaturing conditions was carried out. This final polishing step led to the target protein in pure form (figure 4.1(b)).

4.1.2. Expression of HET-s(156–289) Using Auto-induction

Contrasting the classical protein expression induction using IPTG an alternative approach summarized by Studier was used [113]. When using auto-induction the cell’s

45 46 4 Results

(a) Ni2+-NTA column (b) Superdex 75 column

Figure 4.1. SDS–PAGE gel analysis of the purification of HET-s(156–289). (a) Eluted fraction E1 and E2 from a Ni2+-NTA affinity column contain the protein of interest in high concentration as a monomer and dimer. (b) With a Superdex 75 gel filtration column the target protein was obtained in pure form.

metabolism triggers the beginning of the protein production. This is achieved by supplementing the culture with three different carbohydrates: glucose, lactose and additionally glycerol. In the beginning of the expression there is an excess of glucose present in the culture which is metabolized preferentially by the cell. Additionally glucose acts as an inhibitor for lactose-induction. During the initial growth period of the culture, glucose is depleted leaving lactose and glycerol as potential carbon- and energy-source. Lactose is metabolized into glucose and galactose, the latter cannot be further metabolized by the cell. This means that only half of the energy- and carbon-content are available for the cell’s metabolism. Glycerol on the other hand can be fully used by the cell.

The fundamental difference between these two induction methods is that in the IPTG-induced expression the T7tac-promoter [128] on the vector is activated by externally added IPTG, where as in the auto-induced expression the cell’s metabolism initiates induction by depleting glucose and metabolizing lactose.

Besides the convenience of not having to monitor the growth of the culture and adding IPTG at the right time, auto-induced expression also led to a higher cell density of up to OD600=10. 4.2 Solid-State NMR studies 47

4.1.3. Refolding and Fibrilization of HET-s(156–289)

To induce fibril formation of the denatured pure protein obtained after the final gel filtration step the protein solved in 6 M guanidinium hydrochloride was dialyzed against a buffer containing 50 mM Tris-HCl (pH 8.0). By this procedure the concentration of the denaturant decreased gradually. After 45 min a white cloudy precipitate could be observed in the dialysis tubing by the naked eye. After the first 24 h of dialysis the precipitate was getting more compact and was harvested by centrifugation as described in section 3.2.7. To investigate the fibrils in more detail a negatively stained electron micrograph of the fibrilized material was made. In figure 4.2 two micrographs are shown. In the left picture a bigger protein aggregate is observed. The right picture shows a more linear structure. The fine structure of this fiber suggest that is is composed of many individual fibrils.

Figure 4.2. Electron micrographs of HET-s(156–289) prepared at neutral pH and negatively stained with uranyl acetate. The left picture shows a bigger aggregate of ﬁbrils. In the right picture a bundle of individual ﬁbrils is visible.

4.2. Solid-State NMR studies

4.2.1. Comparing HET-s(218–289) and HET-s(156–289)

As described in section 2.5 the HET-s protein consists of two domains, the globular domain and the fibrillar domain. Whereas the HET-s(218–289) construct consists 48 4 Results of the prion-forming domain only, the protein studied here HET-s(156–289) also has parts of the globular domain attached to the fibrillar C-terminal part. To investigate the influence of these additional residues to the structure of the fibril a DARR spectrum [121] (figure 4.3) and a DREAM spectrum [47] (figure 4.5) of HET-s(156–289) were acquired and compared to spectra of the same type and conditions of HET-s(218–289) . The overlay of the aliphatic region of two 13C–13C DARR spectra shown in figure 4.3 indicates that the homology of the two constructs given by their closely related primary structure manifests itself also spectroscopically. In many regions of the spectrum a high degree of similarity can be observed. For example in the serine and tyrosine CA/CB region the spectra are almost identical. In a more detailed view shown in figure 4.4(a) there are differences visible in the CA/CB region. In particular there are two new signals observable which were tentatively assigned to a alanine CA/CB correlation. As the CA/CB peak position has a characteristic resonance frequency depending on the secondary structure it is indicated that the new alanine is in a random coil conformation. The second new signal is resonating at a frequency which is characteristic for leucine or aspartic acid. As no other signals in this spin system are visible in the spectrum, a distinction between these two options is difficult. Besides these two well resolved resonances there are also new signals visible which are more featureless and appear between 60 and 55 ppm. A slice plotted through this region shows that these resonances are low in intensity which means in this case approximately twice the noise level. The carbonyl region of these two spectra shown in figure 4.4(b) indicates that the black spectrum of HET-s(156–289) has additional intensity which is low-field shifted with respect to HET-s(218–289) . Both the contour plot and the 1D slice show that the resolution is not sufficient to identify individual resonances. There are individual resonances visible such as an alanine CB/CA peak shown in figure 4.4(f). The chemical shifts indicate that this alanine is in a random coil conformation. In figure 4.4(d) a new spin system is outlined. The chemical shifts indicate that this is a valine residue in an alpha-helical conformation. Another residue can be identified which is an isoleucine. The signals of this residue are very weak but are at positions characteristic for an alpha-helical conformation. Furthermore a CB/CA cross peak is observed shown in figure 4.4(c), which could be a leucine or aspartic acid. No other spin could be assigned to this spin system, which makes a distinction 4.2 Solid-State NMR studies 49

30 /ppm ) 40 C 13 (

δ 50

70 60 50 40 30 20 10 δ(13C)/ppm

Figure 4.3. Overlay of a 13C–13C DARR spectrum of HET-s(156–289) (black) and HET-s(218–289) (red). Experimental parameters are given in table 3.1. difficult. In addition to the very robust 13C–13C DARR spectrum 13C–13C DREAM spectra were recorded and compared to DREAM spectra of HET-s(218–289) . An overview of the two spectra is shown in figure 4.5. Although the spectra were at the same static magnetic field but under different experimental conditions such as mixing time and spinning frequency there are many similarities. Because of the carrier placement during the DREAM mixing of 48 ppm there are no correlations from the aliphatic to the carbonyl region visible. The three new spin systems are also present in the DREAM spectra. The assignment that the spin system shown in figure 4.6(d) is a valine residue is supported by the DREAM spectrum. The DREAM mixing is a double-quantum process which generates cross peaks with an inverted sign. The CG/CA peak has the 50 4 Results

64 48 44 40 36 32 28 24 20 16 δ(13C)/ppm

80 70 60 50 40 30 20 δ(13C)/ppm (a) CA/CB region

40 /ppm ) C

13 50 ( 188 184 180 176 172 δ 60 δ(13C)/ppm

70 180 170 δ(13C)/ppm (b) Carbonyl region of the spectra.

44 80 70 60 50 40 60 58 56 δ(13C)/ppm δ(13C)/ppm (c) Leucine or Aspartic acid spin system.

Figure 4.4. Details of the comparison of two PDSD spectra of HET-s(156–289) (black) and HET-s(218–289) (red) shown in ﬁgure 4.3 4.2 Solid-State NMR studies 51

22 Val CG/CA

24 /ppm )

C 30 13

( Val CB/CA δ 32 68 66 80 70 60 50 40 13 δ(13C)/ppm δ( C)/ppm Val CA/CO 66 /ppm ) C 13

( 68 δ 182 178 174 170 180 178 176 174 172 δ(13C)/ppm δ(13C)/ppm (d) Valine spin system in alpha-helical conformation.

Ile CG2/CA alpha-helical 20

25 /ppm ) C

13 30 ( Ile CB/CA δ 35 alpha-helical

65 60 80 75 70 65 60 55 50 δ(13C)/ppm δ(13C)/ppm (e) Isoleucine spin system in alpha-helical conformation.

18 Ala CB/CA random coil 20 /ppm )

C 22 13 (

δ 24 80 70 60 50 40 δ(13C)/ppm 54 52 50 δ(13C)/ppm (f) Alanine CB/CA correlation resonating at random coil shift.

Figure 4.4 (cont.) Details of the comparison of two PDSD spectra of HET-s(156–289) (black) and HET-s(218–289) (red) shown in figure 4.3 52 4 Results same sign as the diagonal which means that it has been inverted twice and is a relayed transfer CG–CB–CA. This behavior is discussed in detail in part II of this thesis. In addition to the DARR spectrum a CG/CB correlation of the same spin system can be observed. The alanine CA/CB peak at the random coil shift is also strongly visible in the spectrum (figure 4.6(c)). The leucine or aspartic acid CA/CB correlation is better visible than in the DARR spectrum (figure 4.6(e)). However also in the DREAM spectrum of HET-s(156–289) no other spins belonging to this spin system could be identified. The very weak correlations in figure 4.4(e) which could be a isoleucine is also weak in the DREAM spectrum. 4.2 Solid-State NMR studies 53

40 /ppm ) C 13 (

δ 50

70 60 50 40 30 20 δ(13C)/ppm

Figure 4.5. Aliphatic region of 13C–13C DREAM spectra of HET-s(156–289) in black/green and HET-s(218–289) in red/blue. Region of interests are shown in detail in ﬁgure 4.6. Experimental parameters are given in table 3.1. Spectrum of HET-s(218–289) was recorded in collaboration with Ansgar Siemer [129] at 30 kHz MAS, mixing time 4.5 ms. 54 4 Results

Ala CA/CB random coil

/ppm 56 ) C 13

( 60

δ 64 44 40 36 32 28 24 20 16 δ(13C)/ppm Leu/Asp CA/CB

80 70 60 50 40 30 20 δ(13C)/ppm

(a) CA/CB region

25 80 75 70 65 60 55 50 45 40 /ppm ) 13

C δ( C)/ppm

13 30 ( δ Ile CB/CA 35 alpha-helical

65 60 δ(13C)/ppm (b) Isoleucine spin system in alpha-helical conformation.

18 Ala CB/CA random coil 20 /ppm )

C 22 13 ( δ 24

54 52 50 80 70 60 50 40 13 δ(13C)/ppm δ( C)/ppm (c) Alanine CB/CA correlation resonating at random coil shift.

Figure 4.6. Details of the comparison of two DREAM spectra of HET-s(156–289) (black/green) and HET-s(218–289) (red/blue) shown in ﬁgure 4.5. 4.2 Solid-State NMR studies 55

Val CG/CB 22 /ppm ) C

13 24 (

δ 32 30 50 40 30 20 10 δ(13C)/ppm δ(13C)/ppm 22 Val CG/CA

24 /ppm )

C 30 Val CB/CA 13 ( δ 32 68 66 δ(13C)/ppm 80 70 60 50 40 δ(13C)/ppm (d) Valine spin system in alpha-helical conformation.

80 70 60 50 40 62 60 58 56 δ(13C)/ppm δ(13C)/ppm (e) Leucine or Aspartic acid spin system.

Figure 4.6 (cont.) Details of the comparison of two DREAM spectra of HET-s(156–289) (black/green) and HET-s(218–289) (red/blue) shown in ﬁgure 4.5. 56 4 Results

4.2.2. Chemical Shift Mapping

To qualitatively examine the similarities between these two constructs, the TOBSY spectrum shown in figure 4.12(a) and the DREAM spectrum shown in figure 4.5 were peak-picked and the peaks compared against the assignment of HET-s(218–289) . The chemical shift deviation of the individual resonances are then plotted against the sequence. Resonances which have been only found once in these two spectra are represented as filled symbols. Comparing both the TOBSY and the DREAM spectra re- vealed that for example a correlation which included CA was found for most amino acids. Specifically for the residues 226–249 and 260–283 excluding residue G269 and G282. The big gap also visible in figure 4.7 is the loop region connecting beta sheet 2b with beta sheet 3a. The two glycine resonances are missing because in glycine a CA nucleus can contribute to a CO/CA correlation only which can be weak in a DARR or DREAM spectrum due to its large chemical shift offset. For the CB a very similar result with respect to visibility is obtained. In this case all CB from residue 226–249 and 260–281 can be found in the spectrum, except the CB of N243. The tolerance for the peak picking procedure was set to Δδ = ±0.6 ppm as described in section 3.4.2. Most peaks however show a significant smaller deviation of about ±0.2 ppm in figure 4.7. The input spectra used for this analysis were recorded 13 ω ( π)= at a static field of 14.1 T, corresponding to a CLarmorfrequencyof 0/ 2 150.6 MHz, which means that 0.2 ppm deviation corresponds to 30 Hz, which is significantly below the line width of the resonances. Furthermore the chemical shift deviation is independent of the position in the sequence, as no trend can be observed.

4.2.3. Low-Temperature Measurements

In the spectra using a cross-polarization as the initial step to generate 13C polarization the fibrillar C-terminal domain of HET-s(156–289) predominantly visible. To slow down dynamics in the protein which could be the reason for the only small number of globular residues visible, a series of 13C CP spectra were acquired at decreasing temperatures. The spectra shown in figure 4.8 a significant broadening of the reso- ◦ ◦ nances especially when comparing the two measurements taken at -22 Ctothe-50 C spectrum. The corresponding 1H spectra at the lower of these two resonances show a very large broadening of the water resonance. In combination with a detuning of the 4.2 Solid-State NMR studies 57

0.6

0.4

C 0.2 CA CB CD

C)/ppm 0 CD1 13

( CD2 CE Δδ -0.2 CG CG1 -0.4 CG2

-0.6 β1a β1b β2a β2b β3a β3b β4a β4b

220 230 240 250 260 270 280 290 Residue Number Figure 4.7. Chemical shift comparison of HET-s(218–289) vs. HET-s(156–289) as described in section 3.4.2. A resonance assignment tolerance of ±0.6 ppm was used. The chemical shift deviation Δδ is signiﬁcantly smaller than this value. Atoms which have been assigned only once are represented with a ﬁlled symbol. Position of the individual β-sheets are indicated along the residue axis.

probe head this indicated that the sample froze between these temperatures. In addition 13C–13C DARR spectra (figure 4.9) were acquired at different temper- ◦ ◦ atures. The spectra acquired at 6 C and -20 C are very similar in respect to signal to noise and line width (see table 4.1). Also the visible resonances of the globular domain discussed in section 4.2.1 show no difference in intensity. The spectrum recorded at ◦ -50 Cissignificantly broadened as a line broadening of a factor 2–3 is observed on isolated peaks (table 4.1). The broadening of the resonances is shown on the example ◦ of the CA/CB region of the spectrum in figure 4.10. The broadening at -50 Cisso large that at higher temperature isolated resonances now overlap significantly. This makes further analysis of this spectrum difficult. 58 4 Results

–50 ◦C

–22 ◦C

–4 ◦C

5 ◦C

180 160 140 120 100 80 60 40 δ(13C)/ppm

Figure 4.8. 13C CP spectra of HET-s(156–289) at different temperatures. 4.2 Solid-State NMR studies 59

10 20 30

/ppm 40 ) C

13 50 (

δ 60 70 80 180 170 70 60 50 40 30 20 10 180 170 70 60 50 40 30 20 10 δ(13C)/ppm δ(13C)/ppm (a) Overlay of all three DARR spectra (b) DARR spectrum acquired at 6 ◦C

10 20 30

/ppm 40 ) C 50 13 ( δ 60 70 80 180 170 70 60 50 40 30 20 10 180 170 70 60 50 40 30 20 10 δ(13C)/ppm δ(13C)/ppm (c) DARR spectrum acquired at –20 ◦C (d) DARR spectrum acquired at –50 ◦C

Figure 4.9. 13C–13C DARR spectra of HET-s(156–289) acquired at different sample temperatures. Experimental parameters can be found in table 3.1. 60 4 Results

50 /ppm

) 55 C 13 ( δ 60

45 40 35 30 25 20 15 δ(13C)/ppm (a) Overlay of the CA/CB region of all three DARR spectra

50 /ppm

) 55 C 13 ( δ 60

45 40 35 30 25 20 15 δ(13C)/ppm (b) CA/CB region of the DARR spectrum acquired at 6 ◦C

50 /ppm

) 55 C 13 ( δ 60

45 40 35 30 25 20 15 δ(13C)/ppm (c) CA/CB region of the DARR spectrum acquired at –20 ◦C

50 /ppm

) 55 C 13 ( δ 60

45 40 35 30 25 20 15 δ(13C)/ppm (d) CA/CB region of the DARR spectrum acquired at –50 ◦C

Figure 4.10. 13C–13C DARR spectra of HET-s(156–289) acquired at different sample temperatures. Experimental parameters can be found in table 3.1. 4.2 Solid-State NMR studies 61

Table 4.1. Line width at half height for selected amino acids from three DARR spectra recorded at 6◦C, ◦ ◦ -20 C- and -50 C. ‡ Valine residue in alpha-helical conformation shown in ﬁgure 4.4(d) and 4.6(d). † resonance is not observable anymore. * resonance is overlapping with neighboring resonances.

Amino acid Resonance Line width at half height [Hz] ◦ ◦ ◦ +6 C –20 C –50 C

Val ‡ CO 243 227 450 CA 193 207 237 CG 155 173 262 Ala 228 CA 109 127 † Ile 231 CG2 117 105 330* Thr 233 CG2 96 106 † Gly 271 CA 115 96 † 62 4 Results

4.2.4. Using non Dipolar-Based Experiments

Another approach to obtain information about flexible parts in which dipolar couplings are strongly scaled is to circumvent this problem by not using the dipolar coupling for preparation of the initial 13C polarization or as transfer mechanism. To compare the intensities of in the 2D spectrum, corresponding 1D experiments were measured to calibrate the intensities. It can be seen that the overall intensity of the CP-based spectrum and the NOE-enhanced spectrum are comparable (figure 4.11), thus no intensity scaling was done on the 2D spectra in figure 4.12.

VACP direct excitation NOE presaturation

75 70 65 60 55 50 45 40 35 30 25 20 15δ(13C)/ppm

Figure 4.11. Overlay of three 1D-13C spectra of HET-s(156–289). The blue and the black spectra are comparable in intensity.

Figure 4.12 shows an adiabatic TOBSY recorded with NOE presaturation followed ◦ by a 90 pulse and its CP-based counterpart. The alpha-helical valine spin system and the random-coil alanine are marked in the spectrum. The peaks of this valine are attenuated in the CP-based spectrum compared to the spectrum recorded with NOE presaturation. Especially on the CA/CO peak this effect can be observed very well. In the aliphatic region of the TOBSY spectra no significant difference besides the already described deviations which are also visible in the DREAM and DARR spectra can be observed. Additionally an INEPT-based HETCOR as a “classic” liquid state, J-based spectrum was recorded (figure 4.13). As indicated in the figure, almost all resonances pre- 4.2 Solid-State NMR studies 63

V CG/CB A CA/CB 20

/ppm 40 C ) 13 (

δ 50

70 V CA/CO V CA/CB V CA/CG

180 170 70 60 50 40 30 20 10 δ(13C)/ppm (a) Initial polarization prepared by cross polarization

V CG/CB A CA/CB 20

40 /ppm ) C 13 ( δ 50

70 V CA/CO V CA/CB V CA/CG

180 170 70 60 50 40 30 20 δ(13C)/ppm (b) Initial polarization prepared by NOE presaturation

Figure 4.12. Comparison of two adiabatic 13C–13C TOBSY recorded with a mixing time of 11.8 ms at 26.6 kHz MAS. Two different ways of preparing the initial polarization on 13C are compared. Alpha- helical valine spin system and random-coil alanine are assigned tentatively. Additional experimental parameters are given in table 3.1. 64 4 Results viously reported by Siemer et. al. [106] were present in the spectrum (colored green in ﬁgure 4.13). In addition, new resonances shown in black are visible. New amino acid types are tyrosine, serine and glycine. In addition two threonine HB/CB correlations are visible, which can be explained by one threonine being in a alpha-helical conformation and the other being in a random coil. To get more insight into possible secondary structure of these residues the average chemical shift values for random coil, alpha helix and beta sheet from Wang et al. [130] were overlayed over the experimental spectrum in ﬁgure 4.14. The length of the axes of the ellipses correspond to the standard deviation in this dimension.

Ile HG12-CG1 Ile HG13-CG1 Val HG2-CG2 Val HG1-CG1 0 Lys HD-CD Ile HG2-CG2 Ile HB-CB Ile HD1-CD1 Asn/Asp HB3-CB Ala HB-CB 2 Lys HE-CE Met HE-CE

/ppm Tyr HA-CA ) Arg HD-CD Thr HG-CG

H Ser HB-CB

1 Lys HG-CG ( δ 4 Arg HG-CG Gly HA-CA Gln HB3-CB Thr HB-CB Glu HG-CG 6 Asn/Asp HB-CB Val HB-CB Val HA-CA Ala HA-CA 80 60 40 20 0 δ(13C)/ppm

Figure 4.13. 1H–13C INEPT-based HETCOR spectra of HET-s(156–289). Green resonances are identical to those reported by Siemer et al. [106]. Other assignments were based on statistical values from Wang et al. [130]. 4.2 Solid-State NMR studies 65

3.5 Tyr Hα-Cα Ala Hα-Cα Thr Hβ-Cβ 4.0 /ppm ) 4.5 Ser Hβ-Cβ Gly Hα-Cα H

1 random coil ( δ 5.0 α-helix β-sheet Val Hα-Cα 5.5 70 65 60 55 50 45 δ(13C)/ppm

Figure 4.14. 1H–13C chemical shifts for different secondary structure elements. The length of the axes of the ellipse in each dimension corresponds to the standard deviation in this dimension. Values were taken from Wang et al. [130].

5. Discussion

5.1. Solid-state NMR Spectra of HET-s(156–289)

The dipolar-based spectra recorded of HET-s(156–289) indicate that the residues 227– 282 forming the fibrillar core have the same chemical shift within the line width as the corresponding residues of HET-s(218–289) which lacks any residues of the globular domain. As shown in section 4.2.2 the chemical shift difference of the CA and the CB in the prion forming domain of HET-s(156–289) to their counterparts in HET-s(218–289) is within the linewidth. This is important as the CA and the CB are a direct indicator for the secondary structure of the protein [131]. The comparison of HET-s(156–289) with HET-s(218–289) showed that in the DARR and DREAM spectra only a few isolated additional residues are visible. As indicated in figure 4.4(b) there is additional signal intensity in the carbonyl region with a higher CO shift compared to HET-s(218–289) . This is an indication for the presence of residues in an alpha-helical conformation. However in this region no isolated peaks can be observed which make the identification of the other spins in the spin system impossible. There are however additional isolated peaks visible in the two spectra which have been assigned tentatively. There is a strong alanine CA/CB correlation visible at a position which is characteristic for an alanine in a random-coil. In the additional globular part of HET-s(156–289) there are 12 alanine residues. From the acquired spectra it is not possible to distinguish individual alanine residues. Another valine spin system could be identified. The chemical shifts of the CA and CB resonance suggest that this residue is in an alpha-helical conformation. In the globular part there are 5 additional valine residues. In this case the whole spin system could be identified, although the distinction between the CG1 and CG2 resonance was not possible. In the CA/CB region of the spectra shown in figures 4.4(a) and 4.6(a) a new peak could be identified. The assignment in this case is difficult as no other spins in

67 68 5 Discussion this spin system could be found. From the chemical shift of CA and CB this peak can be assigned tentatively to an aspartic acid or leucine residue. In the globular part there are 6 aspartic acid and 5 leucine residues, respectively. In the same region additional signal was observed between known HET-s(218–289) resonances but these signals appear broad in the spectrum. The signal to noise of these signals is low as it can be seen from the 1D slices. The last spin system which could be identiﬁed is an isoleucine residue. These peaks are very low in intensity and the CB/CA peak maximum is approximately twice the noise intensity as shown in ﬁgure 4.6(b) and 4.6(b). However, the presence of another peak resonating at the same CA frequency suggests strongly that this is indeed a spin system. The CA and CB chemical shift indicate that this residue is in a alpha-helical conformation.

The chemical-shift analysis shown in figure 4.7 shows that he fibrillar core is not influenced by the presence of the additional globular domain residues as the chemical shift is identical within the line width between HET-s(218–289) and HET-s(156–289). In particular the N-terminal end of the prion forming domain shows no increased chemical shift deviations. In a simplified picture one would assume that the environment of these residues is strongly influenced by the directly attached globular domain. This is not the case. The identification of additional residues is made difficult due to their low signal intensity, especially in the isoleucine and aspartic acid/leucine case. One possible explanation for this is that these N-terminal residues are structurally disordered. The increased flexibility would lead to a scaling of dipolar couplings and diminished transfer efficiency. The presence of alpha-helical and random-coil residues suggest that secondary structure is partially retained.

To slow down dynamics spectra at low temperature were recorded. The 1D-13CCP spectra shown in figure 4.8 show no significant change when lowering the temper- ◦ ◦ ◦ ature from +5 Cto-22 C. At -50 C the resonances show a significant broadening as ◦ ◦ ◦ the sample freezes. The acquired DARR spectra at +6 C, -20 C and -50 C(figure 4.9) show the same behavior. The line width of the peaks increases strongly upon sample freezing, typically by a factor of 2, which diminishes the resolution in the spectrum. In the CA/CB region of the spectra shown in figure 4.10 this effect is demonstrated. This broadening makes further analysis of the spectra very difficult. 5.2 J-Based Spectra 69

5.2. J-Based Spectra

To study parts of the protein which are flexible J-based spectra have been recorded. In the comparison of two TOBSY spectra, which differ in the way initial polarization on 13C was generated, a difference in signal intensity of the globular residues can be observed (shown in figure 4.12). The fact that the globular residues are stronger in the NOE-based spectrum than in the CP-based spectrum support the thesis that the globular domain is more flexible than the prion-forming domain. In the INEPT-based HETCOR spectrum shown in figure 4.13 additional resonances compared to the flexible parts of HET-s(218–289) have been observed. The observed serine, threonine and glycine residues can all be found in the non-fibrillar part of HET-s(156–289). All amino acids visible in this spectrum resonate at chemical shift positions characteristic for amino acids in a random coil. This can be seen from the statistical analysis made by Wang et al. [130] in which the average peak position of each amino acid dependent on its secondary structure is tabulated. The statistical values are shown in a pseudo spectrum in figure 4.14. To investigate the distribution of the visible amino acids of the globular domain they are highlighted in the primary structure shown in figure 5.1. From the fact alone that an amino acid type of the globular domain is visible no information about the number of residues which contribute to that peak can be obtained. Because of this all amino acids of the types visible in the dipolar-based and J-based spectrum are marked in the sequence. In addition, in the sequence the position of the alpha-helices of the folded globular domain without the prion forming domain HETs(1–227) are indicated ,as reported by Schütz et al. [66]. The visible amino acids in HET-s(156–289) are almost evenly distributed over the whole length of the attached part of the globular domain 156–227. 70 5 Discussion

160. 170. 180. 190. 200. MLEKIVDQVARFVDELEKAFPIEAVCHKLAEIEIEEVEDEAsLtILKDAA

† 210. 220. 230. 240. 250. ggIDAAMsDAAAQKIDAIVGRNSAKDIRTEERARVQLGNVVTAAALHGGI

†† 260. 270. 280. 290. RISDQTTNSVETVVGKGESRVLIGNEYGGKGFWDNHHHHHH

Figure 5.1. Sequence of the HET-s(156–289)–His6 protein showing visible residues by different experiments. The prion forming domain is shown in inverted colors. Bold amino acids have been tentatively assigned in DARR and DREAM spectra, lower-case amino acids have been assigned in the INEPT-HETCOR spectrum. Bars over the sequence indicate the position of alpha-helices in HET-s(1– 227)[66]. Amino acids marked with a dagger † are unassigned, because they are in the loop regions of the ﬁbrillar core. 6. Conclusion

The NMR studies on HET-s(156–289) show that the structure of this construct is domi- nated by the hydrophobic core of the amyloid fibril. From the overlay of spectra of the prion-forming domain 218–289 alone and the construct at hand it can be concluded that the structure of this prion forming domain is conserved. A more quantitative treatment showed that the chemical shift differences of corresponding resonances of HET-s(218–289) and HET-s(156–289) are smaller than the line width. The fact that the chemical shift difference does not increase when going to the N-terminal part of the prion-forming domain, excludes that the fibrillar core is getting partially unfolded by the attached globular domain residues. Only a few additional resonances are visible in the spectra. From the recorded spectra it was not possible to identify individual amino acids. However the residue type and the likely secondary structure could be determined. These additional amino acids show chemical shifts typical for a random coil. However there are also two isolated spin systems which have a characteristic alpha-helical shift. In addition, there are also more featureless signals in the carbonyl region of the DARR spectra which also hint at additional alpha-helical residues. These additional residues are however weak in intensity compared to the residues of the prion forming domain and are therefore left unidentified. It has been shown by Schütz et al. [66], that from the crystals of HET-s(1–227) highly resolved NMR spectra can be obtained. As shown in figure 5.1 the residues of this domain are primarily in an alpha-helical conformation. These narrow resonances are obviously lost when a part of this domain is attached to a fibril-forming domain which is the case in HET-s(156–289). A possible explanation is that the driving force of the fibril formation is so strong that it promotes the unfolding of the globular domain in the soluble state and leaves it structurally disordered after fibril formation. This would also explain why the flexible residues visible in the INEPT-HETCOR spectrum are in a random coil. It would also be a possible explanation why the resonances are

71 72 6 Conclusion

so weak in the DARR and the DREAM spectrum due to the scaling of the dipolar couplings. The motion in these flexible part are scaling the dipolar coupling and the structural disorder leads to a distribution of chemical shifts. This can be observed as a line broadening. Slowing down this motion by cooling had only very limited success. Until the ◦ freezing point of about -22 C of the HET-s(156–289) protein in a 1:1 water/glycerol mixture the spectra do not change significantly. After the freezing however the spectra become broad and featureless which have been presented as a 1D CP 13C and a 13C–13C DARR spectrum (figure 4.8 and 4.9). No additional resonances could be observed in the remaining broad spectra. All the observations reported in this part of the thesis conclusively support the hypothesis that the formation of the hydrophobic fibrillar core is the main driving force of the fibril formation. From the fact that HET-s(156–289) can trigger the heterokaryon incompatibility reaction it can be hypothesized that the additional globular resonances have a function in the soluble state of the protein. The question if this globular domain has a secondary structure if the HET-s(156–289) construct is in its soluble form can not be answered here. However the appearance of new random coil resonances and the absence of many alpha-helical amino acids in the spectrum compared to HET-s(1–227) suggests that a possible secondary structure is almost completely lost upon fibril formation. A very similar construct consisting of a globular and a prion forming domain has been recently studied by Wasmer et al. [132]. In their work they describe the spectroscopic properties of the HET-s protein in its wild-type form. Also in this case the resonances of the fibrillar core remain unchanged even if the entire globular domain is attached to it. Compared to the spectra in this work more resonances of the globular domain can be seen in the spectra. The visibility of these resonances is limited by the achievable signal to noise ratio as the signals are very weak. In their work spectra were recorded at a higher static magnetic field (20 T vs. 14.1 T) which increases sensitivity. Furthermore in the wt HET-s the ratio of residues of the globular domain to the fibril forming domain is roughly 3:1, whereas in the construct studied here the ratio is roughly 1:1. This means that in the wt HET-s there are more resonance giving rise to the additional resonances. Part II.

The DREAM Experiment in Multi-Spin Systems

7. Introduction to the DREAM Experiment

The Dipolar Recoupling Enhanced by Amplitude Modulation (DREAM) experiment is an advanced, further evolved version of the homonuclear rotary-resonance (HOR- ROR) experiment [133]. This experiment is carried out under MAS and as a consequence the homonuclear dipolar coupling has to be actively reintroduced to promote polarization transfer between nuclei. This is done in the case of the HORROR experiment by a cw-irradiation with a RF ﬁeld amplitude that fulﬁlls the condition

1 ω = ω . (7.1) 1 2 r

Under these circumstances the RF irradiation which modulates the spin-part of the Hamiltonian interferes with the MAS which modulates the spatial part of the Hamil- tonian leading to an incomplete averaging of the homonuclear dipolar coupling. This process is often called recoupling. In comparison to other recoupling methods relying on RF irradiation such as the ω = ω C7 experiment ( 1 7 r)theRFfield amplitude is quite low [134]. This feature is beneficial as it leads to less sample heating, which could harm thermolabile compounds such as proteins. It is also beneficial with respect to the probe because it allows high-power proton decoupling on thermostabile compounds as the total RF load is minimized. The downside the low RF amplitudes on the active spin during mixing is that it leads to a sensitivity to chemical shift offsets depending on the relative magnitude of the RF irradiation and the chemical shift offset. In the following a theoretical description of the HORROR experiment for the simplest case of a homonuclear, dipolar coupled two-spin systems is derived. Chemical shift offsets are first neglected and explicitly introduced later. The DREAM experiment is introduced and the underlying mechanism of an adiabatic inversion is shown.

75 76 7 Introduction to the DREAM Experiment

Finally, the application of the DREAM experiment in a multi-spin system and the resulting transfer pattern is outlined.

7.1. Theoretical Description

7.1.1. The HORROR Experiment

As shown in section 1.1.2 the transfer characteristics of an NMR experiment can be a evaluated by analyzing the Hamiltonian mediating the polarization transfer. In the simplest case of a HORROR recoupling of a dipolar coupled homonuclear spin pair without considering chemical shift offsets, the mixing Hamiltonian in a tilted interaction frame, in which the z-axis is along the RF irradiation is given by Hˆ ( )=ω ˆ + ˆ + ω(1,2)( ) ˆ ˆ − ˆ ˆ t 1 S1z S2z SS t 3S1xS2x S1S2 . (7.2)

In this example it is assumed that the RF irradiation is much larger than the chemical shift offsets. Under this condition equation (7.2) can be rewritten in the following matrix representation. ⎛ ⎞ ⎛ ⎞ ⎜ 100 0⎟ ⎜ −100 3⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ 000 0⎟ ⎜ 0110⎟ Hˆ ( )=ω ⎜ ⎟ + ω(1,2)( ) 1 ⎜ ⎟ t 1 ⎜ ⎟ SS t ⎜ ⎟ ⎜ ⎟ 4 ⎜ ⎟ ⎜ 000 0⎟ ⎜ 0110⎟ ⎝ ⎠ ⎝ ⎠ 000−1 300−1 ⎛ ⎞ ⎜ ω − 1 ω 00 3 ω ⎟ ⎜ 1 4 SS 4 SS ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ 0 1 ω 1 ω 0 ⎟ = ⎜ 4 SS 4 SS ⎟ ⎜ ⎟ (7.3) ⎜ 1 ω 1 ω ⎟ ⎜ 0 SS SS 0 ⎟ ⎝ 4 4 ⎠ 3 ω −ω − 1 ω 4 SS 00 1 4 SS

From the structure of matrix (7.3) it can be seen that the Hamiltonian can be split 1 into two commuting pseudo spin– 2 subspaces: the zero-quantum subspace indicated 7.1 Theoretical Description 77

with Δ and the double-quantum subspace indicated with Σ.

Σ Δ Hˆ (t)=Hˆ (t)+Hˆ (t) (7.4)

The base operators of the double- and zero-quantum subspace are deﬁned as Δ 1 + − − + Σ 1 + + − − Sˆ = S S + S S Sˆ = S S + S S x 2 1 2 1 2 x 2 1 2 1 2 Δ i + − − + Σ i + + − − Sˆ = − S S − S S Sˆ = − S S − S S (7.5) y 2 1 2 1 2 y 2 1 2 1 2 Δ 1 Σ 1 Sˆ = (S − S ) Sˆ = (S + S ) . z 2 1z 2z z 2 1z 2z

The two Hamiltonians are given by

Σ Σ 1 ( ) Σ 3 ( ) Σ Hˆ (t)=2ω Sˆ − ω 1,2 (t) 1ˆ − ω 1,2 (t) Sˆ (7.6a) 1 z 4 SS 2 SS x Δ 1 ( ) Δ 1 ( ) Δ Hˆ (t)= ω 1,2 (t) 1ˆ + ω 1,2 (t) Sˆ . (7.6b) 4 SS 2 SS x

The initial density operator is aligned with the spin-lock ﬁeld and is given by

ρΣ = ˆΣ ˆ0 2Sz (7.7a) ρΔ = ˆ0 0. (7.7b)

Under these assumptions and in the absence of relaxation only the time-evolution of the double-quantum density operator has to be considered. The double-quantum Hamiltonian is transformed into an interaction-frame representation with the RF con- H H Σ( ) tribution of the Hamiltonian ˆ1 leading to the double-quantum Hamiltonian ˆ t which is time-dependent. H = ω + = ω Σ ˆ1 1 Sˆ1z Sˆ2z 2 1Sˆ (7.8) z Σ 3 ( ) Σ Σ Hˆ (t)=− ω 1,2 (t) Sˆ cos(2ω t)+Sˆ sin(2ω t) (7.9) 2 SS x 1 y 1

The terms proportional to the unity operator were neglected. The MAS-modulated and thus time-dependent dipolar coupling is expanded into a Fourier series with the 78 7 Introduction to the DREAM Experiment

MAS frequency ωr.

2 (1,2) 1 ω (1,2) ω ( )=√ im rt 2 (θ ) (β γ) SS t ∑ e dm 0 m Alm , (7.10) 6 m=−2

2 In equation (7.10) dm0 is the reduced Wigner rotation element of rank 2, the angle θm is the magic angle, β and γ are two Euler angles relating the lab frame to the rotor ﬁxed frame. The coupling constant is not depended on the Euler angle γ as this corresponds to a rotation around the z-axis. Substituting the dipolar coupling into equation (7.9) leads to

2 Σ 3 1 ω (1,2) Σ Σ Hˆ ( )=− √ im rt 2 (θ ) (β γ) ˆ ( ω )+ ˆ ( ω ) t ∑ e dm 0 m Alm , Sx cos 2 1 t Sy sin 2 1 t 2 6 m=−2 (7.11) This Hamiltonian in the interaction frame shows two time-dependencies: the ﬁrst ω(1,2) ω is the dipolar coupling SS which is modulated by the MAS frequency r and the ˆΣ ˆΔ second is the modulation of the spin operators Sx and Sx respectively, by the RF ω ω = 1 ω frequency 1. Under the assumption that 1 2 r and neglecting all the non- secular (time-dependent) terms the zeroth-order average Hamiltonian is given by (0) Hˆ = − √3 β(1,2) δ(1,2) ˆΣ sin 2 Sx . (7.12) 8 2 D

In the discussed case of a dipolar coupled spin pair without chemical shifts the den- ρΣ ˆΣ sity operator in the double-quantum space ˆ0 performs a rotation around Sx when irradiated at the HORROR condition. In the usual rotating frame this leads to an oscil- ρ = latory polarization transfer around 0.5 Sˆ2z with an initial density operator of 0 Sˆ1z. In the usual case where a powdered sample is measured the powder average scales the dipolar coupling and thereby diminishing the transfer. In this case the biggest transfer is obtained after the ﬁrst oscillation with 73%.

In practice the situation of a spin pair without chemical shift offsets is only of minor importance. When taking the chemical shift offsets of the two spins into account the Hamiltonian is expanded by two terms: Hˆ ( )=ω(1) ˆ + ω(2) ˆ + ω ˆ + ˆ + ω(1,2)( ) ˆ ˆ − ˆ ˆ t iso S1x iso S2x 1 S1z S2z SS t 3S1xS2x S1S2 . (7.13) 7.1 Theoretical Description 79

In this case the HORROR experiment is described in a tilted interaction frame θ = with the effective field direction being the quantization axis with the tilt angle k ω ω(k) arctan 1/ iso with respect to the z-axis. The necessary frame transformations are shown in figure 7.1. The effective field strength is given by the length of the sum vec- ( ) ( ) 2 ω k = ω k + ω2 θ tor as eff iso 1. Notice that the tilt angle k is different for each spin k. The tilted-frame Hamiltonian is given by

H ( )=ω(1) + ω(2) ˆ t Sˆ1z Sˆ2z eff eff +ω(1,2)( ) θ + θ θ + θ t 2 Sˆ1z cos 1 Sˆ1x sin 1 Sˆ2z cos 2 Sˆ2x sin 2 SS (7.14) −ω(1,2)( ) ˆ θ − ˆ θ ˆ θ − ˆ θ SS t S1x cos 1 S1z sin 1 S2x cos 2 S2z sin 2 −ω(1,2)( ) ˆ ˆ SS t S1yS2y.

rotating frame tilted frame interaction frame with

Figure 7.1. Frame transformations used to describe the HORROR/DREAM experiment and the effect on the combined RF and chemical shift Hamiltonian. Nota bene that in the case of no chemical shift offset the tilt angle θ is 90◦. The Euler angles of each transformation are speciﬁed in the arrows.

It can been shown easily that the case of no chemical shift offsets corresponds to a θ = θ = ◦ ﬂip angle of 1 1 90 in which equation (7.14) collapses to the simple case given in equation (7.2). To visualize the properties of the different terms, the tilted-frame 80 7 Introduction to the DREAM Experiment

Hamiltonian is expanded and rewritten in terms of raising and lowering operators.

( ) ( ) Hˆ (t)=ω 1 Sˆ + ω 2 Sˆ eff 1z eff 2z ( ) ( ) ( ) 1 + − − + +ω 1,2 (t) A 1,2 Sˆ Sˆ + B 1,2 Sˆ Sˆ + Sˆ Sˆ SS 1z 2z 2 1 2 1 2 ( ) + − ( ) + − (7.15) +R 1,2 Sˆ Sˆ + Sˆ Sˆ + S 1,2 Sˆ Sˆ + Sˆ Sˆ 1z 2 1z 2 1 2z 1 2z + (1,2) ˆ+ ˆ+ + ˆ− ˆ− Q S1 S2 S1 S2

( ) ( ) ( ) ( ) ( ) The scaling factors A 1,2 , B 1,2 , R 1,2 , S 1,2 and Q 1,2 are calculated by rotating the − − cartesian representation of the dipolar Hamiltonian 2Sˆ1zSˆ1z Sˆ1xSˆ1x Sˆ1ySˆ1y around = ( θ )+ ( θ ) the rotation operator Rˆ exp i 1Sˆ1y exp i 2Sˆ2y the commutator relations among the spin operators allows further simpliﬁcation of the scaling factors to:

(1,2) = θ θ − θ θ A 2cos 1 cos 2 sin 1 sin 2 (7.16a) ( ) 1 1 B 1,2 = − − cos θ cos θ + sin θ sin θ (7.16b) 2 2 1 2 1 2 ( ) 1 R 1,2 = − cos θ sin θ − sin θ cos θ (7.16c) 1 2 2 1 2 ( ) 1 S 1,2 = − sin θ cos θ − cos θ sin θ (7.16d) 1 2 2 1 2 ( ) 1 1 Q 1,2 = − cos θ cos θ + sin θ sin θ . (7.16e) 2 2 1 2 1 2

◦ ( ) In the case of vanishing chemical shift differences (θ → 90 ) the coefﬁcients B 1,2 , ( ) ( ) R 1,2 and S 1,2 vanish giving the expected double quantum Hamiltonian. Analogous to the treatment in the case of vanishing chemical shift the time-dependence of the dipolar coupling is given by equation (7.10) in a Fourier series containing

terms modulated by ω r and 2 ω r. To recouple the dipolar interactions the sum of the ω(1) + ω(2) ω effective ﬁelds eff eff has to be matched with the rotor frequency r.

7.1.2. From HORROR to DREAM

The main drawbacks of the HORROR experiment [133] is its high sensitivity to chemical shift offsets and RF ﬁeld inhomogeneities. This is caused by the low RF irradi- ω ation amplitude as compared to typical chemical shift offsets l,iso. This can be at 7.1 Theoretical Description 81

eliminated to a large extend by sweeping the RF ﬁeld through the HORROR condition in an adiabatic fashion vide infra. This experiment is called dipolar recoupling enhanced by amplitude modulation (DREAM) [47]. The considerations used to explain the polarization transfer of the HORROR experiment still hold, as the amplitude change can be parametrized for each spin pair (k, l) by

ω ( )=ω + Δ ( ) 1,(k,l) T (k,l) T . (7.17)

The change in amplitude is much slower than the periodicity of the active Hamil-

tonian, therefore the amplitude can be considered constant over the cycle time τr = 2π/ω r. These two time scales are separated into the fast changing interactions dependent on t and the slow changing amplitude modulation dependent on T.The ω ( ) ω amplitude 1,k T is then described as the amplitude on the recoupling condition Δ ( ) and its offset k T from the recoupling condition which can be different for each spin k. In the typical case when chemical shift offsets are present, the quantization axis of the tilted coordinate system is changed during the sweep of duration τ on the time θ θ scale of the time T. The means that the tilt angles k and l become T-time dependent. The effective, slowly changing Hamiltonian in the tilted frame can be derived analogous to equation (7.12): (0) Hˆ = Δ ( ) ˆΣ − √3 β(k,l) δ(k,l) ˆΣ (k,l) T Sz sin 2 Sx . (7.18) 8 2 D It has been shown by Verel et al. [47] that a tangential sweep for the case of the DREAM experiment in which the amplitude sweep translates into a sweep in the double quantum subspace is beneﬁcial. Contrasting other applications of adiabatic methods such as the adiabatic inversion during homonuclear mixing sequences [26], ˆΣ here only one component Sz of the active Hamiltonian is under experimental control. The trajectory of the mixing Hamiltonian is shown graphically in ﬁgure 7.2. (0) In an ideal picture the Hamiltonian Hˆ would start parallel at time T = 0to + ˆΣ Δ ( )=+∞ the Sz direction (corresponding to a (k,l) 0 ), sweep through the HORROR = τ − ˆΣ condition of that particular spin pair and end at time T along the Sz direction Δ (τ)=−∞ (corresponding to a (k,l) ). If the sweep is carried out in a adiabatic fashion 82 7 Introduction to the DREAM Experiment

Σ Σ Figure 7.2. Trajectory of the Hamiltonian Hˆ and the density operator ρˆ in the double-quantum ˆΣ subspace. The component proportional to Sx is ﬁxed, leading to a minimal adiabaticity Qmin on the resonance condition.

σΣ( )= ˆΣ this leads to an inversion of the initial density operator ˆ 0 2Sx to the final den- τ σΣ(τ)=− ˆΣ sity operator at time ˆ 2Sx . By using the definition of the base operators of the double-quantum and zero-quantum subspace (7.5) it can be shown easily that this corresponds to a 100% transfer from spin 1 to spin 2. The adiabatic condition to be fulfilled is given by the relation

⎛ ⎞ ( ) (k,l) Θ( ) − √3 sin 2 β k,l δ d T ω ( ) Θ( )= ⎝ 8 2 D ⎠ eff T with T arctan Δ ( ) . (7.19) dT (k,l) T

It can be seen that the critical situation during the sweep is at the resonance condition when the length of the effective ﬁeld is given by the dipolar coupling only. To describe the adiabatic condition of equation (7.19) quantitatively, the adiabaticity factor Q is introduced as follows:

ω (T) Q(T)= eff . (7.20) dΘ(T)/dT 7.1 Theoretical Description 83

It is now possible to plot the adiabaticity versus the sweep length. This is shown in ﬁgure 7.3. The passage through the resonance condition is clearly visible as a minimum in the adiabaticity.

100 70 50

20 Adiabaticity 15

0.000 0.001 0.002 0.003 0.004 Sweep time s

Figure 7.3. Adiabaticity during a tangential sweep through the HORROR condition. The minimum indicates the passage through the resonance condition. For this plot a dipolar coupling constant of 2 kHz, a sweep length of 4 ms and a sweep amplitude difference of the beginning and the end of the sweep of 3 kHz was used.

7.1.3. DREAM in Multi-Spin Systems

In multi-spin systems the polarization transfer characteristics of the DREAM experiment can often be described as a sequential recoupling of spin pairs. An example for a three spin system is fully 13C labeled alanine. Each 13C spin is dipolar coupled to the other two spins and each spin has a different chemical shift. During the DREAM mixing the sum of the effective fields of the coupling partners must match the spinning frequency to promote polarization transfer as shown in section 7.1.1. As the amplitude of the RF irradiation is slowly changing also the effective fields of the spins change. This means that the recoupling condition for each spin pair is fulfilled at different points of the sweep. To gain insight into the order of the resonance conditions for each spin pair, the adiabaticity during the sweep is calculated analytically for a single set of dipolar cou- 84 7 Introduction to the DREAM Experiment plings. The minima of the curves in figure 7.5 indicate an active recoupling. In the case of a sweep with a direction from low to high amplitudes recoupling conditions are hit in the order CO/CA–CA/CB meaning that there is a relayed transfer of magnetization from CO via CA to CB active which can be observed as a CO/CB peak with the same sign as the diagonal. In the opposite direction there is no relayed transfer possible because after the transfer CA/CB is active there is no possibility for the magnetization to be transferred to CO as this recoupling condition has been met before. This effect leads to spectra which are asymmetric to the diagonal. In the ideal case when the polarization is fully transferred on the one side of the diagonal there is no direct CO/CA peak but just the CO/CB relay peak and on the other side of the diagonal there is no CB/CO peak (see figure 7.4). The direct CO/CB transfer which is first in the sequence can be neglected as the minimal adiabaticity is much smaller than one. This means that the adiabatic condition in equation (7.19) is violated and the density operator start nutating around the Hamiltonian.

CO CA CB

Figure 7.4. Schematic representation of a 2D DREAM in alanine as a model three spin system. The spectrum shows a strong asymmetry because different polarization transfer pathways are active different points during the mixing sweep. The sign of the peaks are indicated in the spectrum and show the sign inversion typical for double-quantum mixing. 7.2 Simulation Strategies 85

4 10 CO/CA CO/CB CA/CB 2 10

Adiabaticity 10

-2 10 0123456 Time/ms Figure 7.5. Adiabaticity plot of a DREAM sweep using alanine as a model. Spinning frequency was 65 kHz, sweep was centered around 31 kHz with an initial difference of 3 kHz and an estimated dipolar coupling of 1 kHz. Carrier position during mixing was 60 ppm.

7.2. Simulation Strategies

Simulations of NMR experiments are a powerful tool to understand the spin dynamics of a given system. Quantum-mechanical simulations provide a “playground” in which everything is under control of the experimentalist, like the complete analytic treatment of a spin system . This enables direct analysis of which interactions or terms of the Hamiltonian are of importance for the effect under investigation. The GAMMA C++ simulation framework [135] provides data types and methods to carry out calculations. Contrasting other commercially available products like Mat- lab or Mathematica a simulation written in C++ is more portable, as it depends on the availability of a suitable compiler for that processor architecture only. A wide range of processor architectures is supported by the de facto standard GNU Compiler Collection (GCC) [136]. The C++ front-end of the GCC is under very active develop- ment, as this is the underlying compiler for many programs used in the Linux/Unix ecosystem. This means that performance gains by improved compiler design translates directly into improved GAMMA simulation performance. In quantum-mechanical simulations matrix manipulations play a major role. Es- pecially matrix multiplications and diagonalizations are among the most computa- tional-intense steps in a simulation. These steps typically limit the size of the quan- 86 7 Introduction to the DREAM Experiment

tum-mechanical system under investigation as with increasing matrix size these operations are slowed down dramatically. As outlined in section 1.1.2 the outcome of a NMR experiment is described by the Liouville-von Neumann equation (1.19). In the case of the DREAM experiment the Hamiltonian is time-dependent. To transform the doubly time-dependent Hamiltonian into a time-independent one for which the propagator Uˆ can be calculated easily, the coordinate transformations outlined in section 7.1.1 lead to a Hamiltonian which is time-dependent in respect to the MAS frequency ω r only. Two approaches are possible to remove this last time dependence so that the solution given in equation (1.20) can be used to calculate the propagator. The ﬁrst is to divide one rotor period into small time slices during which the Ham- iltonian can be regarded as time-independent. For each time slice the propagator is calculated and concatenated by multiplication to obtain the propagator for a whole rotor cycle Uˆ rot (see ﬁgure 7.6). This approach can be regarded as a sampling of the periodic time-dependent Hamiltonian. From this consideration it is clear that a shorter time slice and thus more time slices per rotor cycle lead to a better approximation but also in more matrix diagonalization and multiplication operations. If the time to be calculated is not an integer multiple of the rotor period an additional prop-

agator Uˆ rest has to be calculated which accounts for a the last non-completed rotor revolution. The second approach is to use Floquet theory. In a Floquet treatment a periodic time-dependent Hamiltonian in Hilbert space can be transformed into a time-independent Hamiltonian in Floquet space. The propagator of this Floquet Hamilto- nian can then again be calculated straightforward with equation (1.20). A finite- dimensional time-dependent operator in Hilbert space is represented in Floquet space as an infinite-dimensional time-independent operator. The operator is expanded by “dressing” it with the Fourier coefficients of the base frequency of the Floquet space [137]. For numerical calculations this Fourier series is truncated to 11 Floquet dimensions, corresponding to the −5, −4,...,0,...,4,5 Fourier components. This truncation implies that the infinite Floquet space can be approximated by taking only 11 components in the center into account. A priori it is not clear if the size of the Floquet space is sufficient. By choosing a larger Floquet space the approximation is better, but the matrix dimensionality grows considerably. The advantage of a Floquet treatment is that the propagator has to be calculated only 7.3 DREAMing Away 87 once. This propagator can be projected back into Hilbert space and used to calculate the time evolution of the density operator of interest. The simulation framework GAMMA supports Floquet space calculations. A detailed description how a Floquet- based simulation is performed can be found in the literature [138, 139].

7.3. DREAMing Away

It has been shown in section 1.3 that the assignment problem is the firsthurdleto overcome to study complicated systems such as proteins by NMR. As pointed out earlier multi-dimensional spectroscopy is necessary to resolve spectral ambiguities. Three-dimensional spectroscopy which has been applied to a wide range of systems in biomolecular liquid-state NMR has been adapted to render its application possible in the solid state, too. The key components of a multi-dimensional experiment are the mixing steps involved. With the right choice of mixing the spectroscopist can tailor spectra to an- swer the questions at hand. The mixing scheme has two important requirements: first, the mixing should be efficient which translates in the two-dimensional case to a spectrum in which the diagonal is void and all intensity is found in cross peaks. Sec- ond, in an n-dimensional experiment at least (n − 1) polarization transfer steps are involved. Therefore magnetization losses e.g. due to relaxation have to be minimal, as a sequence leading to quantitative transfer but during which almost all magnetization relaxes is of very limited use in practical cases where signal to noise is a limiting factor. The DREAM scheme meets these requirements. Concrete examples of three-dimensional spectra involving the DREAM building block are the NCACX and the NCOCA experiments which are outlined in figure 7.7. Polarization is first transferred from the protons to the nitrogen of the amino acids, then selectively to the CA or the CO by using a SPECIFIC CP [140]. In the case of the NCACX experiment polarization is distributed over all spins in the spin system (aliphatic and carbonyl). For the side chain assignment the transfer to the carbonyl group is not desired. The cross peaks in this spectrum are labeled with the nitrogen, CA and the CX frequency of the same spin system. This signature can be used to identify the amino acid type of the spin system which is one of the first steps in the assignment process. In the case of the 88 7 Introduction to the DREAM Experiment

NCOCA the dominant DREAM transfer is CO-CA as there is a considerable chemical shift offset between CO and CA which must be considered in the case when the MAS frequency is not much larger than this chemical shift offset. The cross peaks in this spectrum are labeled with the nitrogen frequency of the current residue and the CO and mostly CA frequency of the previous residue. This experiment can be used to get sequential information. Further information about assignment strategies in proteins can be found in the literature [56]. 7.3 DREAMing Away 89

Figure 7.6. Schematic representation of the time-slicing approach. The rotor period is divided into 10 time intervals for each a propagator Uˆ i is calculated. The sub-propagators are concatenated via multiplication to obtain the propagator over one rotor cycle Uˆ rot. If the time to be calculated is not a multiple of the rotor period, an additional propagator Uˆ rest has to be calculated.

decoupling CW decoupling CP 1H

CP t DREAM 13C 2

t3 CP t CP 15N 1 O O

NCACX Cα C N Cα C H R i-1 Ri O O

NCOCA Cα C N Cα C H

Ri-1 Ri

Figure 7.7. Three-dimensional NMR experiment using the DREAM scheme as key element for homonuclear mixing. Depending on the 13C carrier position of the second CP polarization is transferred to CA or CO leading to correlations in the same or with the previous residue.

8. Experimental

8.1. Simulation of DREAM Transfer

To investigate the DREAM transfer in multi-spin systems the experiment was simulated analytically using the GAMMA C++ framework [141]. Input spin system files were generated with atom coordinates taken from the Cambridge Structural Database [142] and converted to GAMMA format. The homonuclear 13C–13Cdipo- lar coupling constants were determined from the inter-atomic distance. For single amino acids only the isotropic chemical shift values reported by Ye et al. [143] were used. All single amino acids except tryptophane were simulated. In the aromatic amino acids the ring was simplified by taking only one ortho and one meta carbon into account. It has been verified that under experimental conditions the CSA can be neglected. The simulations are the sum of at least 50 crystallite orientations given by the method of Cheng et al. [144]. Simulations were carried out on the Brutus cluster at ETH Zürich based on AMD Opteron processors. This cluster is Linux-based and the simulation program was compiled with the C++ compiler of the Portland Group optimized for the AMD Opteron Shanghai processors. In addition simulations were run on the NMR cluster which is a heterogeneous AMD and SPARC cluster running Solaris and the Sun grid engine software [145]. The simulations for this cluster were compiled using the Sun CC compiler. For spin systems bigger than 4 spins the simulation was divided up into several jobs by calculating different crystallite orientations to allow parallel execution on different cluster nodes. To simulate the tangential amplitude modulation of the DREAM sweep it is sampled in discrete steps. As the CPU time scales linearly with the number of steps the tangent was not sampled at equidistant time points but instead sampled after a fixed change in amplitude. This has the effect that the sampling points are closer together

91 92 8 Experimental at the beginning and end of the sweep and further apart in the middle where the tangent is ﬂat. For these simulations a minimal number of 50 steps on the sweep was sufﬁcient as the results converged for this setting. Unless stated otherwise the sweep was always done in the direction from low to high amplitudes.

Custom scripts written in Perl and Matlab were used to examine the transfer efﬁ- ciency dependency on the position of the carrier during the sweep and the irradiation ﬁeld strength.

8.1.1. Simulating the Mixing Using Time-Slicing

During the mixing step the Hamiltonian involved is modulated by the MAS and the amplitude modulated RF-irradiation. For each amplitude step a propagator is calculated by dividing a rotor period into small steps in which a time-independent Ham- iltonian can be assumed. Unless stated otherwise one rotor cycle was divided into 50 discrete steps. The propagators of each step were combined to a propagator for one rotor revolution. For amplitude steps which are no multiples of the rotor period the propagator needed for the last incomplete revolution was cached during the calculation of the propagator of the full rotor revolution to min

8.1.2. Simulating the Mixing Using Floquet Theory

Floquet theory is used to calculate the evolution of the initial density operator in Floquet space. The propagator in Floquet space is calculated, projected back and applied to the density operator in Hilbert space. The mixing Hamiltonian is expanded in a Fourier series with the MAS rotation frequency. The number of coefﬁcients needed and therefore the dimensionality of the Floquet space was determined experimentally. Unless stated otherwise an 11 dimensional Floquet space with the basis B = {| − 5, |−4,...,|0,...,|4, |5} was used. 8.2 Experimental DREAM Spectra 93

Table 8.1. Standard simulation parameters

Parameter Floquet time-slicing

Powder points 50 Points on amplitude sweep 50

Number of Floquet dimen- 11 – sions

Number of time slices per – 100 rotor revolution

8.2. Experimental DREAM Spectra

8.2.1. DREAM Spectra of Single Amino Acids

To compare the simulated transfer efficiencies DREAM spectra were acquired experimentally. DREAM spectra of single amino acids as model compounds were measured on a Chemagnetics/Varian Infinity+ spectrometer operating at a static field of 7.05 T and 11.74 T corresponding to a proton Larmor frequency of 300 MHz and 500 MHz respectively. A Chemagnetics/Varian T3 2.5 mm double-resonance probe at the lower field and Chemagnetics/Varian T3 2.5 mm triple-resonance probe operating in double-resonance mode at the higher field was used. MAS was actively stabilized ◦ within ±10 Hz. The temperature of the probe was stabilized to 25 C inlet temperature using a Varian VT-controller. Initial polarization on 13C was created using an adiabatic cross-polarization step [20, 22] of 2.5 ms duration. The tangential amplitude sweep of the DREAM mixing and the cross-polarization was approximated by 1000 discrete steps. Both sweeps were performed in the direction from low to high amplitudes. To investigate the influence of the irradiation frequency of the DREAM sweep on the spectrum the carrier during mixing could be set arbitrarily by setting the frequency of the 13C channel before and after mixing explicitly. Proton decoupling during t1 and t2 was done using the TPPM scheme [43] under 20 kHz MAS and the XiX scheme [44] above. Field strength higher than 140 kHz on the proton channel were used during composite pulse decoupling and off-resonance cw decoupling during the DREAM mixing. In 2D spectra sign discrimination in the indirect dimension 94 8 Experimental

was carried out using the States [146] scheme. To facilitate screening of parameters a custom acquisition macro was used which allowed measuring a set of spectra with different carrier positions during the DREAM and DREAM ﬁeld strengths without user interaction.

8.2.2. DREAM Spectra of Ubiquitin

DREAM spectra of U-13C,15N Ubiquitin were acquired on a Bruker AV600 spectrometer operating at a static ﬁeld of 14.09 T corresponding to a proton Larmor frequency of 600 MHz. A Bruker 3.2 mm triple-resonance probe was used. MAS was actively ◦ stabilized within ±10 Hz. The temperature of the sample was stabilized to 3 C using a Bruker VT-controller in combination with a BCU-Xtreme cooling unit. The sample temperature was externally calibrated using the T1 temperature-dependence of KBr [147]. In spectra at 13 kHz MAS the Spinal64 scheme [19] and in spectra at 24 kHz

MAS the XiX scheme [44] was used at a ﬁeld strength of 100 kHz during t1 and t2. During the DREAM mixing sweep cw-decoupling with a ﬁeld strength of 100 kHz was used. The tangential amplitude modulation during mixing was approximated with 1000 discrete steps. In the indirect dimension 1024 points with 16 scans each were acquired using TPPI [123] for sign discrimination. An overview of all experimental details is given in table 8.2.

8.2.3. Data Evaluation

To compare the experimental data to the simulations 2D DREAM spectra were acquired under several different spinning speeds, carrier positions and recoupling field strengths. The spectra of single amino acids were processed using nmrPipe [124]. In the direct dimension a Lorentz to Gauss apodization was done, adding a line broadening of 100 Hz to broaden the multiplet fine structure in one peak. Peak picking and fitting a Gaussian on each individual resonance was done using nmrPipe standard scripts. The Ubiquitin spectra were processed with nmrPipe using a squared cosine apodization function in both dimensions. Peaks were picked using Sparky [125] and resonance lists were evaluated using custom Perl scripts. 8.2 Experimental DREAM Spectra 95

Table 8.2. Experimental details of DREAM spectra acquired on U-13C,15N Ubiquitin.

Parameter DREAM

spectrum Figure 9.6 MAS frequency [kHz] 13 24 ω ω τ CP 1H, 13C [kHz], CP [ms] 86,107,2 80,107,2

mixing time [ms] 5 5 Δ ω DREAM: RF,dest, 1 [kHz] 2,1,6 3,1,11.5 ω ω cw-decoupling 1H [kHz], off [kHz] 100,10 100,10 direction of the sweep low to high ﬁeld decoupling scheme Spinal64 XiX ω τ μ 1H [kHz], 2 [ s] 100,4.8 100,77

t1 increments 1024

scans / t1 increment 16 measurement time [h] 9

SW t1 and t2 [kHz] 50

9. Results

9.1. Simulation Strategies

As pointed out in section 7.2 there are two ways of simulating the DREAM experiment. The two implementations were tested both in terms of convergence and simulation speed. To minimize the duration of the calculations the number of points needed to sample a powder distribution Npow,the number of amplitude steps needed to sample the DREAM sweep Nsw and the number of time slices Nsl on one rotor revolution were optimized. A comparison of different combinations of these three parameters presented in ﬁgure 9.1 show that there is no difference between simulations with a high number of powder orientations, sweep points and time slices and = = = such with a minimal parameter set of Npow 50, Nsw 50 and Nsl 100.

To compare the performance of a simulation using a time-slicing versus a simulation using Floquet theory spin systems of different sizes were simulated and timed. Figure 9.2 shows that the time-slicing approach is signiﬁcantly faster than the Flo- quet simulation. Especially for the largest simulated spin system which consisted of 7 spins a 40-fold increase was observed. One node of the Brutus cluster is about 40% faster than an AMD-based NMR node. The simulation program was proﬁled to investigate which part of the simulation is the time-limiting step. It turned out that 75% of the CPU time is spent in calculating the propagator which involves a matrix diagonalization step and 25% of the time is used to perform matrix multiplications needed for calculate the propagator of the whole sweep. All other operations in the program are of minor importance in terms of CPU time consumption.

Unless stated otherwise all following simulations were done using time-slicing.

97 98 9 Results

0 a) Ile d) Phe -0.2 -0.4 -0.6 0 0 b) e) -0.2 -0.4

Intensity I/I -0.6 0 c) f) -0.2 -0.4 CA → CB CA → CB -0.6 CB → CA CB → CA 100 80 60 40 20 0 80 60 40 20 0 -20 Carrier Position/ppm Carrier Position/ppm

Figure 9.1. Convergence test of a time-slicing based simulation. Phenylalanine and isoleucine were ω 1 ω ( )= simulated at 0( H)=600 MHz ﬁeld and an MAS frequency of r/ 2ı 13 kHz. The DREAM sweep was centered at 6 kHz with an initial offset Δ=2 kHz and an estimated dipolar coupling of δest=1 kHz. Three different sets of powder orientations Npow, number of slices per rotor period Nsl and number = = = of amplitude steps on the sweep Nsw were used: a) and d):Npow 50, Nsl 100, Nsw 50; b) and ======e):Npow 50,Nsl 200, Nsw 100; c) and f) Npow 100, Nsl 200, Nsw 100.

50 Brutus time-slicing 2 10 NMR time-slicing 40 Brutus Floquet NMR Floquet 30 Time ratio Brutus 0 10 Time ratio NMR 20 CPU time/h

-2 10 10

0 Time ratio Floque/time slicing 234567 Number of spins in spin system

Figure 9.2. Comparison of CPU time needed to simulate a DREAM experiment with the time-slicing and Floquet-based approach. Standard parameters shown in table 8.1 were used. Each simulation was repeated 10 times. 9.2 Transfer Efﬁciency Dependence on Carrier Position and RF Field 99

9.2. Transfer Efﬁciency Dependence on Carrier Position and RF Field

In section 7.1.3 it was outlined how different DREAM sweeps can change the cross peak intensity. This effect was investigated by simulating the DREAM experiment for single amino acids with a range of carrier positions during the sweep and RF field amplitudes. Figure 9.4 shows a simulation array of fully 13C-enriched alanine. The maximum of the transfer is reached when the HORROR condition coincides with the center amplitude of the sweep. For spin pairs with small chemical shift offsets such as CA/CB the recoupling is met at 12.5 kHz whereas for the CO/CA and the CO/CB pair which have a larger chemical shift offset the best transfer is reached at 11.5 kHz. For both the direct and the relayed transfer a carrier dependence was observed. The effect is strongest in the relayed case where polarization transfer occurs only in a small carrier interval. It also can be seen that in the case in the parameter region where the CB/CO transfer is strong in the same region in the CB/CA the transfer is attenuated. The same observation can be made by comparing the CO/CB relayed transfer to the CO/CA direct transfer. Another feature especially in the CA/CB and CB/CA case is the occurrence of a more or less pronounced “cleft” along the center of two peak positions. To verify the simulated DREAM spectra, a series of experimental spectra were acquired under the same conditions and processed as described in section 8.2.3. In figure 9.4 the results are presented graphically. The parameter space is more sparsely sampled compared to the simulations due to measurement time restrictions. In addition there are missing data points shown in yellow. There the chemical shift offset is large compared to the RF field leading to an effective spin lock field which is aligned between the x and the z axis. The magnetization then nutates around this field leading to dispersive components to the peak which makes fitting with a Gaussian peak impossible. The dependency of the transfer efficiency of the central sweep amplitude is the same for the experiment. To evaluate the reason for the “cleft” observed in figure 9.3 two simulations with identical simulation parameters were started. The only difference was that in one case the homonuclear 13C–13C J-coupling was neglected. The results of both simulations 100 9 Results

Transfer CO/CA Transfer CA/CO 14 14 CO CA CB CO CA CB

13 13

12 12 Mixing Field/kHz 11 Mixing Field/kHz 11

10 10 180 140 100 60 20 2060100140180 Carrier/ppm Carrier/ppm Transfer CA/CB Transfer CB/CA 14 14 CO CA CB CO CA CB

13 13

12 12

Mixing Field/kHz 11 Mixing Field/kHz 11

10 10 2060100140180 2060100140180 Carrier/ppm Carrier/ppm Transfer CO/CB Transfer CB/CO 14 14 CO CA CB CO CA CB

13 13

12 12 Mixing Field/kHz Mixing Field/kHz 11 11

10 10 2060100140180 2060100140180 Carrier/ppm Carrier/ppm

Figure 9.3. Cross peak intensity of simulated DREAM spectra of alanine. Red colors indicate the opposite sign of peak with respect to the diagonal and blue colors indicate the same sign. The mixing ﬁeld is the center amplitude of the DREAM sweep characterized by an initial offset of 4 kHz and an estimated dipolar coupling of 1 kHz. MAS frequency was 25 kHz with a 1H Larmor frequency of 300 MHz. Other simulation parameters according to section 8.1. 9.2 Transfer Efﬁciency Dependence on Carrier Position and RF Field 101

Transfer CO−CA Transfer CA−CO CO CA CB CO CA CB 13 13

12 12 Mixing Field/kHz 11 Mixing Field/kHz 11

10 10 2060100140180 2060100140180 Carrier/ppm Carrier/ppm Transfer CA−CB Transfer CB−CA CO CA CB CO CA CB 13 13

12 12

Mixing Field/kHz 11 Mixing Field/kHz 11

10 10 2060100140180 2060100140180 Carrier/ppm Carrier/ppm Transfer CO−CB Transfer CB−CO CO CA CB CO CA CB 13 13

12 12 Mixing Field/kHz Mixing Field/kHz 11 11

10 10 2060100140180 2060100140180 Carrier/ppm Carrier/ppm

Figure 9.4. Cross peak intensity of experimental DREAM spectra of alanine. Red colors indicate the opposite sign of peak with respect to the diagonal and blue colors indicate the same sign. Yellow patches indicate a missing data point which can occur at large chemical shift offsets when the peak line shape show disorptive components. The mixing ﬁeld is the center amplitude of the DREAM sweep characterized by an initial offset of 4 kHz and an estimated dipolar coupling of 1 kHz. MAS frequency was 25 kHz with a 1H Larmor frequency of 300 MHz. Other experimental parameters according to section 8.2.1 102 9 Results

are shown in ﬁgure 9.5. The features of a strong carrier dependence of the relayed and direct transfer discussed above are present in both cases, whereas the region of strongly attenuated transfer in the center of two resonances can be observed in the case with active J-coupling only. 9.2 Transfer Efﬁciency Dependence on Carrier Position and RF Field 103

no 13C-13C J-coupling 14000 COCG CA CB COCG CA CB 13500 13000 12500 12000 11500

Mixing Field/Hz 11000 10500 CO−CA CA−CB 14000 COCG1 CA CB COCG1 CA CB 13500 13000 12500 12000 11500

Mixing Field/Hz 11000 10500 CO−CB CB−CA 10000 180160140120100 80 60 40 20 0 160140120100 80 60 40 20 0 −20 Carrier/ppm Carrier/ppm

with 13C-13C J-coupling 14000 COCG CA CB COCG CA CB 13500 13000 12500 12000 11500

Mixing Field/Hz 11000 10500 CO−CA CA−CB 14000 COCG CA CB COCG CA CB 13500 13000 12500 12000 11500

Mixing Field/Hz 11000 10500 CO−CB CB−CA 10000 180160140120100 80 60 40 20 0 160140120100 80 60 40 20 0 −20 Carrier/ppm Carrier/ppm

Figure 9.5. Comparison of the DREAM transfer efﬁciency of aspartic acid with and without the homonuclear J-coupling. The main difference is the absence of a region of attenuated transfer located in the center of two resonances in the simulation without the J-coupling. Simulation parameters: The DREAM sweep is characterized by an initial offset of 4 kHz, an estimated dipolar coupling of 2 kHz and a length of 6 ms. The spinning frequency was 25 kHz at a proton Larmor frequency of 300 MHz. 104 9 Results

9.3. Cross Peak Patterns in Protein Spectra

9.3.1. Experimental DREAM Spectra

After observation of a strong dependence of the cross peak intensity of single amino acids the effect on protein spectra was investigated. Two series of DREAM spectra at 13 kHz and 24 kHz MAS were recorded. For each spinning frequency the carrier δ during the DREAM mixing step mix was set to 30 ppm, 43 ppm and 70 ppm, respectively resulting in 6 spectra in total. An overview of the aliphatic region is shown in figure 9.6. For the three spectra recorded at the slower spinning it can be observed that cross peaks are strongest around the carrier position, which means that the recoupling became band-selective. For example in the spectrum recorded with a carrier set to 70 ppm strong threonine CA/CB correlations can be observed but are absent in the spectrum with a carrier position of 30 ppm (figure 9.7(b)). The opposite effect can be observed on the CB/CA correlations of threonine at 24 kHz MAS frequency. In this case the cross peaks are = strongest at δ mix 30 ppm. The same trend can be found for the valine CG(1/2)/CB region (see figure 9.7(a)). Here the peaks are present if the carrier is placed at 30 ppm but at a carrier position of 43 ppm these peaks are not observable anymore. In contrast = the CG(1/2)/CB peaks are weakly present at δ mix 30 ppm but become stronger at δ = mix 43 ppm. Besides the carrier dependence of the peak intensity also an asymmetry with respect to the diagonal is present. Especially in the spectrum recorded at 13 kHz spinning with a carrier position of 30 ppm, the cross peaks of the CB/CA region are much stronger than in the CA/CB region. In the series of spectra recorded at 24 kHz MAS the cross peak intensity is higher. Also the recoupling is much more broad-band. This can be seen in the upper right spectrum recorded with a carrier position of 30 ppm as strong threonine CA/CB and CB/CA correlations can be observed. In addition there are more cross peaks visible which have the same sign as the diagonal compared to the slower spinning. Cross peaks of this kind are indicating a two-step, relayed transfer via a third spin as discussed in section 7.1.3. Notice that the fewest relay peaks can be observed in the two spectra with the carrier placed at 43 ppm. An asymmetry with respect to the diagonal as observed in the slow spinning case is also present in the fast spinning spectra, here the CA/CB region is strong at a carrier position of 70 ppm and much weaker at 9.3 Cross Peak Patterns in Protein Spectra 105

a carrier position of 30 ppm. For the CB/CA region the opposite is true.

9.3.2. Simulated DREAM Spectra

A set of DREAM simulations was performed in which the transfer pathways of single amino acids were investigated. An overview over the CA/CB and CB/CA transfer in 18 amino acids is given in figures 9.8 and 9.9. In these figure the intensity of a cross peak is plotted against the carrier position of the DREAM sweep. The negative intensity hints at a direct transfer. For the simulations three different sets of chemical shifts for each amino acid were used which are color coded in the plot. The plots show that the small chemical shift deviations do not influence the transfer profile significantly. Two typical curve shapes can be distinguished: First the transfer is symmetric around the center between the CA and CB resonances. This is the case for small amino acids such as alanine, serine but also for larger ones like tyrosine. Second the transfer is asymmetric with respect to the center between the CA and CB resonances. This behavior can be found in bigger amino acids such as valine, isoleucine, glutamic acid and lysine. For the second group of amino acids it is characteristic that the cross peak intensity for the CA/CB down field from the center of the two resonances is strong and the CB/CA peak is attenuated. On the high field side of the center the intensities swap. For both classes a minimum in the envelope of the two curves at the center between CA and CB is present. From the overall shape of the curves in the two figures it can be seen that the transfer is more broadband at the higher spinning frequency.

9.3.3. Comparing Simulated and Experimental DREAM Spectra

To compare the simulated transfer with the experimental results a more detailed analysis of the cross peaks between CA/CB and CA/CG was done in ﬁgures 9.10-9.13. In ﬁgures 9.10 and 9.11 the transfer characteristics of valine are investigated. The simulation of cross peak intensities of the aliphatic carbons of valine indicate that the cross peaks of these carbons strongly depend on the carrier position of the DREAM sweep. In the plot of the simulation different colors are indicating different correlated atoms, whereas the line style (dashed or continuous) indicates the direction of the transfer. 106 9 Results

13 kHz MAS 24 kHz MAS

30 Carrier /ppm ) 40 C 13 (

δ 50

70 10

30 /ppm ) 40 C Carrier 13 (

δ 50

70 10

30 /ppm ) 40 C 13 (

δ 50

70 Carrier 70 60 50 40 30 20 10 70 60 50 40 30 20 10 δ(13C)/ppm δ(13C)/ppm

Figure 9.6. Overview over the aliphatic region of a series of DREAM spectra of fully labeled ubiquitin. The spectra were acquired at 13 kHz and 24 kHz MAS frequency, the carrier position during the mixing period is indicated by the arrow. It can be seen that the cross peak pattern strongly depends on the carrier position and spinning frequency. Experimental parameters are given in table 8.2. The colors are indicating the sign of the peak. 9.3 Cross Peak Patterns in Protein Spectra 107

13 kHz MAS 24 kHz MAS

20 V5CG1 V5CG1 V17CG1 V26CG2 V17CG1 V26CG2 V70CG2 V70CG2 22 V70CG1 V70CG1 30 ppm V17CG2 V17CG2 V5CG2 V26CG1 V5CG2 V26CG1 24 20 V5CG1 V5CG1 V17CG1 V17CG1

/ppm V26CG2 V26CG2 ) V70CG2 V70CG2 43 ppm C 22 V70CG1 V70CG1

13 V17CG2 V17CG2 ( δ V5CG2 V26CG1 V5CG2 V26CG1 24 20 V5CG1 V5CG1 V17CG1 V26CG2 V17CG1 V26CG2 V70CG2 V70CG2 70 ppm 22 V70CG1 V70CG1 V17CG2 V17CG2 V5CG2 V26CG1 V5CG2 V26CG1 24 38 36 34 32 30 38 36 34 32 30 δ(13C)/ppm (a) The valine CGx/CB region.

13 kHz MAS 24 kHz MAS CA/CB CB/CA CA/CB CB/CA 30 ppm 68 T66 68 T66 60 T9 T66 T9 60 T9 T66 T9 T55 70 T55 70 T22 T14 T22 T14 62 T7 T12 62 T7 T12 72 T7 72 T7 T12 T14 T12 T14 64 T22 T55 64 T22 T55 74 74 43 ppm 68 T66 68 T66 /ppm ) T9 T66 T9 T9 T66 T9

C 60 60 T55 T55

13 70 70 ( T22 T14 T22 T14 δ 62 T7 T12 62 T7 T12 72 T7 72 T7 T12 T14 T12 T14 64 T22 T55 64 T22 T55 74 74 70 ppm 68 T66 68 T66 60 T9 T66 T9 60 T9 T66 T9 T55 T55 70 70 T22 T14 T22 T14 62 T7 T12 62 T7 T12 T12 T14 72 T7 T12 T14 72 T7 64 T22 T55 64 T22 T55 74 72 70 68 74 74 72 70 68 74 64 62 60 64 62 60 δ(13C)/ppm δ(13C)/ppm (b) The threonine CA/CB and CB/CA region.

Figure 9.7. Details of the DREAM ubiquitin spectra shown in ﬁgure 9.6 for two amino acids. 108 9 Results

In a spectrum a difference between two lines of the same color would correspond to an asymmetry with respect to the diagonal. In the case of valine at 24 kHz MAS the CA/CB correlation is strongly dependent on the carrier position. The simulation suggests that there will be a strong cross peak at a carrier position of 70 ppm , a weaker cross peak at 43 ppm and no transfer between these two nuclei if the carrier is placed at 30 ppm during mixing. The details of the three spectra show this behavior. For the reverse transfer CB/CA the simulation predicts the opposite dependence of cross peak intensity to the mixing carrier, but on the low ﬁeld side of the center between the CA and CB resonance the intensity of the cross peak goes to zero but then gets more intense again. The experiment shows that this prediction holds. For the CA/CG correlation the simulation predicts a positive peak indicating a relayed transfer at a carrier of 30 ppm and vanishing and small negative peaks at 43 ppm and 70 ppm respectively. In the spectra there are strong positive peaks at 30 ppm and the spectrum at 43 ppm shows only weak negative CA/CG peaks. At 70 ppm however there are stronger negative peaks where in the simulation only weak transfer is predicted. On the other side of the diagonal in the CG/CA case the same sign change in cross peaks when measuring the spectrum with different carrier positions during mixing is observed. In the slower spinning case with a MAS frequency of 13 kHz the transfer efﬁciency with respect to the carrier position is more narrow band and especially the relayed transfer is not as pronounced as under fast spinning. Isoleucine is a spin system which is similar to valine, but its two gamma carbons are different in chemical shift because CG1 is a methylene group and CG2 is a methyl group. This different topology has a direct impact on the transfer pathway pattern which is predicted by the simulations. The CA/CB and the CB/CA show the same dependency as the corresponding atoms in valine. The relayed transfers CG1/CA is also similar to valine but the CA/CG1 transfer is lower on the side of the center where it would be active. The intensity of the relayed peaks with respect to the spinning frequency is stronger when spun faster. 9.3 Cross Peak Patterns in Protein Spectra 109

0.5 Ala CA→ CB 0 CB→ CA -0.5 0.5 Arg 0 -0.5 0.5 Asn 0 -0.5 0.5 Asp 0 -0.5 0.5 Cys 0 -0.5 0.5 Gln 0 -0.5 0.5 Glu 0 -0.5 0.5 Gly 0 -0.5 0 0.5 His 0 -0.5 0.5 Ile 0 -0.5 Intensity I/I 0.5 Leu 0 -0.5 0.5 Lys 0 -0.5 0.5 Met 0 -0.5 0.5 Phe 0 -0.5 0.5 Pro 0 -0.5 0.5 Ser 0 -0.5 0.5 Thr 0 -0.5 0.5 Tyr 0 -0.5 0.5 Val 0 -0.5

180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 -10 -20 Carrier position/ppm

Figure 9.8. DREAM cross peak intensity of the CA/CB and CB/CA correlations for 18 amino acids. Parameters for simulation were the same as for the DREAM spectra recorded on ubiquitin under 13 kHz MAS. Three different sets of chemical shift values were used: in black the shifts of crystalline amino acids as reported by Wang [130] were used, in blue are the alpha-helical shift and in red the beta-sheet shifts which were extracted from the BMRB [126]. 110 9 Results

0.5 Ala CA→ CB 0 CB→ CA -0.5 0.5 Arg 0 -0.5 0.5 Asn 0 -0.5 0.5 Asp 0 -0.5 0.5 Cys 0 -0.5 0.5 Gln 0 -0.5 0.5 0.25 Glu 0 -0.5 0.5 Gly 0 -0.5 0 0.5 His 0 -0.5 0.5 Ile 0 -0.5 Intensity I/I 0.5 Leu 0 -0.5 0.5 Lys 0 -0.5 0.5 Met 0 -0.5 0.5 Phe 0 -0.5 0.5 Pro 0 -0.5 0.5 Ser 0 -0.5 0.5 Thr 0 -0.5 0.5 Tyr 0 -0.5 0.5 Val 0 -0.5

180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 -10 -20 Carrier position/ppm

Figure 9.9. DREAM cross peak intensity of the CA/CB and CB/CA correlations for 18 amino acids. Parameters for simulation were the same as for the DREAM spectra recorded on ubiquitin under 24 kHz MAS. Three different sets of chemical shift values were used: in black the shifts of crystalline amino acids as reported by Wang [130] were used, in blue are the alpha-helical shift and in red the beta-sheet shifts which were extracted from the BMRB [126]. 9.3 Cross Peak Patterns in Protein Spectra 111

Simulated transfer efficiency of valine

0.6 CA/CB 0.3 CA/CG1 0 CA/CG2 0 CB/CA M(t)/M -0.3 CG1/CA -0.6 CG2/CA 100 90 80 70 60 50 40 30 20 10 0 Carrier position/ppm

Experiment carrier position 30 ppm CA/CB CA/CG CB/CA CG/CA 30 V17CG1 18 58 V17CG2 V17CG1 32 V5 V5CG1 V70CG1 V26 V17 /ppm V70 20 V26CG2 ) V70CG2 /ppm 60 ) V17CG2 C

/ppm V17 C ) 34 13 C ( V5 V5CG2 V5CG1 13 22 V70 ( V26CG1 V70CG2 δ 13 δ ( 66 36 V5CG2 δ V26CG1 V70CG1 V26CG2 24 V26 68 66 60 58 68 66 60 58 68 13 δ(13C)/ppm δ( C)/ppm 36 34 32 22 20 18 δ(13C)/ppm Experiment carrier position 43 ppm CA/CB CA/CG CB/CA CG/CA V17CG1 30 58 V17CG2 18 V70CG1 V17CG1 V17 V70CG2 32 V5 V5CG1

60 /ppm V26 /ppm ) V70 ) V26CG2 /ppm 20 ) C C V5 V5CG2 V5CG1 V17 V17CG2 34 C V70 13 13 ( ( 13 δ 66 ( 22 δ V26CG1 V26CG1 V70CG2 δ V26 V26CG2 36 V5CG2 68 24 V70CG1 68 66 60 58 36 34 32 22 20 18 68 66 60 58 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm Experiment carrier position 70 ppm

CA/CB CA/CG CB/CA CG/CA V17CG1 30 58 V17CG2 18 V17CG1 V70CG1 32 V26 V5 V5CG1 V17 V70CG2 V70 V26CG2

60 /ppm 20 ) V17CG2 /ppm V17 /ppm ) ) V5 V5CG2 V5CG1 C 34 C V70 C 13 22 ( V70CG2 13

13 V26CG1

( δ 66 V26CG1 36 ( V5CG2 δ δ V26 V26CG2 24 V70CG1 68 68 66 60 58 68 66 60 58 36 34 32 22 20 18 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm

Figure 9.10. Comparison of transfer efficiencies of valine in ubiquitin. Details were taken from DREAM spectra shown in figure 9.6. The simulation shown at the top was taken from figure 9.8. The three dashed vertical lines indicate the three carrier positions used in the experiments. Simulations and spectra were taken at 13 kHz MAS frequency. 112 9 Results

Simulated transfer efficiency of valine

0.6 CA/CB 0.3 CA/CG1 0 CA/CG2 0 CB/CA M(t)/M -0.3 CG1/CA -0.6 CG2/CA 100 90 80 70 60 50 40 30 20 10 0 Carrier position/ppm

Experiment carrier position 30 ppm CA/CB CA/CG CB/CA CG/CA 30 V17CG1 18 58 V17CG2 V17CG1 32 V5 V5CG1 V70CG1 V26 V17 /ppm V70 20 V26CG2 ) V70CG2 /ppm 60 ) V17CG2 C

/ppm V26

/ppm 60 ) V70 ) V26CG2 /ppm 20 ) C C V5 V5CG2 V5CG1 V17 V17CG2 34 C V70 13 13 ( ( 13 δ 66 ( 22 δ V26CG1 V26CG1 V70CG2 δ V26 V26CG2 36 V5CG2 68 24 V70CG1 68 66 60 58 36 34 32 22 20 18 68 66 60 58 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm Experiment carrier position 70 ppm

CA/CB CA/CG CB/CA CG/CA V17CG1 30 58 V17CG2 18 V17CG1 V5 V5CG1 V17 V70CG1 32 V26 V70CG2 V70 20 V26CG2 60 /ppm ) V17CG2 /ppm V17 /ppm ) ) V5 V5CG2 V5CG1 C 34 C V70 C 13 22 ( V70CG2 13

13 V26CG1

( δ 66 ( V26CG1 36 V5CG2 δ δ V26 V26CG2 24 V70CG1 68 68 66 60 58 68 66 60 58 36 34 32 22 20 18 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm

Figure 9.11. Comparison of transfer efficiencies of valine in ubiquitin. Details were taken from DREAM spectra shown in figure 9.6. The simulation shown at the top was taken from figure 9.8. The three dashed vertical lines indicate the three carrier positions used in the experiments.Simulations and spectra were taken at 24 kHz MAS frequency. 9.3 Cross Peak Patterns in Protein Spectra 113

Simulated transfer efficiency of isoleucine

0.6 CA/CB 0.3 CA/CG1 0 CA/CG2 0 CB/CA M(t)/M -0.3 CG1/CA -0.6 CG2/CA 100 90 80 70 60 50 40 30 20 10 0 Carrier position/ppm

Experiment carrier position 30 ppm CB/CA CG/CA

CA/CB CA/CG1 CA/CG2 16 I44 I61 I13 34 58 I36 18 I30 I23 I36 I44 CG2/CA I3 I36 I36 36 I23 I44 60 I61 CG1/CA I36 I23 I3 I44 I13 I3 38 I30 26 I13 I3 I13 I13 I36 /ppm

) 62 I3 C I61 40 I13 28 I23

13 I61 ( 64 I30 I23 I30 δ I30 I61 I3 I61 I44 I23 42 30 66 I30 I44 44 44 42 40 38 36 34 30 28 26 18 16 66 64 62 60 58 66 64 62 60 58 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm

Experiment carrier position 43 ppm CB/CA CG/CA CA/CB CA/CG1 CA/CG2 16 I44 I61 I13 34 58 I36 I30 I23 I36 I44 18 CG2/CA I3 I36 I36 36 I23 I44 60 I61 CG1/CA I36 I23 I3 I44 I13 I3 38 I30 I13 I3 /ppm I13 26 ) 62 I13 I36

C I3 I61 I13 I23 13 40 ( 28 I61 I23 δ 64 I30 I61 I30 I30 I3 I61 I44 I23 42 30 66 I30 I44 44 44 42 40 38 36 34 30 28 26 18 16 66 64 62 60 58 66 64 62 60 58 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm

Experiment carrier position 70 ppm CB/CA CG/CA 16 CA/CB CA/CG1 CA/CG2 I44 I61 I13 34 58 I36 I30 I23 I36 I44 18 CG2/CA I3 I36 I36 36 I23 I44 60 I61 CG1/CA I36 I23 I3 I44 I13 I3 38 I30 26 I13 I3 /ppm I13 ) 62 I13 I36

C I3 I61 I13 I23 13 40 28 ( I61 I23 δ 64 I30 I30 I30 I61 I3 I61 I44 I23 42 30 66 I30 I44 44 44 42 40 38 36 34 30 28 26 18 16 66 64 62 60 58 66 64 62 60 58 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm

Figure 9.12. Comparison of transfer efficiencies of isoleucine in ubiquitin. Details were taken from DREAM spectra shown in figure 9.6. The simulation shown at the top was taken from figure 9.8. The three dashed vertical lines indicate the three carrier positions used in the experiments. Simulations and spectra were taken at 13 kHz MAS frequency. 114 9 Results

Simulated transfer efficiency of isoleucine

0.6 CA/CB 0.3 CA/CG1 0 CA/CG2 0 CB/CA M(t)/M -0.3 CG1/CA -0.6 CG2/CA 100 90 80 70 60 50 40 30 20 10 0 Carrier position/ppm

Experiment carrier position 30 ppm CB/CA CG/CA

CA/CB CA/CG1 CA/CG2 16 I13 I44 34 I61 I30 58 I36 18 I23 I36 I44 CG2/CA I3 I36 I36 36 I23 60 I44 I61 CG1/CA I36 I23 I3 I44 I13 I3 38 I30 26 I13 I3 I13 I13 I36 /ppm

) 62 I3

C I13 I61 40 28 I23

13 I61 ( 64 I30 I23 I30 δ I30 I61 I3 I61 I44 I23 42 30 66 I30 I44 44 44 42 40 38 36 34 30 28 26 18 16 66 64 62 60 58 66 64 62 60 58 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm

C I3 I61 I13 I23 13 40 ( 28 I61 I23 δ 64 I30 I61 I30 I30 I3 I61 I44 I23 42 30 66 I30 I44 44 44 42 40 38 36 34 30 28 26 18 16 66 64 62 60 58 66 64 62 60 58 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm

C I3 I61 I13 I23 13 40 28 ( I61 I23 δ 64 I30 I30 I30 I61 I3 I61 I44 I23 42 30 66 I30 I44 44 44 42 40 38 36 34 30 28 26 18 16 66 64 62 60 58 66 64 62 60 58 δ(13C)/ppm δ(13C)/ppm δ(13C)/ppm

Figure 9.13. Comparison of transfer efficiencies of isoleucine in ubiquitin. Details were taken from DREAM spectra shown in figure 9.6. The simulation shown at the top was taken from figure 9.8.The three dashed vertical lines indicate the three carrier positions used in the experiments. Simulations and spectra were taken at 24 kHz MAS frequency. 10. Discussion

10.1. Simulation Strategies of DREAM Spectra

The GAMMA simulation framework is a powerful tool to conduct an NMR experiment in silico. In this thesis two approaches are presented of how a spin system evolving under a doubly time-dependent Hamiltonian can be simulated. It has been shown that matrix multiplication and especially matrix diagonalization are the two time-limiting operations of the simulations. For these two operations the matrix size is of extreme importance for the performance. The matrix representation quantum mechanical operators of a system containing n 1 n× n τ spin- 2 is a 2 2 matrix. In the case of a time-slicing algorithm one rotor period r is divided into m time slices (see ﬁgure 7.6). In consequence m diagonalization and m − 1 multiplication operations per amplitude step have to be calculated. This is only true if the length of the amplitude step is an integer multiple of the rotor period. If it

is shorter than one full rotor period less sub-propagators Uˆ i have to be diagonalized and multiplied to calculated the total propagator. In the case of an amplitude step which is longer than one rotor period but not a multiple of it there is an additional

propagator Uˆ rest which has to be calculated. In the simulations performed this propagator was cached during the calculation of Uˆ r to save additional diagonalization and multiplication steps. When using a Floquet-based algorithm the number of time-limiting matrix operations is different. In a Floquet treatment only one propagator per amplitude step is calculated and only one multiplication step has to be performed to concatenate the propagators of individual amplitude steps on the sweep to the whole sweep propagator. The drawback of this algorithms is that these matrix calculations are carried out with matrix representations of operators in Floquet space. As outlined in section 7.2 1 the matrices in the Floquet space for a n spin- 2 system are inﬁnitely large. In practice

115 116 10 Discussion

this matrix is truncated to a size of (N 2n)×(N 2n) with N being the number of Flo- quet dimension which was set to eleven. This corresponds to a basis of the Floquet space of B = {| − 5, |−4,...,|0,...,|4, |5} which was sufficient to converge to the results of the time-slicing calculations. The Floquet calculation is slower than the time-slicing approach under the given set of simulation parameters because of the fact that the time needed for matrix diagonalization is increasing very fast for larger matrices. It is therefore faster to perform 100 diagonalizations of a matrix representation of operators in the Hilbert space plus the necessary multiplication steps to obtain a propagator for one amplitude step than doing just one diagonalization of a matrix representation of operators in the (truncated) Floquet space. This situation will change in two possible cases: firstiftheam- plitude steps get longer and second if the spinning gets faster resulting in a shorter rotor period. In both cases the number of diagonalization steps in the time-slicing approach stays the same whereas the number of multiplications increases which are needed to join the propagators of a full rotor revolution to the propagator of the whole amplitude step. In the case of a Floquet-based simulation the number of the two time-limiting steps mentioned above stays the same. The Floquet calculation will be performing better in the limit of fast spinning or long mixing times. As shown in figure 9.2 the simulations performed in this work are not in this regime. Besides these mathematical considerations also technical issues in computer design play a role. The largest spin system simulated consisted of 7 spins. This corresponds to a matrix size of 128×128 of the operator representation in Hilbert space and to a size of 1408×1408 in an eleven-dimensional Floquet space. In the GAMMA implementation an operator in Floquet space is represented as a dedicated class which stores besides the actual matrix representation also other properties needed for book keeping such as the base frequency of the Floquet space or the matrix representation of the basis in which the operator is defined. To estimate the size of such a construct in memory a best case is assumed: the Floquet matrix is represented by an array of complex numbers in which the real and imaginary part is represented as a double precision variable. Each element of this matrix is stored in 8 bytes for the real and 8 bytes for imaginary part, respectively giving 16 bytes total. This very lightweight data structure makes no differentiation between special classes of matrices such as diagonal, block diagonal or sparse matrices. This is usually done to implement more efficient ways of data storage and matrix handling. 10.2 Transfer Efficiency Dependence on Carrier Position and RF Field 117

The Floquet matrix of the spin system above contains 14082 = 1, 982, 464 elements. If this matrix is represented in memory with the discussed data structure 1, 982, 464 · 16 bytes = 30.25 MiByte of space is needed for one matrix. In contrast the same operator in Hilbert space is 121 times smaller which corresponds to 0.25 MiByte. To diagonalize this large matrix the individual values have to be transferred from the main memory of the system to the CPU. This transfer is relatively slow compared to the data transfer rates inside the CPU. To minimize this direct main memory access CPUs use fast accessible memory as a buffer in which copies of the most frequently used main memory locations are stored. This memory is called cache. Modern CPUs implement a sophisticated system of caches to store instructions, data and translation buffer for memory management [148, 149]. Current main-stream CPUs ship with a 4 to 6 MiByte cache. In the implementation of the Floquet-based approach the Floquet matrix can not be completely held in the CPU cache, so the main memory has to be accessed to load data prior and during calculation. In a time-slicing approach four matrices are needed: one for the current

sub-propagator Uˆ i, one for the accumulation of all sub-propagators for one rotor- cycle Uˆ rot, one for caching the propagator of the rest Uˆ rest and ﬁnally the propagator which holds the result of the complete amplitude modulation. All of these four operators can be held in the CPU cache for optimal performance. These low-level effects will be observable in the case of large matrices only, as then the cache is not sufﬁcient anymore and the amount of data to be transferred from the CPU to the main memory is large. The discrepancy of rapid CPU speed increase but only slow increase in main memory access bandwidth is a general problem in computer science and is called “memory wall”. A review of how this problem was found and which strategies are to circumvent it can be found in the literature [150].

10.2. Transfer Efﬁciency Dependence on Carrier Position and RF Field

To investigate the DREAM transfer characteristics dependence on the carrier position during mixing and the center RF ﬁeld strength simulations with different combinations of these parameters were done. Calculated intensities of the cross peaks 118 10 Discussion

are presented as two dimensional parameter plots (e.g. figure 9.3). The regions of high transfer efficiencies are are located on a parable-like curve with the extrema centered between the two resonances to be recoupled. The reason for this is that ω = along these lines the sum of the effective fields on the individual spins tot(1,2) Ω2 + ω2 + Ω2 + ω2 1 RF 2 RF is constant. If the matching of the recoupling condition ω = ω which is given by tot(1,2) r would be the only factor determining the transfer efficiency a symmetric transfer profile around the center of the two resonances would be obtained. The simulations however show that there are regions in the parameter space which fulfill the recoupling condition but where the transfer is attenuated. This effect can be observed in the CO/CA transfer efficiency of alanine (figure 9.3). It can be understood if the CO/CB relayed transfer is taken into consideration. The CO/CA transfer and the CO/CB transfer show complementary behavior: where the CO/CA peak is strong, no CO/CB signal can be observed and vice versa. This complementary transfer pattern is widely found in the DREAM transfer analysis plots (e.g. the CB/CO transfer and the CB/CA transfer are complementary). The fact that the carrier position determines if a CO/CA/CB relayed transfer or a CB/CA/CO relayed transfer is possible implies that the order in which the recoupling conditions of the involved spin pairs are hit is inverted. The center between CO and CB is position Ω where the order is inverted. The chemical shift offset i is defined as follows:

Ω = ω − ω i iso,i car (10.1)

recoupling occurs if ω = Ω2 + ω2 + Ω2 + ω2 = ω tot(i,k) i RF k RF r (10.2)

if the carrier is placed centered between CO and CB their chemical shift offset is given by

Ω = −Ω = Ω CO CB (10.3) (10.4) 10.2 Transfer Efﬁciency Dependence on Carrier Position and RF Field 119

the sum of effective ﬁelds for the CO/CA and CA/CB pairs is given by ω ( ) = Ω2 + ω2 + Ω2 + ω2 (10.5) tot CA,CO CA RF CO RF ω = Ω2 + ω2 + Ω2 + ω2 tot(CA,CB) CA RF CB RF (10.6)

with equation (10.3) the sum of effective ﬁelds can be simpliﬁed to ω ( ) = Ω2 + ω2 + Ω2 + ω2 (10.7) tot CA,CO CA RF RF ω = Ω2 + ω2 + (−Ω)2 + ω2 tot(CA,CB) CA RF RF (10.8) ⇒ ω = ω tot(CO,CA) tot(CA,CB). (10.9)

The derivation above shows that if the carrier is placed centered with respect to CO and CB the recoupling of the CO/CA and the CA/CB pair occurs simultaneously. Changing the carrier position to the left or to the right results in complementary sequential recoupling of the two spin pairs. Another feature of the simulated spectra is a region of strongly attenuated single step transfer e.g. in the case of CA/CB or CB/CA transfer in alanine in figure 9.3. This “cleft” is located exactly in the middle of the two resonances to be recoupled. A separate set of simulations on aspartic acid given in figure 9.5 shows that this feature occurs if there is a J-coupling active between the nuclei. As shown in section 1.1.1 the J-coupling is an isotropic interaction and therefore is not modulated by the MAS. As a consequence this coupling is active at arbitrary ratios of MAS frequency and RF field strength. A typical value for a 13C–13C J-coupling constant is 35 Hz which is more than one order of magnitude smaller than the homonuclear dipolar coupling. This means that in general the J-coupling can be neglected because it is truncated by the much larger dipolar coupling. In the case where the carrier is placed exactly between two resonances however this contribution can induce zero-quantum transfer which has the opposite sign as the double-quantum transfer induced by the dipolar coupling and thereby attenuating the peak. To verify the simulations arrays of experimental DREAM spectra were measured and plotted in figure 9.4 to compare it to the simulated intensities in figure 9.3. The characteristic asymmetry in transfer efficiency if a relayed transfer is possible which 120 10 Discussion

was predicted by the simulation is confirmed by the experimental data. A quantitative comparison of simulated and experimental data is difficult because it is not possible to determine how big the initial polarization is which is distributed by the DREAM mixing. Furthermore it is difficult to estimate the relaxation of magnetization during the DREAM sweep because there are single-quantum and double- quantum contributions involved. Furthermore the initial cross-polarization step can also lead to different starting polarization on each spin. The experimental data show the same major features which have been discussed above. The strong asymmetry of the transfer with respect to the carrier position during mixing can be also observed experimentally. Also minor details like the recoupling region at low RF field strengths and a carrier position of 20 ppm in figure 9.4 are reproduced by the simulation (figure 9.3). In this case the recoupling condition in the experiment is broadened in the RF dimension. In the probe head the coil produces an inhomogeneous RF field which leads to a distribution of RF fields which corresponds to a blurring of the resonances in the RF dimension. In practice this means that the carrier placement offers more fine-grained control over the transfer characteristics.

10.3. Cross Peak Patterns in Protein Spectra

A DREAM transfer step is used as an efficient transfer technique in biomolecular solid-state NMR. To characterize the DREAM transfer pattern three spectra with different carrier positions at two different MAS frequencies were recorded (figure 9.6). At both spinning speeds a flip of peaks around the diagonal in the spectrum can be observed when changing the carrier. This is the same effect which was discussed for alanine before which is dependent on the order of how the resonance conditions are passed. Especially in the fast spinning case the appearance of relayed peaks changes from one side of the diagonal to the other when the carrier is changed from 30 ppm to 70 ppm. At both spinning speeds the same flipping of the relayed peaks can be observed, but at 13 kHz MAS these peaks are much weaker. The reason for this lies in the lower RF field amplitude at slow spinning needed to match the recoupling condition. As a consequence the minimal adiabaticity of the amplitude sweep is decreased. If the adiabaticity is not sufficiently high at all points of the sweep the magnetization starts nutating around the spin lock field and is dephased. It is therefore important 10.3 Cross Peak Patterns in Protein Spectra 121

to note that the DREAM transfer works best at high spinning frequencies. The cross peak intensities of the spectra recorded with a carrier of 43 ppm are attenuated. A conclusive reason for this behavior is that the carrier is then placed in the region between two resonance in which the homonuclear J-coupling is not truncated and interferes with the dipolar transfer. This leads to low transfer efficiencies as shown in figure 9.5 for aspartic acid. To mimic the application of a DREAM transfer step in a protein, the transfer pattern of 19 amino acids were simulated. The results of the carrier dependence of the CA/CB and CB/CA transfer are shown in figures 9.8 and 9.9. In many cases a strong carrier dependence of the CA/CB and CB/CA Transfer can be observed. This asymmetry depends strongly on the presence of a third spin, a CG to which the relayed transfer can grow at the expense of the direct CA/CB transfer. In the case of the small amino acids which have no CG like alanine, cysteine and serine the transfer profile is symmetric. Also in these transfers there is an dip located in the middle of the two resonances where the J-coupling becomes important. The two aromatic amino acids tyrosine and phenylalanine show the same behavior as the small amino acids despite the fact that there is a CG atom present. In these amino acids the CG is the ipso carbon of an aromatic ring and has a chemical shift in the range of 120–130 ppm. This spin topology does no lead to the as symmetric CA/CB transfer because the recoupling is not broad-band enough to lead to an efficient CB/CG transfer. In this respect the aromatic amino acids can be regarded as a pseudo two spin system. For aspartic acid and asparagine the same pseudo two spin behavior is found. In these two amino acids the CG is a carbonyl group which resonates at very low field around 170 ppm and can not be recoupled either. In the more common case where there is a CG carbon which has no big chemical shift difference to the CB so that it is recoupled, the asymmetry of the transfer is strong. This situation is typical for aliphatic amino acids where the CG is a methylene or a methyl group. In this case an efficient CB/CG transfer is able to transfer the polarization from the CB to the CG which came initially from the CA. This process can be observed as the appearance of relayed peaks in the spectra between CA and CG and a strong attenuation of the CA/CB peak. In figures 9.10 to 9.13 a direct comparison of the simulated data and the peaks in the measured spectra on ubiquitin is outlined. The amino acids valine and isoleucine have two CG carbons which are close to the CB in terms of chemical shift so an asym- 122 10 Discussion

metric behavior is expected. In figure 9.11 the situation for valine in ubiquitin under 24 kHz MAS is shown. The simulated peak intensity which is shown at the top of the figure shows very clearly that the CA/CG1 and the CA/CG2 correlations grows in expense of the CA/CB peak. In the plot this can be seen as parallel lines of the same color but different styles (continuous or dashed). This situation can also be found in the reverse transfer. In the spectra this behavior is observed also. Notice well that in the case where there is no relayed CA/CG transfer possible because of the wrong order of resonance passage, there is still the possibility of a direct CA/CG transfer. In valine negative peaks in the CA/CG plot are observed if the carrier during recoupling is centered around 70 ppm. In this amino acid the distance between the directly bound CA and CB is ≈ 150 pm, the distance between CA and one of the CGs is ≈ 250 pm. The difference in distances translates into a factor of 4.5 in dipolar coupling constants. This can lead to an effect which is called dipolar truncation which means that in the presence of a large dipolar coupling the transfer via a weak dipolar coupling is quenched [151]. In the experimental DREAM spectra of ubiquitin both transfers can be observed despite of their big difference. The reason for this is that these two dipolar couplings are not active at the same time during the sweep. As recoupling under these conditions is performed sequentially there is no competition between the two transfers. An analogy to this effect is for example the band-selective dipolar recoupling using the SPC-5 sequence which shows better efficiency compared to its broad-banded counterpart due to the absence of dipolar truncation [152] or the determination of longer distances in the presence of strong dipolar couplings using the rotational-resonance experiment [153, 154]. Direct transfers over longer distances, meaning transfer between atoms which are not covalently bound, can be observed only in the case of a spinning frequency of 24 kHz. The reason for this is the same as for the appearance of relayed peaks: the adiabaticity has to be sufficiently high throughout the sweep. 11. Conclusion

In this work the performance and the transfer pathways of the DREAM experiment in multi-spin systems was characterized. It has been shown that quantum-mechanical simulations provide a powerful tool to investigate the transfer mechanisms. The simulated data are in good agreement with the experiments. It has also been shown that the approach of how time-dependent Hamiltonians are treated in simulations greatly influence the performance. The size of spin systems is limited by the computation time needed. The performance of the underlying time-limiting matrix operations such as diagonalization and multiplications could be improved by applying modern methods such as multi-threading or using the graphics processing unit. On the one hand this would open up the possibility of simulating more complex spin systems on the other hand if the simulations could be completed in the order of minutes they could also serve as a guideline while setting up the real experiment at the spectrometer. It has been presented that in the case when the DREAM experiment is not performed in the fast-spinning limit, there are experimental conditions that influence the presence or absence of cross peaks in the spectra significantly. This effect allows the spectroscopist to tailor the cross-peak pattern within a certain range depending on the chemical shift topology. In the context of biomolecular NMR the DREAM transfer step can be used in spectra typically used for assignment purposes. By adjusting the carrier and the RF field of the sweep different classes of amino acids can be excluded in the spectra. This leads to a significant simplification of the spectra and thereby facilitating the assignment process. Thesametypeofsimplification can be obtained by differentiating the amino acids chemically. This is achieved by incorporating isotopic labels at specific positions in the molecule. The chemical approach is powerful because no selective experiments are needed as the selection has been done by synthetic means. The disadvantage

123 124 11 Conclusion of this approach is that the synthesis can be difficult, time-consuming and costly. Besides that the possible correlations and transfer pathways are encoded in the atomic structure and cannot be changed later. The selective DREAM method described in this work can achieve similar results by using a uniformly labeled compound only. Besides the ofter easier synthesis of the sample this method offers much higher flexibility as the resonance pathways of interest can be chosen “on the fly” by the spectroscopist. 12. Outlook

In this work solid-state NMR techniques are applied to HET-s (156–289) and furthermore a known NMR experiment is characterized with respect to its application in biomolecular NMR in the solid state. In the case of the prion protein studied here it was demonstrated that the prion forming domain of HET-s is the same regardless of the presence of additional globular residues. Further analysis of this construct to gain insight into what is promot- ing the heterokaryon incompatibility reaction is difficult. New spectra recorded at a higher static field could allow the identification of more alpha-helical residues by increased sensitivity and resolution. The residues of the globular domain are structurally disordered but nevertheless trigger the incompatibility reaction contrasting to the construct HET-s(218–289) consisting of the prion forming domain alone. It would be interesting to investigate if the primary sequence of the additional residues to the prion forming domain is important for triggering this reaction. The main focus of this thesis is the characterization of the DREAM experiment when applied to multi-spin systems. It has been shown how quantum-mechanical numerical simulations can help understanding the complex interplay between different contributions in the Hamiltonian. From the benchmarks of the used simulation programs it becomes obvious that simulating the spectrum of a system as complex as a protein will be impossible. However in our case it was often sufficient to examine one amino acid at a time as the DREAM experiment is used to correlate spins of the same spin system only. Besides the fact that these simulations can be time- consuming the creation of a simulation program requires detailed knowledge of the quantum-mechanical properties and interactions of the system at hand. In addition medium-level programming skills are required to set up and analyze the results of a simulation program. To make this valuable tool accessible for scientists beyond the solid-state NMR community large efforts would have to be made to simplify its usage by providing a more intuitive user interface. Furthermore a standard set of building

125 126 12 Outlook

blocks to be combined into an pseudo pulse program would enable a wider user base to write simulations for their current problems. It has been shown by simulations and experiments that the DREAM transfer pattern in in multi-spin systems such as amino acids often strongly depends on the carrier position during the DREAM transfer and thus is under control of the experimentalist. By changing the carrier position the CA/CB peak or the CB/CA peak can be amplified depending on the chemical shift topology of the spin system. In the context of three dimensional spectra such as NCACX this property can be advantageous as it allows to select which peaks are visible in the spectrum. In the idealized picture of only CA polarization being present after the 15N–13C transfer, only amino acids with an active CA/CB transfer would give rise to cross peaks in the spectrum. In future research the influence of the mixing duration and the sweep shape on the filtering efficiency could be investigated. There is a need in the context of three dimensional NMR of a selective and efficient method to promote CO/CA transfer. Methods like DARR are capable of generating correlations between these spins but the transfer efficiencies achieved are only modest. In principle the DREAM experiment is able to promote polarization transfer between two nuclei with such a large chemical shift offset. However the spinning frequency must be sufficiently large compared to the chemical shift offset. Currently MAS rotors with an outer diameter of 3.2 mm are widely used for recording spectra. This rotor size is often a reasonable trade off between achievable MAS frequencies and active sample volume. In combination with large chemical shift offsets between CO and CA at proton Larmor frequencies of 850 MHz and beyond the DREAM transfer efficiency at moderate spinning frequencies like 19 kHz is attenuated. The straightforward way of solving this problem would be to spin faster which is possible with modern MAS probes with which spinning frequencies up to 65 kHz can be reached. However the drastically reduced sample volume in the used 1.3 mm rotors and the frictional heating can be problematic. For recoupling spins with a moderate chemical shift offset such as the aliphatic carbons in amino acids the standard spinning frequency of 19 kHz is sufficient. How- ever the selectivity of which amino acid give rise to a correlation between CA and CB is dependent on the chemical shift of a third coupling partner and is only modest. A possible approach to tailor the transfer pathway patterns in a more sophisticated fashion would be to use a sweep with an additional modulation such as a cosine 127 modulation. This would generate two sidebands around the carrier separated by the cosine modulation frequency which could promote recoupling. This could allow more fine-grained control over the recoupling of different amino acids with different chemical shift topology.

Bibliography

[1] Bloch, F., 1946. Nuclear Induction. Phys. Rev. 70:460–474. [2] Slichter, C. P., 1978. Principles of Magnetic Resonance. Springer Verlag Berlin Heidelberg New York. [3] Fano, U., 1957. Description Of States In Quantum Mechanics By Density Matrix And Operator Techniques. Rev.Mod.Phys.29:74–93. [4] Shriver, J., 2005. Product operators and coherence transfer in multiple-pulse NMR experiments. Conc. Magn. Reson. A 4:1–33. [5] Haeberlen, U., and J. S. Waugh, 1968. Coherent Averaging Effects in Magnetic Resonance. Phys. Rev. 175:453. [6] Mehring, M., 1983. Principles of High Resolution NMR in Solids, 2nd edition. Springer, Berlin. [7] Andrew, E., A. Bradbury, and R. Eades, 1958. Nuclear Magnetic Resonance Spectra From A Crystal Rotated At High Speed. Nature 182:1659–1659. [8] Lowe, I., 1959. Free Induction Decays Of Rotating Solids. Phys. Rev. Lett. 2:285– 287. [9] Herzfeld, J., and A. Berger, 1980. Sideband Intensities In NMR-Spectra Of Sam- ples Spinning At The Magic Angle. J. Chem. Phys. 73:6021–6030. [10] Maricq, M. M., and J. S. Waugh, 1979. NMR in rotating solids. J. Chem. Phys. 70:3300. [11] Abragam, A., 1961. The Principles of Nuclear Magnetism. Clarendon Press, Oxford. [12] Baum, J., R. Tycko, and A. Pines, 1985. Broadband and adibatic inversion of a two-level system by phase-modulated pulses. Phys. Rev. A 32:3435. [13] Tannus, A., and M. Garwood, 1997. Adiabatic pulses. NMR In Biomedicine 10:423–434.

129 130 Bibliography

[14] Haase, J., M. S. Conradi, C. P. Grey, and A. J. Vega, 1994. Population Transfers for NMR of Quadrupolar Spins in Solids. J. Magn. Reson. Ser. A 109:90–97.

[15] Schäfer, H., D. Iuga, R. Verhagen, and A. Kentgens, 2001. Population and coherence transfer in half-integer quadrupolar spin systems induced by simulta- neous rapid passages of the satellite transitions: A static and spinning single crystal nuclear magnetic resonance study. J. Chem. Phys. 114:3073–3091.

[16] Garwood, M., K. Ugurbil, A. Rath, M. Bendall, B. Ross, S. Mitchell, and H. Merkle, 1989. Magnetic-Resonance Imaging With Adiabatic Pulses Using A Single Surface Coil For Rf Transmission And Signal-Detection. Magn. Reson. Med. 9:25–34.

[17] Kupce, E., and R. Freeman, 1995. Adiabatic Pulses for Wideband Inversion and Broadband Decoupling. J. Magn. Reson. Ser. A 115:273–276.

[18] Fu, R. Q., and G. Bodenhausen, 1996. Evaluation of adiabatic frequency- modulated schemes for broadband decoupling in isotropic liquids. J. Magn. Reson. Ser. A 119:129–133.

[19] Fung, B. M., A. K. Khitrin, and K. Ermolaev, 2000. An improved broadband decoupling sequence for liquid crystals and solids. J. Magn. Reson. 142:97–101.

[20] Hediger, S., B. H. Meier, N. D. Kurur, G. Bodenhausen, and R. R. Ernst, 1994. NMR Cross-Polarization by Adiabatic Passage through the Hartmann-Hahn Condition (APHH). Chem. Phys. Lett. 223:283–288.

[21] Hediger, S., B. H. Meier, and R. R. Ernst, 1995. Adiabatic Passage Hartmann- Hahn Cross-Polarization in NMR under Magic-Angle Sample-Spinning. Chem. Phys. Lett. 240:449–456.

[22] Hediger, S., B. H. Meier, and R. R. Ernst, 1995. Rotor-synchronized amplitude- modulated NMR spin-lock sequences for improved cross polarization under fast magic angle sample spinning. J. Chem. Phys. 102:4000.

[23] Kupce, E., and R. Freeman, 1995. Stretched adiabatic pulses for broadband spin inversion. J. Magn. Reson. Ser. A 117:246–256.

[24] Kupce, E., and R. Freeman, 1996. Optimized adiabatic pulses for wideband spin inversion. J. Magn. Reson. Ser. A 118:299–303.

[25] Kupce, E., and W. Hiller, 2001. Clean adiabatic TOCSYs. Magn. Reson. Chem. 39:231–235.

[26] Hardy, E. H., A. Detken, and B. H. Meier, 2003. Fast-MAS total through-bond correlation spectroscopy using adiabatic pulses. J. Magn. Reson. 165:208–218. Bibliography 131

[27] Pervushin, K., R. Riek, G. Wider, and K. Wüthrich, 1997. Attenuated T-2 relaxation by mutual cancellation of dipole-dipole coupling and chemical shift anisotropy indicates an avenue to NMR structures of very large biological macromolecules in solution. Proc. Natl. Acad. Sci. 94:12366–12371.

[28] Ernst, R. R., and W. A. Anderson, 1965. Application of fourier Transform Spec- trsocopy to Magnetic Resonance. Rev. Sci. Instrum. 37:93–102.

[29] Styles, P., N. Soffe, C. Scott, D. Cragg, F. Row, D. White, and P. White, 1984. A High-Resolution NMR Probe In Which The Coil And Preampliﬁer Are Cooled With Liquid-Helium. J. Magn. Reson. 60:397–404.

[30] Ernst, R. R., 1975. Two-Dimensional Spectrsocopy. Chimia 29:179–182.

[31] Kessler, H., S. Mronga, and G. Gemmecker, 1991. Multidimensional NMR Ex- periments Using Selective Pulses. Magn. Reson. Chem. 29:527–557.

[32] Emsley, L., and G. Bodenhausen, 1990. Gaussian Pulse Cascades - New Analyt- ical Functions For Rectangular Selective Inversion And In-Phase Excitation In NMR. Chem. Phys. Lett. 165:469–476.

[33] Waugh, J., 1982. Theory Of Broad-Band Spin Decoupling. J. Magn. Reson. 50:30– 49.

[34] Shaka, A. J., and J. Keeler, 1987. Broadband spin decoupling in isotropic liquids. Prog. Nucl. Magn. Reson. Spectrosc. 19:47–129.

[35] Shaka, A. J., J. Keeler, and R. Freeman, 1983. Evaluation of a new broadband decoupling sequence - Waltz-16. J. Magn. Reson. 53:313.

[36] Cavanagh, J., 2007. Protein NMR spectroscopy: principles and practice. Aca- demic Press.

[37] Griesinger, C., O. Sørensen, and R. Ernst, 1989. 3-Dimensional Fourier Spec- troscopy - Application To High-Resolution NMR. J. Magn. Reson. 84:14–63.

[38] Bloch, F., W. W. Hansen, and M. Packard, 1946. The Nuclear Induction Experi- ment. Phys. Rev. 70:474–485.

[39] Purcell, E. M., H. C. Torrey, and R. V. Pound, 1946. Resonance Absorption by Nuclear magnetic moments in a Solid. In Phys. Rev. 37–38. H.

[40] Chevelkov, V., B. J. van Rossum, F. Castellani, K. Rehbein, A. Diehl, M. Hohwy, S. Steuernagel, F. Engelke, H. Oschkinat, and B. Reif, 2003. 1H detection in MAS solid-state NMR Spectroscopy of biomacromolecules employing pulsed ﬁeld gradients for residual solvent suppression. J. Am. Chem. Soc. 125:7788–7789. 132 Bibliography

[41] Samoson, A., T. Tuherm, and Z. Gan, 2001. High-ﬁeld high-speed MAS resolution enhancement in H-1 NMR spectroscopy of solids. Solid State Nucl. Magn. Reson. 20:130–136.

[42] Brunner, E., D. Freude, B. Gerstein, and H. Pfeifer, 1990. Residual Linewidths Of NMR-Spectra Of Spin-1/2 Systems Under Magic-Angle-Spinning. J. Magn. Reson. 90:90–99.

[43] Bennett, A. E., C. M. Rienstra, M. Auger, K. V. Lakshmi, and R. G. Grifﬁn, 1995. Heteronuclear Decoupling in Rotating Solids. J. Chem. Phys. 103:6951–6958.

[44] Detken, A., E. H. Hardy, M. Ernst, and B. H. Meier, 2002. Simple and efﬁcient decoupling in magic-angle spinning solid- state NMR: the XiX scheme. Chem. Phys. Lett. 356:298–304.

[45] Scholz, I., P. Hodgkinson, B. H. Meier, and M. Ernst, 2009. Understanding two- pulse phase-modulated decoupling in solid-state NMR. J. Chem. Phys. 130.

[46] Hartmann, S. R., and E. L. Hahn, 1962. Nuclear Double Resonance in Rotating Frame. Phys. Rev. 128:2042.

[47] Verel, R., M. Ernst, and B. H. Meier, 2001. Adiabatic dipolar recoupling in solid- state NMR: The DREAM scheme. J. Magn. Reson. 150:81–99.

[48] Gullion, T., and J. Schaefer, 1989. Rotational-echo double-resonance NMR. J. Magn. Reson. 81:196.

[49] Levitt, M. H., 2002. Symmetry-based pulse sequences in magic-angle spinning solid-state NMR. In D. M. Grant, and R. K. Harris, editors, Encyclopedia of Nuclear Magnetic Resonance, John Wiley & Sons, Chichester, volume 9, 165– 196.

[50] Böckmann, A., 2008. 3D Protein Structures by Solid-State NMR Spectroscopy: Ready for High Resolution. Angew Chem Int Ed Engl 47:6110–6113.

[51] Baldus, M., 2007. ICMRBS founder’s medal 2006: Biological solid-state NMR, methods and applications. J. Biomol. NMR 39:73–86.

[52] Jeener, J., 1971. Amperère Summer School, Basko Polje, Yugoslavia.

[53] Aue, W., E. Bartholdi, and R. Ernst, 1976. 2-Dimensional Spectroscopy - Appli- cation To Nuclear Magnetic-Resonance. J. Chem. Phys. 64:2229–2246.

[54] Bax, A., and R. Freeman, 1981. Investigation Of Complex Networks Of Spin- Spin Coupling By Two-Dimensional NMR. J. Magn. Reson. 44:542–561. Bibliography 133

[55] Rance, M., O. Sørensen, G. Bodenhausen, G. Wagner, R. Ernst, and K. Wüthrich, 1983. Improved Spectral Resolution In COSY 1H-NMR Spectra Of Proteins Via Double Quantum Filtering. Biochem. Biophys. Res. Commun. 117:479–485.

[56] Wüthrich, K., 1986. NMR of Proteins and Nucleic Acids. J. Wiley & Sons, New York.

[57] Doddrell, D., D. Pegg, and M. Bendall, 1982. Distortionless Enhancement Of NMR Signals By Polarization Transfer. J. Magn. Reson. 48:323–327.

[58] Dotsch, V., R. Oswald, and G. Wagner, 1996. Amino-acid-type-selective triple- resonance experiments. J. Magn. Reson. Ser. B 110:107–111.

[59] Van Melckebeke, N., J. Simorre, and B. Brutscher, 2004. Amino acid-type edited NMR experiments for methyl-methyl distance measurement in 13C-labeled proteins. J. Am. Chem. Soc. 126:9584–9591.

[60] Merriﬁeld, R. B., 1963. Solid Phase Peptide Synthesis – First Synthesis of a Tetrapeptide. J. Am. Chem. Soc. 85:2149–2154.

[61] Goto, N., and L. Kay, 2000. New developments in isotope labeling strategies for protein solution NMR spectroscopy. Curr. Opin. Struct. Biol. 10:585–592.

[62] LeMaster, D. M., and D. M. Kushlan, 1996. Dynamical mapping of E-coli thiore- doxin via 13C NMR relaxation analysis. J. Am. Chem. Soc. 118:9255–9264.

[63] Castellani, F., B. van Rossum, A. Diehl, K. Rehbein, and H. Oschkinat, 2003. Determination of solid-state NMR structures of proteins by means of three- dimensional 15N-13C-13C dipolar correlation spectroscopy and chemical-shift analysis. Biochemistry 42:11476–11483.

[64] Vuister, G., S. Kim, C. Wu, and A. Bax, 1994. 2D And 3D NMR-Study Of Pheny- lalanine Residues In Protein By Reverseisotopic Labeling. J. Am. Chem. Soc. 116:9206–9210.

[65] Detken, A., E. Hardy, M. Ernst, M. Kainosho, T. Kawakami, S. Aimoto, and B. Meier, 2001. Methods for sequential resonance assignment in solid, uniformly 13C, 15N labelled peptides: Quantiﬁcation and application to antamanide. J. Biomol. NMR 20:203–221.

[66] Schütz, A., C. Wasmer, B. Habenstein, R. Verel, J. Greenwald, R. Riek, A. Böck- mann, and B. Meier, 2010. Protocols for the Sequential Solid-State NMR Spec- troscopic Assignment of a Uniformly Labeled 25 kDa Protein: HET-s(1–227) 11:1543–1551.

[67] Grifﬁth, J., 1967. Self-Replication And Scrapie. Nature 215:1043–&. 134 Bibliography

[68] Crick, F., 1970. Central Dogma Of Molecular Biology. Nature 227:561.

[69] Prusiner, S., 1982. Novel Proteinaceous Infectious Particles Cause Scrapie. Sci- ence 216:136–144.

[70] Alper, T., W. Cramp, D. Haig, and M. Clarke, 1967. Does Agent Of Scrapie Replicate Without Nucleic Acid. Nature 214:764–&.

[71] Anﬁnsen, C., 1973. Principles That Govern Folding Of Protein Chains. Science 181:223–230.

[72] Prusiner, S., M. McKinley, K. Bowman, D. Bolton, P. Bendheim, D. Groth, and G. Glenner, 1983. Scrapie Prions Aggregate To Form Amyloid-Like Birefringent Rods. Cell 35:349–358.

[73] Nilsson, M., 2004. Techniques to study amyloid ﬁbril formation in vitro. Meth- ods 34:151–160.

[74] Shorter, J., and S. Lindquist, 2005. Prions as adaptive conduits of memory and inheritance. Nat. Rev. Genet. 6:435–450.

[75] Aguzzi, A., and A. M. Calella, 2009. Prions: Protein Aggregation and Infectious Diseases. Physio. Rev. 89:1105–1152.

[76] German, M., L. Moss, J. Wang, and W. Rutter, 1992. The Insulin And Islet Amy- loid Polypeptide Genes Contain Similar Cell-Speciﬁc Promoter Elements That Bind Identical Beta-Cell Nuclear Complexes. Mol. Cell. Biol. 12:1777–1788.

[77] Hoppener, J. W., B. Ahren, and C. J. Lips, 2000. Islet Amyloid and Type 2 Dia- betes Mellitus. N. Engl. J. Med. 343:411–419.

[78] Collinge, J., 2001. Prion diseases of humans and animals: Their causes and molecular basis. Annu. Rev. Neurosci. 24:519–550.

[79] Mathiason, C. K., J. G. Powers, S. J. Dahmes, D. A. Osborn, K. V. Miller, R. J. Warren, G. L. Mason, S. A. Hays, J. Hayes-Klug, D. M. Seelig, M. A. Wild, L. L. Wolfe, T. R. Spraker, M. W. Miller, C. J. Sigurdson, G. C. Telling, and E. A. Hoover, 2006. Infectious prions in the saliva and blood of deer with chronic wasting disease. Science 314:133–136.

[80] Wells, G., A. Scott, C. Johnson, R. Gunning, R. Hancock, M. Jeffrey, M. Daw- son, and R. Bradley, 1987. A Novel Progressive Spongiform Encephalopathy In Cattle. Vet. Rec. 121:419–420.

[81] Wyatt, J., G. Pearson, T. Smerdon, T. Gruffyddjones, and G. Wells, 1990. Spongi- form Encephalopathy In A Cat. Vet. Rec. 126:513–513. Bibliography 135

[82] Collinge, J., J. Whitﬁeld, E. McKintosh, J. Beck, S. Mead, D. J. Thomas, and M. P. Alpers, 2006. Kuru in the 21st century - an acquired human prion disease with very long incubation periods. Lancet 367:2068–2074.

[83] Ironside, J., 2006. Variant Creutzfeldt-Jakob disease: risk of transmission by blood transfusion and blood therapies. Haemophilia 12:8–15.

[84] Baxa, U., T. Cassese, A. V. Kajava, and A. C. Steven, 2006. Structure, function, and amyloidogenesis of fungal prions: ﬁlament polymorphism and prion vari- ants. Adv Protein Chem 73:125–180.

[85] Balguerie, A., S. Dos Reis, C. Ritter, S. Chaignepain, B. Coulary-Salin, V. Forge, K. Bathany, I. Lascu, J.-M. Schmitter, R. Riek, and S. J. Saupe, 2002. Domain Organization and Structure-Function Relationship of the HET-s Prion Protein of Podospora anserina. EMBO J. 99:2071–2081.

[86] Saupe, S. J., 2000. Molecular Genetics of Heterokaryon Incompatibility in Fila- mentous Ascomycetes. Microbiol. Mol. Biol. Rev. 64:489–502.

[87] Coustou, V., C. Deleu, S. J. Saupe, and J. Bégueret, 1997. The Protein Product of the het-s Heterokaryon Incompatibility Gene of the Fungus Podospora Anserina Behaves as a Prion Analog. Proc. Natl. Acad. Sci. 94:9773–9778.

[88] Balguerie, A., S. Dos Reis, B. Coulary-Salin, S. Chaignepain, M. Sabourin, J. M. Schmitter, and S. J. Saupe, 2004. The sequences appended to the amyloid core region of the HET-s prion protein determine higher-order aggregate organization in vivo. J. Cell Sci. 117:2599–2610.

[89] Lange, A., and B. H. Meier, 2008. Fungal prion proteins studied by solid-state NMR. C. R. Chimie 11:332–339.

[90] Tycko, R., 2006. Molecular structure of amyloid ﬁbrils: insights from solid-state NMR. Q Rev Biophys 39:1–55.

[91] Heise, H., W. Hoyer, S. Becker, O. C. Androesi, D. Riedel, and M. Baldus, 2005. Molecular-level secondar structre, polymorphism, and dynamics fo full-length α-synuclein ﬁbrils studied by solid-state NMR. Proc. Natl. Acad. Sci. 102:15871– 15876.

[92] Iwata, K., T. Fujiwara, Y. Matsuki, H. Akutsu, S. Takahashi, H. Naiki, and β Y. Goto, 2006. 3D structure of amyloid protoﬁlaments of 2-microglobulin fragment probed by solid-state NMR. Proc. Natl. Acad. Sci. U. S. A. 103:18119–18124. 136 Bibliography

[93] Jaroniec, C. P., C. E. MacPhee, V. S. Bajaj, M. T. McMahon, C. M. Dobson, and R. G. Grifﬁn, 2004. High-resolution molecular structure of a peptide in an amyloid ﬁbril determined by magic angle spinning NMR spectroscopy. Proc. Natl. Acad. Sci 101:711–716.

[94] Petkova, A. T., R. D. Leapman, Z. Guo, W. M. Yau, M. P. Mattson, and R. Ty- cko, 2005. Self-propagating, molecular-level polymorphism in Alzheimer’s β- amyloid ﬁbrils. Science 307:262–5.

[95] Petkova, A. T., W. M. Yau, and R. Tycko, 2006. Experimental constraints on quaternary structure in Alzheimer’s β-amyloid ﬁbrils. Biochemistry 45:498–512.

[96] Ranson, N., T. Stromer, L. Bousset, R. Melki, and L. Serpell, 2006. Insights into the architecture of the Ure2p yeast protein assemblies from helical twisted ﬁbrils. Prot. Sci. 15:2481–2487.

[97] Bousset, L., F. Briki, J. Doucet, and R. Melki, 2003. The native-like conformation of Ure2p in ﬁbrils assembled under physiologically relevant conditions switches to an amyloid-like conformation upon heat-treatment of the ﬁbrils. J. Struct. Boil. 141:132–142.

[98] Brachmann, A., U. Baxa, and R. Wickner, 2005. Prion generation in vitro: amyloid of Ure2p is infectious. EMBO J. 24:3082–3092.

[99] Bousset, L., N. Thomson, S. Radford, and R. Melki, 2002. The yeast prion Ure2p retains its native α-helical conformation upon assembly into protein ﬁbrils in vitro. EMBO J. 21:2903–2911.

[100] Loquet, A., B. Bardiaux, C. Gardiennet, C. Blanchet, M. Baldus, M. Nilges, T. Malliavin, and A. Boeckmann, 2008. 3D structure determination of the Crh protein from highly ambiguous solid-state NMR restraints. J. Am. Chem. Soc. 130:3579–3589.

[101] Gardiennet, C., A. Loquet, M. Etzkorn, H. Heise, M. Baldus, and A. Böckmann, 2008. Structural constraints for the Crh protein from solid-state NMR experiments. J. Biomol. NMR 40:239–250.

[102] Loquet, A., L. Bousset, C. Gardiennet, Y. Sourigues, C. Wasmer, B. Habenstein, A. Schuetz, B. H. Meier, R. Melki, and A. Boeckmann, 2009. Prion Fibrils of Ure2p Assembled under Physiological Conditions Contain Highly Ordered, Natively Folded Modules. J. Mol. Biol. 394:108–118.

[103] Böckmann, A., and B. Meier, 2010. Prions: en route from structural models to structures. Prion 4. Bibliography 137

[104] Ritter, C., M.-L. Maddelein, A. B. Siemer, T. Luhrs, M. Ernst, B. H. Meier, S. J. Saupe, and R. Riek, 2005. Correlation of structural elements and infectivity of the HET-s prion. Nature 435:844–848.

[105] Siemer, A. B., C. Ritter, M. Ernst, R. Riek, and B. H. Meier, 2005. High-resolution solid-state NMR spectroscopy of the prion protein HET-s in its amyloid conformation. Angew Chem Int Ed Engl 44:2441–2444.

[106] Siemer, A. B., A. A. Arnold, C. Ritter, T. Westfeld, M. Ernst, R. Riek, and B. H. Meier, 2006. Observation of Highly Flexible Residues in Amyloid Fibrils of the HET-s Prion. J. Am. Chem. Soc. 128:13224–13228.

[107] Wasmer, C., A. Lange, H. Van Melckebeke, A. B. Siemer, R. Riek, and B. H. Meier, 2008. Amyloid ﬁbrils of the HET-s(218-289) prion form a beta solenoid with a triangular hydrophobic core. Science 319:1523–1526.

[108] Balguerie, A., S. Dos Reis, C. Ritter, S. Chaignepain, B. Coulary-Salin, V. Forge, K. Bathany, I. Lascu, J.-M. Schmitter, R. Riek, and S. J. Saupe, 2003. Domain organization and structure-function relationship of the HET-s prion protein of Podospora anserina. EMBO J. 22:2071–2081.

[109] Dalstra, H., R. van der Zee, S. Klaas, R. Hoekstra, S. Saupe, and A. Debets, 2005. Non-mendelian inheritance of the HET-s prion or HET-s prion domains determines the het-S spore killing system in Podospora anserina. Fungal Genetics and Biology 42:836–847.

[110] Sen, A., U. Baxa, M. N. Simon, J. S. Wall, R. Sabate, S. J. Saupe, and A. C. Steven, 2007. Mass analysis by scanning transmission electron microscopy and electron diffraction validate predictions of stacked beta-solenoid model of HET-s prion ﬁbrils. J. Biol. Chem. 282:5545–5550.

[111] Hanahan, D., 1983. Studies on transformation of Escherichia coli with plasmids. J. Mol. Biol. 166:557–580.

[112] Studier, F. W., A. H. Rosenberg, J. J. Dunn, and J. W. Dubendorff, 1990. Use of T7 RNA polymerase to direct expression of cloned genes. Methods Enzymol 185:60–89.

[113] Studier, F. W., 2005. Protein production by auto-induction in high-density shaking cultures. Protein Expression Purif. 41:207–234.

[114] Wessel, D., and U. I. Flügge, 1984. A Method for the Quantitative Recovery of Protein in Dilute-Solution in the Presence of Detergents and Lipids. Anal. Biochem. 138:141–143. 138 Bibliography

[115] Earl, W. L., and D. L. Van Der Hart, 1982. Measurement of 13-C Chemical Shifts in Solids. J. Magn. Reson. 48:35–54.

[116] Morcombe, C. R., and K. W. Zilm, 2003. Chemical shift referencing in MAS solid state NMR. J. Magn. Reson. 162:479–486.

[117] Harris, R., E. Becker, S. Cabral De Menezes, P. Granger, R. Hoffman, and K. Zilm, 2008. Further conventions for NMR shielding and chemical shifts IU- PAC recommendations 2008. Solid State Nucl. Magn. Reson. 33:41–56.

[118] Baldus, M., D. G. Geurts, S. Hediger, and B. H. Meier, 1996. Efﬁcient 15N–13C polarization transfer by adiabatic-passage Hartmann-Hahn cross polarization. J. Magn. Reson. A 118:140–144.

[119] Verel, R., M. Baldus, M. Ernst, and B. H. Meier, 1998. A homonuclear spin-pair ﬁlter for solid-state NMR based on adiabatic-passage techniques. Chem. Phys. Lett. 287:421–428.

[120] Bloembergen, N., E. M. Purcell, and R. V. Pound, 1948. Relaxation Effects in Nuclear Magnetic Resonance Absorption. Phys. Rev. 73:679–712.

[121] Takegoshi, K., S. Nakamura, and T. Terao, 2001. C-13-H-1 dipolar-assisted rotational resonance in magic-angle spinning NMR. Chem. Phys. Lett. 344:631–637.

[122] Baldus, M., and B. H. Meier, 1996. Total correlation spectroscopy in the solid state. The use of scalar couplings to determine the through-bond connectivity. J. Magn. Reson. A 121:65–69.

[123] Marion, D., and K. Wüthrich, 1983. Application of Phase Sensitive Two- Dimensional Correlated Spectroscopy (Cosy) for Measurements of H-1-H-1 Spin-Spin Coupling-Constants in Proteins. Biochem. Biophys. Res. Commun. 113:967–974.

[124] Delaglio, F., S. Grzesiek, G. W. Vuister, G. Zhu, J. Pfeifer, and A. Bax, 1995. NM- RPipe: a multidimensional spectral processing system based on UNIX pipes. J. Biomol. NMR 6:277–293.

[125] Kneller, D., and I. Kuntz, 1993. UCSF Sparky - An NMR Display, Annotation and Assignment Tool. J. Cell. Biochem. 254–254.

[126] Ulrich, E. L., H. Akutsu, J. F. Doreleijers, Y. Harano, Y. E. Ioannidis, J. Lin, M. Livny, S. Mading, D. Maziuk, Z. Miller, E. Nakatani, C. F. Schulte, D. E. Tolmie, R. Kent Wenger, H. Yao, and J. L. Markley, 2008. BioMagResBank. Nucl. Acids Res. 36:D402–408.

[127] The Perl Programming Language. http://www.perl.org. Bibliography 139

[128] Dubendorf, J., and F. Studier, 1991. Controlling basal expression in an inducible T7 expression system by blocking the target T7 promoter with lac repressor. J. Mol. Biol. 219:45 – 59.

[129] Siemer, A. B., 2006. Structure Determination With Solid-State NMR: The HET-s Prion Protein. Ph.D. thesis, ETH Zürich.

[130] Wang, Y. J., and O. Jardetzky, 2002. Probability-based protein secondary structure identiﬁcation using combined NMR chemical-shift data. Protein Sci. 11:852–861.

[131] Wishart, D., and B. Sykes, 1994. The 13C chemical-shift index: a simple method for the identiﬁcation of protein secondary structure using 13C chemical-shift data. J. Biomol. NMR 4:171–180.

[132] Wasmer, C., A. Schütz, A. Loquet, C. Buhtz, J. Greenwald, R. Riek, A. Böck- mann, and B. H. Meier, 2009. The molecular organization of the fungal prion HET-s in its amyloid form. J. Mol. Biol. 394:119–27.

[133] Nielsen, N. C., F. Creuzet, R. G. Grifﬁn, and M. H. Levitt, 1992. Enhanced double-quantum nuclear magnetic resonance in spinning solids at rotational resonance. J. Chem. Phys. 96:5668.

[134] Lee, Y. K., N. D. Kurur, M. Helmle, O. G. Johannessen, N. C. Nielsen, and M. H. Levitt, 1995. Efﬁcient dipolar recoupling in the NMR of rotating solids. A sev- enfold symmetric radiofrequency pulse sequence. Chem. Phys. Lett. 242:304.

[135] Smith, S. A., T. O. Levante, B. H. Meier, and R. R. Ernst, 1994. Computer- Simulations In Magnetic-Resonance - An Object-Oriented Programming Ap- proach. J. Magn. Reson. Ser. A 106:75–105.

[136] GCC, the GNU Compiler Collection. http://gcc.gnu.org.

[137] Shirley, J. H., 1965. Solution of Schrodinger Equation with a Hamiltonian Peri- odic in Time. Phys. Rev. 138:B979.

[138] Baldus, M., T. Levante, and B. Meier, 1994. Numerical-Simulation Of Magnetic- Resonance Experiments - Concepts And Applications To Static, Rotating And Double Rotating Experiments. Z. F. Naturf. Sec. A 49:80–88.

[139] Levante, T., M. Baldus, B. Meier, and R. Ernst, 1995. Formalized Quantum- mechanical Floquet Theory and its Application to Sample Spinning in NMR. Mol. Phys. 86:1195–1212. 140 Bibliography

[140] Baldus, M., A. Petkova, J. Herzfeld, and R. Griffin, 1998. Cross polarization in the tilted frame: assignment and spectral simplification in heteronuclear spin systems. Mol. Phys. 95:1197–1207. [141] Smith, S., T. Levante, B. H. Meier, and R. R. Ernst, 1994. Computer Simulations in Magnetic Resonance: An Object Oriented Programming Approach. J. Magn. Reson. Ser. A 106:75–105. [142] Allen, F., 2002. The Cambridge Structural Database: a quarter of a million crystal structures and rising. Acta Cryst. B 58:380–388. [143] Ye, C., R. Fu, J. Hu, L. Hou, and S. Ding, 1993. 13C Chemical-Shift Anisotropies Of Solid Amino-Acids. Magn. Reson. Chem. 31:699–704. [144] Cheng, V. B., H. H. Suzukawa, and Wolfsber.M, 1973. Investigations Of A Non- random Numerical-Method For Multidimensional Integration. J. Chem. Phys. 59:3992–3999. [145] The Grid Engine Project. http://gridengine.sunsource.net/. [146] States, D., R. Haberkorn, and D. Ruben, 1982. A Two-dimensional Nuclear Overhauser Experiment With Pure Absorbtionphase In 4 Quadrants. J. Magn. Reson. 48:286–292. [147] Thurber, K. R., and R. Tycko, 2008. Biomolecular solid state NMR with magic- angle spinning at 25 K. J. Magn. Reson. 195:179–186. [148] Wikipedia, 2010. CPU cache — Wikipedia, The Free Encyclopedia. Online, accessed June 13, 2010]. [149] Goodman, J. R., 1998. Using cache memory to reduce processor-memory traffic. In ISCA ’98: 25 years of the international symposia on Computer architecture (selected papers). ACM, New York, NY, USA, 255–262. [150] McKee, S. A., 2004. Reflections on the memory wall. In CF ’04: Proceedings of the 1st conference on Computing frontiers. ACM, New York, NY, USA, 162. [151] Bayro, M. J., M. Huber, R. Ramachandran, T. C. Davenport, B. H. Meier, M. Ernst, and R. G. Griffin, 2009. Dipolar truncation in magic-angle spinning NMR recoupling experiments. J. Chem. Phys. 130. [152] Hohwy, M., C. Rienstra, and R. Griffin, 2002. Band-selective homonuclear dipolar recoupling in rotating solids. J. Chem. Phys. 117:4973–4987. [153] Williamson, P., A. Verhoeven, M. Ernst, and B. Meier, 2003. Determination of internuclear distances in uniformly labeled molecules by rotational-resonance solid-state NMR. J. Am. Chem. Soc. 125:2718–2722. Bibliography 141

[154] Verhoeven, A., P. Williamson, H. Zimmermann, M. Ernst, and B. Meier, 2004. Rotational-resonance distance measurements in multi-spin systems. J. Magn. Reson. 168:314–326.

Acknowledgements

Starting a doctorate is a bit like setting sails into the unknown. Many people were involved in providing help and support in very different ways. First of all there is Prof. Dr. Beat H. Meier. I would like to thank Beat for the freedom to let me learn so many things about NMR, software, hardware and biochemistry. I also enjoyed especially the challenging discussion when we fought about arguments. PD Dr. Matthias Ernst had always an open door for my questions and worries being it about spectrometer hardware, theoretical or computer problems. I also enjoyed the very well-prepared lectures of Beat and Matthias about the fundamentals of solid-state NMR which provided an invaluable basis to conduct my thesis. The two parts of my thesis were inspired and coined by two persons: First Dr. Ansgar Siemer with whom I really enjoyed interacting both on a professional, personal and musical level. I learned a lot about Britta and what it means being a good colleague. I also want to thank Ansgar for his patience with me when I did all the be- ginner’s mistakes at the spectrometer. Furthermore, the well-known “Ansgar Maria Siemer Quartett” interpreted classical music in previously unthinkable ways. The second part of my thesis, the analysis of transfer patterns in amino acids in the DREAM scheme, was very much supported by “Mister DREAM” himself, Dr. René Verel. He was always a great advisor and I was always impressed that his answers to many of my questions started with “do you have my thesis somewhere?” just to recognize that this question has already been addressed. This really motivated me to learn more and ask more questions. Also his great expertise on Chemagnetics NMR hardware should not be left unmentioned. When doing a thesis it is also important to have an ofﬁce mate that provides support on a professional but even more on a personal level. I had the very big luck of sharing the ofﬁce with Dr. Theofanis Manolikas for over four years. I am not sure if I had made it as good through the hard times as without your constant support and the unforgettable Reef calendar.

143 144 Acknowledgements

During my time at ETH Zürich I had the opportunity of interacting with many graduate and undergraduate students in our group. I would like to thank Michael Batel, Kai Eberhard, Julia Gath, Andreas Grommek, Matthias Huber, Ingo Scholz, Ivan Tomka and Christian Wasmer for their discussions about a wide range of topics in and outside of the coffee room. Speaking about the coffee room there must one person in the group not be forgotten which takes special care of an intensive interaction among the group members: Rosmarie Joss. I wish all of you big luck and success in all of your projects. There were also several post-docs and Oberassistenten I loved to work with. I would like to thank Dr. Jacco van Beek, Dr. Hélène van Melkebecke, Dr. Giorgia Zandomeneghi and Dr. Paul Schanda. When pushing equipment to the limit and sometimes beyond it is very important to have a great supportive and competent team of electronics engineers and mechanical engineers present. I would like to thank Urban Meier, Oliver With and Alexander Däpp for their advice and repairs over the years. Also the help of the LPC infrastruc- ture in the persons of Konrad Boss and Markus Imbach should not be left unmentioned. I also enjoyed visiting the LPC workshop team in particular Andreas Hunkeler. It often felt like the typical scene in a James Bond movie when 007 goes to Q and plays around with all the gimmicks lying around. I would also like to thank the secretaries of the group Romy Isenegger, Loredana Di Pietro and Gabriele Roder for help with the bureaucratic aspects of ETH. There is also a life outside the lab and there I would like to thank all my ﬂat mates of the Rebhüsliweg and the members of TGT and TGM Gisela Fontaine, Michelle Flück- iger and Tobias Hoheisel for all the nice and motivating words and the uncounted BBQs. I would also like to thank Kathrin for her support in the hot phase of my thesis and accepting me the way I am. All this would not have been possible without a strong foundation which is my family. I would like to thank my mother and my sister Martina for their unconditional support and love. Curriculum Vitae

Name: Thomas Westfeld

Date of birth: September 9, 1979

Place of birth: Cologne (Federal Republic of Germany)

Nationality: German

Education

02/2005–Present Ph.D. studies in the group of Prof. Beat H. Meier at the laboratory of physical chemistry at ETH Zürich, (Switzerland)

04/2002–10/2004 Undergrad studies in chemistry at ETH Zürich, (Switzerland)

09/1999–04/2002 Undergrad studies in chemistry at University of Cologne,(Ger- many).

09/1990–06/1999 Gymnasium Lessing–Gymnasium (Cologne, Germany). Main sub- jects: mathematics, geography.

Work Experience

02/2005–Present ETH Zürich Ph.D. thesis in the solid-state NMR group of Prof. Beat H. Meier.

02/2005–Present ETH Zürich Teaching assistant accompanying following lectures and laboratory courses: ﬁrst year physical chemistry, kinetics, ﬁrst and second year practical course in physical chemistry, practical course in NMR.

145 146 Curriculum Vitae

04/2004–07/2004 ETH Zürich Diploma thesis in the organic chemistry group of Prof. Peter Seeberger. Synthesis of an Arabinofuranoside Monomer and Preparation of a Diarabinoside Found in the Cell Wall of Mycobac- terium tuberculosis.

06/2000—8/2000 Bayer AG (Leverkusen, Germany) Working student in the production of base chemicals. Publications

Siemer, A. B., A. A. Arnold, C. Ritter, T. Westfeld, M. Ernst, R. Riek, and B. H. Meier, 2006. Observation of Highly Flexible Residues in Amyloid Fibrils of the HET-s Prion. J. Am. Chem. Soc. 128:13224–13228.

Seraﬁmov, J., T. Westfeld, B. Meier, and D. Hilvert, 2007. Trapping and Structural Elucidation of an Intermediate in the Macrophomate Synthase Reaction Pathway. J. Am. Chem. Soc 129:9580–9581.

Manuscripts in Preparation

Westfeld, T., R. Verel, A. Böckmann and B. Meier, 2010. Polarization Transfer Dynam- ics in Multi-Spin Systems Using the DREAM Scheme. in preparation.

147