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Solid state NMR investigation of protein based biomaterials : Pacific hagfish slime thread and recombinant… Depew, Thomas A. 2008

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Solid State NMR Investigation of Protein Based Biomaterials Pacific Hagfish Slime Thread and Recombinant Insect Resilin by Thomas A. Depew B.A.Sc., Queen’s University, 2004 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Applied Science in The Faculty of Graduate Studies (Physics)  The University Of British Columbia May, 2008  ©  Thomas A. Depew 2008  Abstract Nuclear Magnetic Resonance (NMR) was employed to investigate the structure and mechanics underlying the material properties of two remarkable biomaterials. Hydrated hagfish intermediate filament (IF) proteins were identified as having a two component nature, consistent with current structural models. One component is relatively rigid and immobile, the other rubbery, in which the protein backbone reorients with correlation times on the order of 60 ns. In order to investigate Ca ions in + the role of calcium ions in the formation of hagfish slime, hagfish IFs were exposed to 2 solution. Energy dispersive X-ray spectroscopy revealed that the filaments did bind Ca ions after exposure. These results were variable and depended largely on the preparation technique. Recombinant resilins from Drosophila melanogaster and Anopheles gambiae were shown to have a highly elastic structure. Direct polarization spectra from each protein were analysed and the majority of the ‘ C peaks assigned successfully. Relaxation measurements report backbone 3 correlation times on a scale of 2 to 8 ns, providing a molecular scale explanation the outstanding macroscopic resilience. Tyrosine residues in the resilin protein exhibited longer correlation times in the aromatic carbons, reflecting decreased mobility near dityrosine crosslinks.  11  Contents Abstract  II  Contents  111  List of Tables  V  List of Figures  vi  Acknowledgements  x  1  Introduction  1  2  Nuclear Magnetic Resonance  2  2.1  Zeeman Interaction  2  2.2  Fundamentals of the NMR Experiment  4  2.3  Relaxation of Magnetization  5  2.4  NMR Spectroscopy  6  2.5  Density Matrix Representation  7  2.6  Theoretical Tools  8  2.6.1  Frame Transformations  8  2.6.2  Average Hamiltonian Theory  9  2.7  2.8  3  4  NMR Interactions  10  2.7.1  Chemical Shielding  11  2.7.2  Dipolar Coupling  14  2.7.3  Quadrupolar Interaction  17  Relaxation Theory  18  2.8.1  Correlation Function and Spectral Density  18  2.8.2  Dipolar Coupling  22  2.8.3  Chemical Shift Anisotropy  23  Experimental Techniques  24  3.1  Heteronuclear Decoupling  24  3.2  Magic-Angle Spinning  24  3.3  Phase Cycling  26  3.4  Cross-Polarization  26  3.5  Energy Dispersive X-ray Spectroscopy  Introduction to Proteins  111  4.1  5  6  7  32  4.1.1  Random Coil  33  4.1.2  Alpha Helix  33  4.1.3  Beta Strand  34  Hagfish Slime Threads  34  5.1  Sample Preparation  37  5.2  Structure and Mechanical Properties  37  5.3  Nuclear Relaxation in Hagfish IF Proteins  41  Resilin: A Resilient Rubber-Like Protein  49  6.1  Chemical Shift Assignment of Recombinant Resilins  51  6.2  Secondary Structure of Recombinant Resilin  55  6.3  Relaxation Measurements  57  Incorporation of Metal Ions into Hagfish IF: Preliminary Work  59  7.1  Sample Preparation  60  7.2  Using REAPDOR to Determine Metal Binding Site  61  7.3 8  Protein Secondary Structure  7.2.1  2 Relaxation in Hagfish IFs T  66  7.2.2  REAPDOR Simulation  68  Energy Dispersive X-Ray Spectroscopy  69  Concluding Remarks  74  References  77  A  81  Lineshape Simulation Code  iv  List of Tables 5.1  Mechanical properties of some biomaterials and high performance synthetic materi als, adapted from [8, 13]  35  5.2  Amino acid composition of hagfish IF polypeptides  35  5.3  1 relaxation times for hagfish IFs. A single number indicates a one component T exponential fit; two numbers represent a two component fit  43  5.4  Simulated r results for the mobile carbonyl carbons  48  6.1  Amino Acid content of resilin samples. Residues not listed are not present in either sequence  50  6.2  Simulated chemical shift variance  57  6.3  rec-1 relaxation times and corresponding correlation times r. Temperature depen dence trend indicates that backbone and aromatic carbons are in the slow regime.  58  6.4  an-16 relaxation times and corresponding correlation times r  59  7.1  2 relaxation times T  67  8.1  Summary of dynamic characteristics for structural proteins  76  v  List of Figures 2.1  Evolution of magnetic moment about a static magnetic field  3  2.2  Energy levels for spin-1/2 in a static magnetic field B 0  3  2.3  The Rotating Frame (x’, y’, z’): A frame taken to precess at  Wrf  about the static  0 or the lab frame z-axis field B  9  2.4  A simple pulse sequence  2.5  Electron orbitals are influenced by the external field, B , inducing an opposing field, 0  10  B, which causes the shielding effect 2.6  11  A powder lineshape produced by all possible orientations in the Zeeman field. The IUPAC standard has ciii  22 S  533,  the 33 component representing the lowest  frequency 2.7  14  The dipolar interaction between two spins I and S; a result of the coupling of the magnetic fields produced by the dipole moments. 0 and  are the polar and  azimuthal angles of the internuclear vector r with respect to the static field B . 0  .  15  .  2.8  State transitions corresponding to the various components of the dipolar Hamiltonian 16  2.9  The random relative motion of atoms or molecules contributes to relaxation. Here the variation of the dipolar interaction between two spins due to rotational tumbling is pictured. The local magnetic fields B , 1 0 are dependent on the relative orientations of the two nuclei with magnetic moments depicted by the dark arrows  18  2.10 Definition of r; a longer interval generally results in very different local fields B(t).  .  19  2.11 Temperature effects and r, T . The Cold and Hot markers denote the direction in 1 which the T 1 value will move in each regime as the temperature is changed  22  3.1  Magic Angle Spinning  25  3.2  Phase cycling  26  3.3  Bloch Decay NMR experiment employing cross-polarization pulse to induce trans verse magnetization in the ‘ C nuclei 3  27  3.4  The toggling frame or interaction representation  28  3.5  Trial data from EDX experiment showing elemental content of GTC bundle  31  4.1  Protein amino acids are all similar, differing in the attached side chain R  4.2  The peptide unit; a) the trans form with  vi  =  180°; b) the cis form with w  1 =  0°.  .  32  4.3  (a) The alpha helix structure, hydrogen bonds (dashed lines) between carbonyl oxy gen and amides; (b) the single beta strand and beta sheet, showing hydrogen bonding between adjacent beta strands via the peptide unit. Image taken from [6]  5.1  33  Pacific Hagfish slime; an effective defense mechanism. Photo courtesy of D. Fudge, P. Guerette  5.2  34  A schematic model of the polypeptide composing the hagfish slime gland thread cell (GTC). Image taken from [13]  5.3  36  X-ray diffraction results for a) unstrained b) high strain hagfish IFs. Images taken from [13]  5.4  36  The proposed nature of the transition from cr-helix to /3-strand under strain. Image taken from [13]  5.5  36  Stress strain curves for hagfish IFs a) Q-helical, elastic region b) deformation into plastic, /3-sheet region. Images taken from [13]  37  5.6  Direct Polarization results for hagfish IFs at 20°C. Arrows indicate citrate peaks.  38  5.7  Cross polarized experimental results for hagfish IFs at 20°C  39  5.8  Direct Polarization results for hagfish IFs at varying temperature. Temp  5.9  20° C, 5°C,  =  —  15°C  40  Temperature dependence of mobile C=O peak in DP spectra of hagfish IFs  41  5.10 T 1 inversion recovery experiment employing cross-polarization pulse to study longi tudinal relaxation of the ‘ C nuclei. Note the 3  pulses are generally not the same  duration on both channels  42  5.11 Spectrum from T 1 inversion recovery experiment with r  =  ims, Temp  =  20°C.  .  .  .  43  5.12 T 1 experimental data for (a) carbonyl, (b) cv-carbons, (c) other side chain carbons at Temp  20°C; (d) carbonyl data requires a two component fit at Temp  5.13 The Tyr q-peak T 1 results for Temp  =  =  —20°C  20°C experiment  5.14 A simulated lineshape overlayed on a DP spectrum collected at Temp correlation time of r  =  44 45  =  20°C. A  0.06,us acheives a reasonable fit  5.15 Simulated r temperature dependence results displaying Arrhenius fit with Ea  47 =  40.3  kJ/mol  48  6.1  Amino acid sequence of recombinant resilin, rec-1  50  6.2  Amino acid sequence of an-16 resilin  50  vii  6.3  Dityrosine complex formed via photo-crosslinking. The crosslink site is shown here at the c-carbon but may also occur at the ö-carbon  6.4  51  DP experimental spectra (a) rec-1 resilin (b) an-16 resilin. The broad peak centered at l2Oppm is due to probe background  6.5  51  rec-1 resilin DP spectra peak assignment (a) carbonyl and aromatic region (b) aand 3-carbon region  6.6  52  an-16 resilin DP spectra peak assignment (a) carbonyl and aromatic region (b) aand /3-carbon region  6.7  red  54  and an-16 DP spectra overlay (a) carbonyl and aromatic region (b) a- and  /3-carbon region 6.8  6.9  Deviation from observed chemical shift (a) rec-1 resilin, N  =  13 (b) an-16 resilin,  N=8  56  T experiment employing background suppression via phase modulation  57  6.10 T 1 spectra with 7.1  55  r  =  0.Ols and Temp  =  4°C a) rec-1 resilin b) an-16 resilin  57  3,4-dihydroxy-L-phenolalanine (L-DOPA). (a) DOPA is much like the amino acid tyrosine but has a second hydroxyl group on the aromatic ring; (b) a divalent metal j may form an ionic bond with the oxygen atoms 2 (in this case Ca  7.2  A REAPDOR pulse sequence. The x and y are hard r pulses at  60 inervals. The  pulse on the S channel is an adiabatic passage recoupling pulse  62  7.3  The adiabatic passage pulse is required to invert an adequate population of S spins  65  7.4  An example of a REAPDOR experimental curve  66  7.5  Hahn spin echo experiment with cross-polarization. The delays similar, but the acquisition may start sooner than  Ti  Ti  and  T2  are very  after the ir pulse to ensure the  full echo is captured 7.6  66  The spin echo. Vectors represent transverse magnetization in a frame rotating at the Larmor frequency after time  r  ; 0 w  (a) Initial transverse magnetization following  the magnetization has dephased due to spins precessing at frequencies  slightly different from the Larmor frequency,  wj =  wo  + öw; (c) a r pulse is applied,  inverting magnetization; (d) magnetization refocuses at time 7.7  pulse; (b)  Spin Echo experimental spectrum.  yR  =  5kHz  viii  T  after the r pulse.  .  67 68  7.8  REAPDOR Simulation for DOPA-Ca binding:  =  5kHz,  Vd  =  57Hz,  x  =  50kHz,  2 limit for the tyrosine q-carbon The arrow indicates the T  68  3 contaminant Trial SEM micrograph of GTC bundle with nearby CaCO  70  S 7.9  R 11  =  .  7.10 EDX spectra for control samples a) pure b) contaminated  71  7.11 EDX spectra for samples treated with CaCO 3 a) positive results b) contaminated c) no apparent Ca presence  72  7.12 EDX spectra for samples treated with CaCl 2 a) positive results b) contaminated c) no apparent Ca presence 8.1  73  DP spectra comparison of elastin (C) with rec-1 resilin (A) and hagfish IF (B) spectra. (C) was taken from [32] and displays spectra for strained (dotted) and unstrained (solid) elastin  75  ix  Acknowledgments A student undergoes many trials throughout their academic career as they progress from regurgi tating simple facts, to learning to think critically and answer the questions that begin to materialize in their increasingly complex world. The student is lucky when they are allowed the opportunity to work with someone who nurtures and guides this learning process. I’m incredibly grateful to Carl Michal for being that someone. In addition to helping me over those little hurdles along the way, (and picking through some horrendously messy computer code), he has been a friend and mentor, thank you Carl. Peers also play an important role in the students growth, growing alongside one another and helping along the way; be it with a homework problem, a helping hand while submitting your thesis, or to make you stop staring at the computer screen and drag you out to the pub for a relaxing beverage. Thanks to my lab mates, Jenny Chien-Hsin Tso, David Katz, Ronald Dong, Matthew Lam and Simon Hastings, for support and friendship. I would like to thank my collaborators, John Gosline and the nice folks in his zoology lab. Paul Guerette, thank you for sliming me, without you and your fish I would not have had a project. To Chris Elvin and Dan Dudek I owe a great deal for providing material and support with the resilin samples. I would also like to thank my friends and pseudo-family in Vancouver, thanks for putting up with my completely uninteresting ramblings on the topics of biophysics. Tim, Nick, Jason and Sara I wouldn’t have survived out here without you. Finally, I thank my family; William, Cathy, Sarah and David. Without you I wouldn’t be here, you have provided guidance, support and unconditional love my entire life and I love you all.  x  1  Introduction  For many years, NMR has been used to successfully probe the nuclear environments of materials and elucidate structural information. Because the NMR spectrum allows the resolution of various chemical environments and reflects characteristics of molecular dynamics, it is ideally suited to the study of biological materials such as proteins. Chapter 2 discusses the fundamentals of NMR and Chapter 3 relates some commonly used experimental techniques in NMR as well as a brief discussion of energy dispersive x-ray spectroscopy (EDX), which was also used in this study. The two types of proteins investigated in this dissertation; Hagflsh gland thread cell protein and recombinant forms of resilin protein, are the basis of promising structural biomaterials. One of the goals of research in biomaterials is to find biologically inspired solutions to com mercial, scientific and engineering problems. Many synthetic structural materials produced today have harmful side effects during manufacturing processes. Hagfish slime threads are composed of a conglomeration of dual helix protein pairs, forming an intermediate filament structure. The threads have interesting material properties, being remarkably elastic but also tough under high strain. Although the threads are not as mechanically robust as some synthetic materials, they may provide insight into structural or compositional factors that impart the desired characteristics to a material. The hagfish intermediate filaments also provide an excellent candidate for the study of intermediate filament structure and dynamics, difficult to expose in other living systems, such as within cells. In Chapter 5, a variety of NMR experiments are employed to describe the structure and mechanics of the hagfish IFs on a molecular scale. A possible key factor in the formation of the hagfish IFs is the incorporation of metal ions into the protein structure. Chapter 7 investigates the binding of Ca 2 to the protein using EDX and NMR experiments. The recombinant resilin material is inspired by a rubber-like substance found in many arthro pods. In nature, resilin provides a variety of energy storing functions in insects, from locomotion to sound production. The resilin material is attractive for its highly resilient properties; its ability to store and release mechanical energy over millions of cycles without appreciable loss in efficiency. This type of material could contribute substantially to devices or materials requiring a high cycle lifetime, such as biomedical implants or micromechanical actuators or sensors. Chapter 6 exposes the underlying molecular structure and dynamics that are believed to provide the mechanical properties of the material.  1  Nuclear Magnetic Resonance  2  Nuclear Magnetic Resonance (NMR) is a phenomenon that is exhibited by many nuclear species. An NMR active nucleus must have an intrinsic nuclear magnetic moment; this is a result of the nucleus containing an odd number of protons or neutrons. These nuclei and their chemical envi ronments are stndied by alignment of the magnetic moments in a large static magnetic field and observing the response of the nuclei to perturbing electromagnetic fields.  2.1  Zeeman Interaction  The starting point in understanding NMR is to examine the effect of a static magnetic field, B , 0 on a nucleus. The nuclei interact with magnetic fields via their magnetic moment, which is defined by (2.1) in which 7 is the gyromagnetic ratio and I is the angular momentum of the nucleus. The effect of the magnetic field is to exert a torque, T, on the nuclei. This torque is defined as the time rate of change of the nuclear spin: T  (2.2)  = ,  and is dependent on the magnitude and direction of the static magnetic field  . 0 T=pxB  (2.3)  Combining equations 2.2 and 2.3, a c)assical equation of motion for the nucleus is formulated:  =  7t  x B . 0  (2.4)  -  Solving 2.4 will show the magnetic moment precessing about the magnetic field at a rate w  =  , called the Larmor frequency (see Figure 2.1). 0 B 7 — The Hamiltonian for this simple system can be obtained by substituting the classical com ponents by their quantized operator counterparts. For example,  ji  becomes l  =  h1 and the 7  Hamiltonian is Hz  =  0 i. —B  2  (2.5)  0 B  L’0  Figure 2.1: Evolution of magnetic moment about a static magnetic field. By convention, the static magnetic field direction is assigned as the laboratory z-axis. Substi tuting Equation 2.1 for  t,  the Zeeman Hamiltonian is written:  =  (2.6)  —y/tBof.  The most trivial case is when dealing with a spin-i nucleus, such as 13 C, where Equation 2.6 gives a two level eigensystem with energies Em  =  hB with spin quantum number m denoting the 7 —m , 0  eigenstate. A schematic of this two level system is shown in Figure 2.2.  I  —  )  1 E_  =  hB 7 + 0  1 E  =  —-yhBo  hB 7 0  Figure 2.2: Energy levels for spin-1/2 in a static magnetic field B 0 NMR experiments deal with large numbers of quantum particles, and thus, can be described statistically in most cases. A spin ensemble, that is a collection of interacting nuclei, in the above described Zeeman field, reach a thermal equilibrium which can be characterized by the Boltzmann distribution. The population, Pm of a given energy level is e_Em/T  Pm  z  (2.7)  where kB is the Boltzmann constant, T the temperature and Z is a normalization factor, the  3  so-called partition function: Z  =  e_Em/’T.  (2.8)  At equilibrium in non-zero temperature, there is a difference in the populations of the energy levels. This population difference elicits a net magnetization in the sample oriented parallel to the external magnetic field. The two energy levels in the spin-i system correspond to magnetic moments which are anti-parallel to each other. The net sum of all the magnetic moments in the ensemble is the total magnetization M 0  2.2  =  of the sample.  Fundamentals of the NMR Experiment  Most NMR experiments observe the response of the system after being subjected to a radiofrequency (rf) pulse. The pulse is administered via a current carrying coil which generates a fluctuating magnetic field, penetrating the sample inside the coil.  The signal obtained is the  precession of transverse magnetization created by the perturbing electromagnetic pulse. The signal is often received in the same coil; a fluctuating current created by the precessing magnetization. The applied rf pulse must have a frequency close to the Larmor frequency  (wo  =  ) to perturb 0 B 7  nuclei of that species. The classical formula for a spin in a magnetic field, Equation 2.4, can be adapted to account for the average overall magnetization, M in a sample:  = M 7 xB.  (2.9)  This expression is known as the Bloch Equation and gives a classical representation of a nuclear spin system. The benefit of the Bloch Equation is that it gives reasonable and intuitive results that can be calculated in a straightforward manner, without the need for involved quantum mechanical treatment. This formulation of the Bloch Equation has neglected nuclear relaxation effects which will be treated in the next section. The applied rf-field B 1 (t) is an oscillating field normally transverse to the static field direction (i.e. B 1  =  cosrft). The applied field exerts a torque on the magnetization, moving it from its  equilibrium position parallel to the Zeeman field, into the xy-plane. The rate of the nutation away from the z-axis is proportional to the strength of the rf-field;  wri  =  B. The resulting position 7  of the magnetization is then dependent on the duration of the pulse, t. The tip angle can be  4  controlled by either the pulse length or rf-field strength:  =  ‘yBt,.  (2.10)  The tip angle is an important feature to control in NMR experiments.  2.3  Relaxation of Magnetization  Relaxation is the process by which a macroscopic system returns from some non-equilibrium state to its statistical equilibrium. In the case of NMR, the macroscopic system referred to is the state of the magnetization. The processes by which relaxation can occur are many, however, the most prominent for nuclei such as ‘ C and ‘H are the dipolar coupling and the chemical shift anisotropy. 3 These mechanisms will be discussed in a later section. Relaxation can be described on a phenomenological level as the time taken for the magnetization of a sample to return to equilibrium after a perturbing rf pulse. Nuclear relaxation is characterized by two parameters which describe the timescales on which the longitudinal (parallel with the Zeeman field), and transverse (perpendicular to the Zeeman field) magnetization takes to “relax”, that is, return to the thermal equilibrium. The classical equation of motion for the macroscopic net magnetization, M, is the Bloch Equation (2.9). When relaxation is accounted for, the longitudinal relaxation time, T, and the transverse relaxation time, T 2 govern the time dependence of the magnetizations Ma, where  Q  X  ,  Z.  M(t)  =  M(0)cos(wot)e  (t) 9 M  =  My(0)sinQiot)e  M(t)  =  Mo+(M(0)—Mo)e.  (2.11)  Here, M 0 is the equilibrium value of the magnetization. Consequently, the Bloch Equation becomes:  =  yM x B  -  R(M  00 R=  oo 00*  5  -  Mo)  (2.12)  1 and T The relaxation times T 2 are observed characteristic timescales describing the recovery rates of the net magnetization in the sample.  However, they have a link to deeper quantum  mechanical processes that will be developed in Section 2.8.  2.4  NMR Spectroscopy  The precessing magnetization M after a pulse produces an oscillating current in the coil, and the resulting signal is tracked over time. This signal is known as the free induction decay (FID) of the system. Typical FID signals are on the order of MHz and are mixed down by a quadrature receiver with the rf-pulse frequency  The sample will have a range of frequencies depending  Wrf.  on the various environments of the spins under the influence of multiple interactions, as discussed in later sections.  The observed frequency range  =  wo  —  Wrf  is then centered around zero  frequency and usually in the range of a few tens or hundreds of kHz. This mixing down of the acquired frequencies reduces the demand on electronics and the amount of data required. The FID is received in quadrature, the  The signals  sR, s  two  signals are of the form  SR(t)  cx  sj(t)  cx  cos(2jt)e_t/T  3 sin(12jt)et’T2  (2.13)  should be understood as a superposition of signals with  various frequencies,  If the signals are combined into a single, complex time dependent function,  s(t)  =  SR(t)  +  isj(t),  then frequencies faster than the rf frequency can be distinguished from those lower than the rf frequency (i.e.  <  0). This time domain signal is transferred to frequency space by Fourier  transformation:  f  S(l)  s(t)e_tdt.  (2.14)  The result is S()  1/T =  —  2+ (1/T)  (  )2 —  i  (2.15)  —  2 + (l (1/T)  —  These are the real (absorption) and imaginary (dispersion) part of a Lorentzian peak. Note that a fast decay will result in a broader peak, a slow decay results in a sharper peak.  6  2.5  Density Matrix Representation  Instead of representing the sample as an ensemble or superposition of single quantum states, it is often convenient to use density matrix representation, in which the spin system is described by a single density operator being in the state  ,  .  Representing a collection of spins, each of which has a probability p . of 1  by a superposition state ‘I’ can be cumbersome as one must account for each  spin individually. The expectation value of some operator  A  in our spin ensemble must include a  summation over all possible states for each spin:  (A)  =  (IJIAI’IJ)  =  pd,i,(’,bIAI’t,b).  (2.16)  This can be simplified by representing the spin states in terms of a set of basis states,  j,  convenient  for our interacting spin ensemble. Now the possible states are  (2.17)  and the expectation value becomes  (A)  (2.18) i,j  The advantage is now apparent, noting that the matrix elements less of the state  we are dealing with. The  th  are the same regard  density matrix elements are defined  ,  and Equation 2.18 can be rewritten as  (A)  =  3 Ap  =  (Ap)  where A is the matrix representing the operator  A  =  Tr(Ap),  (2.19)  in the basis qj. The expectation value of any  observable can be determined by simply taking the trace of the product of the observable with the density matrix. The operator corresponding to the density matrix can be deduced from the matrix elements: =  p,j)(?/’j.  (2.20)  The Schrödinger equation can be used to formulate a relation which describes the time evolution  7  of the density matrix. This relation is known as the Liouville-von Neumann equation:  (2.21)  The solution of Equation 2.21 is 1 3(t)  =  U(t, O)(O)Ut(t, 0), where (0) is the initial density operator  and U(t, 0) is a time evolution operator. The evolution operator is often termed the propagator and can be defined for general time-dependent Hamiltonians in the form:  U(t,0)  =  ie*fo(t’)dt’,  (2.22)  where 1’ is the Dyson time-ordering operator which ensures that the order of propagators is properly maintained.  2.6  Theoretical Tools  When dealing with spin systems and their response to electromagnetic perturbations from the rf field, there are a few mathematical and conceptual tricks that can be played to greatly simplify the analysis of the problem. Two that will be briefly discussed here are frame transformations and average Hamiltonian theory. 2.6.1  Frame Transformations  NMR experiments invariably entail the oscillating components of the spin operators in the static magnetic field due to Larmor precession. Since this action is universal, NMR problems are almost always simplified by examining the system in the rotating frame. The rotating frame is taken to rotate at the applied rf-frequency about the static lab frame z-axis (parallel to the static field B , 0 see Figure 2.3). This frame transformation is enacted analytically by subjecting the lab frame Hamiltonian to a rotation operator 1?  =  in the following way:  (2.23)  H’R H 1 RWrfIz.  Normally the pulses are applied on (or very close to) resonance  (Wv!  WO),  thus the effective field  Beff is simply that of the pulse B 1 in the rotating frame. The advantage of such a transformation  8  z,z’  z’  0 B  Bo(1_JL) -  I  X  /  11’  - - - - - - - - - - - - - - - - - - - -  Wjf  Figure 2.3: The Rotating Frame (x’, y’, z’): A frame taken to precess at 0 or the lab frame z-axis. B  Wrf  about the static field  is that when resonance is achieved, the only field present in the rotating frame is the applied field, . Furthermore with the frame rotating at the rate of spin precession, terms associated with the 1 B static field, the Zeeman terms, are effectively nulled by the  term (a result of insisting that the  time-dependent Schrödiuger equation is invariant under the transformation). In the rotating frame, the magnetization is affected solely by Bj’f. It will precess about the effective magnetic field direction at a rate w  =  tBeff. In the lab frame, there is still precession  about B 0 and the resulting motion is complicated. There is nutation at a rate w, about an axis rotating about the lab frame z-axis at wo. 2.6.2  Average Hamiltonian Theory  Because of the oscillatory nature of the interactions in NMR experiments, another convenient tool is Average Hamiltonian theory. This technique is employed by approximating periodic Hamilto nian terms as the average of the term over the required time. Average Hamiltonian theory can be especially useful for certain pulse sequences in which the sequence is made up of a chain of identical blocks. In this case, the propagator LI is described by a chronologically ordered product of propagators. The propagator for the pulse sequence shown in Figure 2.4 is  CT(t) =  146 e’  ö t Hf T3 e 6  9  fö2ethlfeT2euh’rfS1  (2.24)  63  T4  T2  T1  64  t=o Figure 2.4: A simple pulse sequence where Hrf denotes the Hamiltonian during the rf irradiation, Hf e the Hamiltonian during free evolution and 6, r are the respective time periods over which each Hamiltonian acts. An equivalent propagator can be determined by using the Magnus expansion:  (t)  1o+1i+I2+...  =  )dt 1 1(t  Io =  1i  fdtf  =  2 H  2 3!th  =  +  where the  fi  represent the  ),1(ti)] dt 2 [I(t 1  fdtfdtf  ([(t ) 3 ,  1 ) 2 [(t ) ,I(t ]]  [1(ti), 2 [I(t ) , I(t )]]) dt 3 , 1  th  (2.25)  order term of the Hamiltonian. The expansion takes advantage of  the properties of exponential operators, i.e.  eAe =exP{A+E+  Here  [A, E]  [A,E]  ([A, [A,E]]  +  denotes the commutator of operator  +  [[A,E] ,E])  +...}  (2.26)  A with operator E.  Equation 2.25 appears daunting, however it is frequently the case that the zeroth order term , is sufficient to describe the resultant NMR spectrum. In fact, it is often the case that the 0 ft Hamiltonians commute and all higher order terms will be zero. The zeroth order term is simply the time average of the piecewise Hamiltonians in the propagator U(t). 2.7  NMR Interactions  There are a variety of phenomena that occur in an NMR active sample. These range from in— teractions between adjacent spins to interactions with magnetic and electric fields, and they have a variety of effects on the resulting spectra. The following sections will discuss some of these 10  interactions important to the subsequent work. 2.7.1  Chemical Shielding  The chemical shielding interaction is a result of the external magnetic field. The static field induces preferential circulation of the electrons, and this motion in turn, generates additional magnetic field (Figure 2.5). This effect is primarily intramolecular; it is also seen in nearby nuclei but is normally not as dramatic due to the 1/r 3 dependence of the magnetic potential. 0 B  Fignre 2.5: Electron orbitals are influenced by the external field, B , inducing an opposing field, 0 which causes the shielding effect. Generally in a large molecnle, each nucleus has a slightly different chemical environment and thus experiences a slightly different local field  This means that each spin will precess at a  different frequency and a range of frequencies arises in the resulting spectrum. As alluded to above, the chemical shielding normally has an orientational dependence. This is a manifestation of the fact that the electronic environment around a nucleus is in general non-isotropic. The chemical shielding is thus characterized by a second rank tensor o 3 describing the directional dependence of the orientation of the atom or molecule in the static field. In the principal axis frame (PAF) of the nucleus, u 3 is diagonal:  JPAF_  QPAF  0  0  0  JPAF  0  0  0  JPAF  (2.27)  To a good approximation, the chemical shielding is linearly proportional to the static field and the Hamiltonian is H = 3 -yI•cBo.  (2.28)  The shielding tensor is rarely aligned with the static field and thus the resulting frequencies pro11  duced will be dependent on the lab frame shielding components o, c,  The lab frame  xe,.  chemical shielding tensor components can be calculated by performing a suitable Euler transfor mation on the PAF components. A further simplification can be made by transforming to a rotating frame as described in Section 2.6.1. The first order chemical shift Hamiltonian becomes  (2.29)  ‘yIuBo,  =  where the periodic x and y components in the rotating frame average to zero. Equation 2.29 can be extended to find the first order contribution to the energy levels of the spin states:  E  =  huzzBo(1,m11z11,m) 7  =  7 h Bom,  (2.30)  and the contribution to the frequency observed in the NMR signal is  =  22 o 7 0 B -  =  —“,ooz.  (2.31)  The total spectral frequency is the Larmor frequency plus the chemical shielding contribution, however, absolute frequencies are not measured in an NMR experiment. Rather, the frequency offsets from the applied rf frequency are measured with respect to the signal generated by a reference compound. In the case of ‘H and ‘ C NMR, the reference compound is normally tetramethylsilane 3 (TMS) since it has a smaller amount of shielding compared to most other compounds and the shielding is also relatively orientation independent. The displacement of the observed frequency from the reference signal is termed the chemical shift of the nuclear species in question. Since the frequencies obtained in an NMR experiment are field dependent, the chemical shifts ö are universally reported in parts per million (ppm). In this work, the 5-scale will be employed, following IUPAC convention: obs  —  ref  ref  X  106  (2.32)  The diagonal PAF components are conventionally labeled ö, 622, 633, where These components are often represented by their isotropic  12  anisotropic  H 6  (s),  622 >  633.  and asymmetry  (?]),values. The isotropic value is defined:  iso 6  The definitions of  =  (6ii  +  22  +  (2.33)  633).  and?] are dependent on the relative sizes of the components, if  I’i  —  633 >  o—iI then 8 k5i =  o33oiso  =  —ö 1 6 22 1  =  iso11 6  =  33-522  (2.34)  otherwise  (2.35)  If the PAF of the nucleus is oriented at respective polar and azimuthal angles, 0 and  ,  then the  frequency contribution can be written in terms of the PAF components:  =  —wo  (  n+ 6 (  622  +  633)  +  611  2 0 cos sin 2  +  622  2 0 5ifl sin 2  +  633  2 cos  o).  (2.36)  Using the definitions in Equations 2.34 and 2.33, Equation 2.36 becomes  =  (iso  +  2 0 (3 C05  —  1  —  ?] Sjfl 2  0 COS 2)).  (2.37)  If a sample under NMR investigation had simply bare nuclei, the resulting spectrum would show an infinitely sharp single line at the resonant frequency of the nucleus. When dealing with solids, the variety of chemical environments normally encountered, especially in large organic molecules, spreads the line out into a broad peak, a collection of effective resonant frequencies, altered from the Larmor frequency by the chemical shielding. The anisotropy effectively characterizes the spread in the frequencies, see Figure 2.6. The isotropic value is the average of the principle components and the asymmetry provides a measure of the deviation from a cylindrically symmetric tensor, in which  22  =  13  22 Siso  11 533  increasing ppm Figure 2.6: A powder lineshape produced by all possible orientations in the Zeeman field. The JUPAC standard has S 1 S 22 > 533, the 33 component representing the lowest frequency. 2.7.2  Dipolar Coupling  The dipolar interaction stems from the fact that a magnetic dipole produces a field of its own. This field will influence other dipoles through space, but is not normally far-reaching as it also has a 1/r 3 dependence. Classically, the energy of interaction between two nuclei represented by magnetic dipoles  and  2 j.L  with an internuclear distance r is  =  —  \  3011  r  .  2 r) r)(.t 5 r j4ir .  (2.38)  Recalling the fact that the magnetic moment is represented by the operator  =  yhi, the dipolar  coupling Hamiltonian can be written:  =  (!  —  (J. r)( r)) .  .  (2.39)  Here the subscripts 1 and 2 have been represented by spins I and S, respectively. Equation 2.39 is conventionally rearranged into spherical coordinates and separated into 6 terms representing various couplings between the states of the spins.  Hd=-()  ‘[A+B+C+D+E+F]  14  (2.40)  where:  A B  I,  and  I_,  = =  I&(3cos o 2 —1) _(I++I+)(3cos2o_1)  c =  (I+ +  D =  (Iz.’_ + I_&) sinO cos Oe  sinO cos Oe  E  =  .2 I+S+)s1n Ue —2ith  F  =  2 Oe (I__) sin 2  (2.41)  L are the raising and lowering operators that act on spins I and S, respectively.  The polar and azimuthal angles 8 and q are defined in Figure 2.7. The rearrangement of the dipolar  z 0 B  S  y  x Figure 2.7: The dipolar interaction between two spins I and S; a result of the coupling of the magnetic fields produced by the dipole moments. U and are the polar and azimuthal angles of the internuclear vector r with respect to the static field B . 0 Hamiltonian is beneficial as it separates the interactionsin terms of energy level transitions. Figure 2.8 shows an energy diagram representing the states of a spin-i system with two nuclei and relates the transitions to each of the components in Equation 2.41. There are two classes of dipolar interaction; homonuclear dipolar coupling between like species of nuclei, and heteronuclear dipolar coupling between unlike species. Incidentally, homonuclear dipolar couplings would display an energy level splitting as in Figure 2.8, whereas heteronuclear energy level splittings will be different depending on the type of nuclei involved. Both types of dipolar coupling Hamiltonians can be simplified greatly by a transformation to the rotating frame. When this is done for the homonuclear case, the terms C-F acquire periodic 15  A 4  ——  C,D  c,D/ B +-  -+ E,F!  A  / C,D  C,D\ I  ++  A Figure 2.8: State transitions corresponding to the various components of the dipolar Hamiltonian. time dependence with frequency uio, and can be averaged away using average Hamiltonian theory (see Section 2.6). Similarly, these terms adopt periodic dependence with the heteronuclear case, however, the B term will also average away with a periodic dependence of w 0 due to the fact that terms of the form  are affected by the rotation operator when I and S are not the same  spin type. The first order average Hamiltonians for the dipolar interaction are thus:  0=(3cos2O_l)(3Izz_j.)  (242)  —d (3 cos 2 o — i)  (2.43)  jetero  =  where we have labeled the dipolar coupling constant d:  d  =  h  Ito  ()  1  (2.44)  yrys  The dipolar interaction can be expressed in tensor form fid  —21 D S. In the PAF: .  .  00 0 0  .  (2.45)  d  Because the dipolar interaction depends on the internuclear distance, it can be exploited to reveal information about the structure of the sample under investigation.  16  2.7.3  Quadrupolar Interaction  Nuclei that have spin I  >  ,  exhibit a feature known as the quadrupole interaction. This phe  nomenon is a result of the distribution of charge in the nucleus, giving rise to the electric quadrupole moment, which interacts with electric field gradients. An electric field gradient can arise naturally at the nuclear site by virtue of the distribution of charges in the vicinity, i.e. other nuclei and their electrons. The strength of the quadrupolar interaction can be quite large, often on the order of the interaction of the nucleus with an applied rf field. Thus it has a substantial effect on the spectrum and must be taken into account where necessary. The quadrupolar Hamiltonian describes the effect of the interaction between the nuclear electric quadrupole  Q  and the electric field gradient V:  (2.46)  .  21(21—1)h  =  for a spin I, where e is the charge on an electron. The expansion of Equation 2.46 is  =  where  ,  [  61(21-1) h  (ii + II)  -  oI2],  (2.47)  3 refer to the x, y and z coordinates of the defining reference frame, and ö is the  Kronecker delta acquiring a value of 1 if o  =  3 and 0 otherwise. The quadrupolar interaction can  be represented in tensor form much like the chemical shift and dipolar tensors. The quadrupole coupling tensor in the PAF is  X  =  =  VPAF  0  0  0  VPAF  0  0  0  VPAF  (2.48)  The electric field gradient tensor, V is traceless in the PAF and has no isotropic component. The anisotropy, eq and asymmetry,  T/Q  of the interaction are conventionally defined in the same manner  as the chemical shift:  eq  =  =  VPAF VPAF  —  VPAF  VPAF  17  (2.49)  The quadrupolar PAF generally does not align with the Zeeman field and the interaction Hamil tonian is quite complex. Fortunately, if the Zeeman interaction is dominant in the system, then only the secular parts of the quadrupolar Hamiltonian contribute significantly to the energies of the spin states. The first order Hamiltonian of the quadrupolar interaction has a form very similar to the chemical shift interaction:  =  2.8  8II— 1)  (3cos O 2 — 1  —QcOS(2)sifl O 2 )  [3I —1(1+ l)i].  (2.50)  Relaxation Theory  The Bloch characterization of the relaxation times developed in Section 2.3 does give a general idea of the timescale of equilibration in a sample, but more information regarding molecular dynamics and structure can be obtained. The cause of relaxation for spins- is the fluctuation of magnetic fields at the site of the nucleus, primarily due to thermal motion. The fluctuating magnetic fields stem from the various interactions that the NMR nuclei can experience and a quantum mechanical treatment can illuminate dynamic characteristics of the sample.  2.8.1  Correlation Function and Spectral Density  For systems of organic molecules involving spin-  nuclei, the primary mechanisms behind the  fluctuating magnetic fields are the dipolar interaction and the chemical shift anisotropy. Both of these interactions are orientation dependent, so if there is any relative motion of nuclear sites, these interactions acquire some time dependence, see Figure 2.9. The time dependence of the local  Figure 2.9: The random relative motion of atoms or molecules contributes to relaxation. Here the variation of the dipolar interaction between two spins due to rotational tumbling is pictured. The local magnetic fields Bj , are dependent on the relative orientations of the two nuclei with 0 magnetic moments depicted by the dark arrows. magnetic fields can be described by a correlation function, G(r). G(r) is essentially a measure of 18  how well the local magnetic field at a time t matches that at a time t +  T.  This can be described  classically by the ensemble average of the product of the magnetic fields  G(r)  =  B(t)B(t + r)  (2.51)  where the overbar denotes an average over all spins in the sample. If the interval r is long compared to the speed of the fluctuations then the correlation function will decay rapidly. Otherwise the magnetic fields will in general be similar for most spins and the correlation function will decay more slowly. Figure 2.10 shows this relation between the timescale of fluctuation and the interval T. Tshort  B  I I  sNVJtf\\v\\J:  Figure 2.10: Definition of r; a longer interval generally results in very different local fields B(t). Quantum mechanically, we have a Hamiltonian H  =  +H describing the spin system subject 0 H 1  to the Zeeman field and a randomly fluctuating Hamiltonian that accounts for the various relaxation mechanisms. In the rotating frame, the evolution of the density operator is given by the Liouville von Neumann equation: =  _[i , 1 ].  (2.52)  Through integration and use of the Magnus expansion, the value of the density matrix can be obtained for some arbitrary time t.  (t)  =  )  i  -  f  -  [t’), (0)] dt’  f f dt’  (t’), 1 1 [ [ ( t”), (0)]] dt” +  ...  (2.53)  The time t is chosen such that the density operator undergoes a small change and the second order term is sufficient to describe the density operator (t). The first order term vanishes as the average is zero. The form of the relaxing Hamiltonian fi is:  FmImeiL)0t,  19  (2.54)  where the m are the spin operators and the Fm are the spatial functions which randomly change due to the thermal motion discussed above. The  term comes from the frame transformation  e0t  on the spin operators. With this notation the correlation function, Equation 2.51 becomes  G(r)  =  Fm(t)F,tn(t +  (2.55)  T).  The random motion may be caused by rotational, translational or vibrational motions or com binations of the three. An exponential correlation function agrees well with observed results  G(r)  =  Ce,  (2.56)  where C is a constant depending on the interaction type which is causing the relaxation, normally itself depending on the position and orientation of nuclei involved; r is referred to as the correlation time and is representative of the timescale on which the interaction Hamiltonian is changing. In theory, the correlation function need not be exponential, but it provides a simple model. The Fourier transform of the correlation function is called the spectral density function. It describes the frequencies at which energy may be exchanged between the nucleus in question and its surroundings. These are, in fact, the transitions allowed by the Hamiltonian H . Since the 1 correlation function is exponential, the spectral density function, labeled J(w), is Lorentzian,  J()  =  C  I  ee_Wt  =  C  i—co  2r 1+  (2.57)  2 (T)  The correlation function and subsequently the spectral density function materialize in Equation 2.53 when the substitution for the Hamiltonian H 1 (Equation 2.54) is made:  (t)  —  (O)  =  [m  [c,, (o)]] f f dt’  The main contributions to the variation of r  =  t’  —  Gmm’ (t’  —  tIf)eimt’_wm/t”)dtll.  are those in which m  =  (2.58)  m’. A change of variables  t” allows the realization of the correlation function in Equation 2.58: pt  J  0  pt’  dt’  j  Gmm(t’  —  t)ei(Lm(t’_t”)dthI  0  =  J  (t  —  r)Gmm(r)emTdT.  (2.59)  0  If the time t is assumed to be much longer than the correlation time r, then Gmm() will be  20  negligible for values of r much less than the integration limit. Consequently, t  —  r  t and the  upper limit of integration can be considered infinite. Thus, the integral in 2.59 becomes the spectral density function J(w), pt  J  p00  (t  —  (r)emrdr 0000 r)G  2  tJ  0  Gmm(r)eimrdr  0 =  (2.60)  tJmm(wm).  This leads to the master equation for the evolution of  , 3  recalling that t is short enough that the  density operator undergoes only a small change, (t) =  The evolution of any physical observable  (Q)  [Dm,  [t]j Jmm(°m).  (2.61)  can now be determined:  =  =  _Jmrn(Wm){({[tn],1a])_([[,tn],t])eq}. (2.62)  Note that to get to the second line of 2.62, the substitution ,ô  =  —  eq 3 I  has been made, accounting  for the initial thermal equilibrium value of the density operator. Using Equation 2.62 an expression for the longitudinal relaxation time T 1 can be derived upon insertion of the proper observable; the longitudinal magnetization described by I,. The relaxation time can then be related to the correlation time via the master equation. Relaxation times have a somewhat complicated dependence on r,, to be discussed in the next section. A plot ofT 1 versus r for a typical dipolar interaction, Figure 2.11, exhibits a T 1 minimum at a correlation time just over 1 ns. To the left of the minimum, the correlation times are considered in the fast regime. This is the regime in which small molecules in non-viscous liquids generally appear. Larger molecules or viscous liquids tend to exhibit correlation timescales in the slow regime, to the right of the T 1 minimum. The dependence of relaxation time on temperature is different in the fast and slow regimes. Nuclei characterized by fast correlation times display an increase in relaxation time as the temperature is increased, whereas in the slow regime, sample is cooled.  21  ‘1  increases as the  0.5  0.4 0.3 Cl)  I—  0.2  0.1 0 0  2  1  3 r  4  5  [ns]  Figure 2.11: Temperature effects and r, T . The Cold and Hot markers denote the direction in 1 which the T 1 value will move in each regime as the temperature is changed. 2.8.2  Dipolar Coupling  The first mechanism of relaxation that is relevant to this study is the dipolar coupling. The dipolar interaction Hamiltonian is  >  _  Fm(8, Y1m(I ),  (2.63)  where, I and S denote in general two different spins. The derivation will be limited to the case where I and S are both spin-i. The spatial functions Fm are orientationally dependent and there is a random distribution of 8 and  throughout the ensemble which will ultimately result in the  exponential correlation function. The spin operators 1 ’m are the spherical tensors:  0 F  =  /(3c052o_1)  =  +3 sin8 cos  =  2 2 Oe± sin  =  =  2 T  (2.64)  =  22  This is simply a different way of writing Equation 2.39, however it is worthwhile noting that in relaxation studies the non-secular terms (B-F in Equations 2.41) are important. Using the Hamiltonian 2.63 and using the observables I and S, the longitudinal magnetiza tions, with Equation 2.62 one obtains two coupled expressions of the form  1 R  ((I)  -Ris  ((I)  =  z)  Iz)eq)  -  (Iz)eq)  -  -  -  () Rs ((&)  Ris  -  -  (z)eq) (z)eq),  (2.65)  with  1 R  1  h 7 2 ‘y  =  r  15 R =  2 1 (fLo’\277h 10 4}  4  (  3 + 1 + (ir) 1+ 2  1  6 1 + ((wi + ws)r) 2  —  6 1 + ((wj +  ws)r) 2 1 1 + ((wi ws)r) 2  ((wi  (  +  —  2 ws)r)  (2.66)  —  The terms Ra are interpreted as rates; the longitudinal relaxation time (assuming that the I spin is the species under investigation) would be T 1  =  -j. The terms with Ri represent cross relaxation  between the I and S spins. By symmetry Rs(ws, wi) 2.8.3  =  Ri(wj, ws).  Chemical Shift Anisotropy  Relaxation due to anisotropic chemical shift is analogous to the dipolar interaction. In this situation a spin I interacts with a small field proportional to the Zeeman field H  =  . The Hamiltonian 0 H  is +2  Hes  Fmi’m,  (2.67)  with  0 F  =  1 F  z0  2 F  =  0 T  =  1 T  =  2 T  =  1  ’7IözrI 7  3HI-i1  —-HI  23  (2.68)  The chemical shift tensor components ö, are those of a traceless tensor and are related to the lab frame components discussed in Section 2.7.1:  =  —  (2.69)  , 50 cr  and (2.70) Using the same technique as in Section 2.8.2, one can determine the expressions for the relaxation due to chemical shift anisotropy. The longitudinal relaxation time is  =  (i +  1 T  2 + (wor)  (2.71)  For a detailed derivation of the correlation function, spectral density functions and their relation to the master equations the reader is referred to [1] and [27].  3  Experimental Techniques  The following sections outline some of the experimental techniques used in the NMR experiments, and an explanation of energy dispersive x-ray spectroscopy.  3.1  Heteronuclear Decoupling  Decoupling is used to reduce broadening of spectral lines caused by heteronuclear broadening of dilute spins by nearby abundant spins, such as the situation of ‘ C and ‘H in organic materials. To 3 employ heteronuclear decoupling, high power rf irradiation is simply applied to the abundant spin channel during acquisition on the observe channel. A simple description of decoupling is that the high power irradiation causes the abundant spins to undergo transitions at a rate determined by the rf amplitude. For protons, the time averaged dipolar coupling contribution will be zero since the spin quantum number, mH oscillates between ±.  3.2  Magic-Angle Spinning  Magic-angle spinning (MAS) is used frequently in solid-state and protein NMR. The primary effect is the removal of the chemical shift anisotropy but it also aids in removal of homo- and 24  heteronuclear dipolar coupling. The result is an improvement in resolution, narrowing lines that have been broadened by these interactions. Figure 3.1 displays the basic setup; the sample is contained within a rotor at an angle  M 0  with respect to the lab z-axis. The rotor spins at a speed  Z LAB  ZR  0 B  yLAB  LAB  Figure 3.1: Magic Angle Spinning.  WR.  If the angle between the z-axis in the PAF and the lab frame z-axis is 0, then the first order  molecular orientation dependence for the discussed interactions will have the form 3 cos 0  —  1. In  a powder sample, all orientations 0 are represented resulting in a broad lineshape. If the sample is spun, 0 will become time dependent. Furthermore, if the spinning rate is fast compared to the anisotropy of the interaction, only the average of the orientation dependence, (3 cos 20  —  1) will  contribute to the spectrum. The average value can be shown to be  (3cos 0 2 —1)  =  (3cos20M_1) 2 (3cos / 3—1),  (3.1)  where 3 is the angle between the z-axis in the PAF and the rotor axis. If the rotor angle, OM is set to 54.74° then the term (3 cos 2 OM  —  1)  =  0. Thus, the average (3 cos 20  —  1) is zero also. This  means that the anisotropy will be averaged away to zero, leaving just the narrow isotropic peak. If the spinning speed is not greater than the magnitude of the anisotropy of the interaction being spun out, then spinning sidebands will appear. The spinning sidebands are sharp lines that radiate out from the central isotropic line at intervals equal to the spinning rate. These lines will be seen in later spectra in Section 5.3. Spinning sidebands can be problematic if they obscure 25  desired signals, or if multiple sidebands from different peaks overlap.  3.3  Phase Cycling  Phase cycling is a technique used in almost all pulsed NMR experiments to eliminate undesirable signals due to effects such as field inhomogeneity or background signals.  It can also alleviate  problems caused by imperfect pulse lengths, especially in experiments requiring long pulse trains. In Chapter 7, such an experiment is considered, where uncompensated pulse imperfections have a dramatic effect on the performance of the sequence. Phase cycling is the strategy used to mitigate these problems. Figure 3.3 shows a situation where the pulse length is just slightly too long. A  7r  (or 180x)  pulse is one that rotates the magnetization by 1800 about the x-axis. Here the pulse is imperfect, causing the magnetization to precess an extra amount dx, past the —z axis. If the next pulse were 180x  l8Oy  180x  l8Oy  Figure 3.2: Phase cycling. another  7r  pulse, then it would compound the discrepancy and the magnetization would move  further and further away from the desired orientation on the +z-axis. To correct this, the phase of the pulses is alternated, first nutating magnetization about the x-axis and then the y-axis. As can be seen, the result is the correction of the discrepancy after a series of four pulses. Background signals, or magnetization induced in materials outside the coil (not part of the sample) can be selectively removed from the spectrum through careful consideration of phase cycling.  3.4  Cross-Polarization  A cross-polarization (CP) experiment, Figure 3.3, employs simultaneous rf excitation on two chan nels to enable magnetization transfer, normally from an abundant species to dilute spins. For 26  example, excitation on the proton ( H) and carbon (‘ 1 C) channels, induces the transverse mag 3 netization of carbons for acquisition of an FID through spin-spin coupling. Here, the successful employment of CP is dependent on the close proximity of protons and  130  nuclei, and therefore  may provide some information about structure. 7T  H____________________  c 13 cP  Figure 3.3: Bloch Decay NMR experiment employing cross-polarization pulse to induce transverse magnetization in the 130 nuclei. In the OP experiment an initial  pulse creates ‘H magnetization along the —y-axis of the ‘H  rotating frame. The subsequent OP pulse, known as the spin-locking pulse, is applied on resonance along the —y-axis. This results in a static field BH along the rotating frame —y-axis, creating a situation which is analogous to the static Zeeman field, but facilitated by the applied rf-field. In essence, the OP pulse creates a new axis of quantization for the protons, with an energy gap /EH  =  h7HBH. A CP pulse is applied simultaneously at the resonance of the ‘ C nuclei on the ‘ 3 C 3  channel. This has a similar effect on the ‘ C spin system, creating a static field in the rotating frame 3 and a new axis of quantization for the ‘ C spins; accordingly, /.E 3 0  =  B 7 h . 0 0 When the amplitudes  of these pulses are matched in a way to make the nutation frequencies equal (i.e. 7HBH a condition arises which allows the transfer of magnetization from the protons to the  =  130  nuclei.  This can be considered a matching of the energy level seperations of the rotating frame spin states of each nuclear species and is called Hartmann-Hahn matching. The magnetization transfer occurs through mutual spin flips via the heteronuclear dipolar interaction, Equation 2.43, between the protons and the nearby carbon nuclei. Since the secular Hamiltonian only contains operators and  I,.  it is unaffected by the transformation to the doubly rotated frame. Though it appears that  the Hamiltonian (2.43) only contains the “A”-type term (see Section 2.7.2) that would not result in magnetization transfer, the application of the pulses imparts additional interactions.  27  C surrounded by protons is 3 The rotating frame Hamiltonian Hrot, for a ‘  f-rot where I and S denote the  jth  =  HHH + HHC +  lix + “jCx,  WH  (3.2)  proton and a ‘ C nucleus, respectively. The final two terms represent 3  the rf pulses in the rotating frame, with wH  =  7HBH and wc  =  7GBC. The Zeeman Hamiltonian  is nulled in the rotating frame transformation, thus only the homonuclear HHH and heteronuclear HHC dipolar terms appear in their rotating frame forms, Equations 2.42 and 2.43. It is assumed  due to low abundance of 13 C that the homonuclear interaction for carbons is negligible. At this point, it is prudent to do a further frame transformation into what is known as the interaction representation or the toggling frame.  The toggling frame is an analogous extension  of the rotating frame in which the applied pulse in the rotating frame is nulled by a similar rotational transformation. Much like adopting a frame rotating about the Zeeman axis at the Larmor frequency, the toggling frame is rotating about the applied field in the rotating frame, see Figure 3.4. In the present case, a doubly rotating frame (for both protons and carbon nuclei) is 0 B  /  ,  I /  j?  •1  Figure 3.4: The toggling frame or interaction representation. required, implemented by applying the rotation  R  (3.3)  =  28  to the rotating frame Hamiltonian, resulting in the toggling frame representation:  tog 1 f =  As in Section 2.6.1, the extra  Ij,  f—’fif  WH  —  (34)  L’JCS.  and S terms cancel perfectly with the pulse terms from Equation  3.2. The toggling frame Hamiltonian is thus rewritten:  og t f  _jtOgtOg  (35)  with 11  =  G(J  —  (i. .13  —  (3.6)  3II)  i>j  1[  C(1 [(Zi  = —  +  (z  Iiz& +  +  1iy’y) cos(wH  z, I) sin(H  —  —  wc’)t (3.7)  WC)t],  and  ,HH  —  —  0(10  Here,  =  lI’O7HfQ  3 24irr  ,cos 2  O7H7C 1  O—1). 2 (3cos  and Ojj denote the internuclear distance between protons i and  (3.8)  j  and the polar angle  between the applied field and the vector r , respectively. Similarly, r and O are the internuclear 3 distance between the  th  proton and the carbon nucleus, and the polar angle between that vector  and the applied field. Only the heteronuclear dipolar interaction is significant for cross-polarization, although the homonuclear coupling between protons does have an impact on the redistribution of magnetization. The Hartmann-Hahn condition (wH  wO)  leaves terms of the form  The latter term can be represented as I+S_ + I_S+ which  and  removes the time dependence from Equation 3.7 and  is, in fact, a “B”-type term promoting mutual spin flips between the I and S spins (see Equation 2.41 and Figure 2.8). Because the energy level separation is the same for both species under the matching condition, there is no loss of energy and there is no net change in magnetization when  29  there is a transfer of magnetization from the protons to the 13 C nuclei. Thus the heteronuclear system is allowed to come to an equilibrium; the plentiful high energy state protons redistributing magnetization to the nearby carbon nuclei. The result is a net magnetization of ‘ C in the xy-plane 3 which can then be observed on the carbon channel. This technique is simple to implement, and can reveal qualitative structural information regarding molecular mobility. It also provides a dramatic sensitivity enhancement over direct polarization ‘ C spectra, for two separate reasons. The first is 3 that the experiment may be repeated more frequently than the direct polarized version, because the ll T, is usually much shorter than the 13 C T . The second reason is that the population 1 difference induced by the magetic field is much greater for  nuclei than ‘ C, because the ‘H 3  gamma is a factor of ‘-.4 greater. This enhanced population difference is then, in part, transferred to the ‘ C by CP. 3  3.5  Energy Dispersive X-ray Spectroscopy  Energy dispersive x-ray spectroscopy (EDX) is a useful tool for characterizing chemical composition. The mechanics of EDX rely on the fact that different elements have different electronic structures, thereby eliciting a varied response under stimulation by an impinging beam of electrons or photons. The incoming beam particles excite and subsequently eject an electron from the inner shell of an atom in the beam path, leaving a hole. This hole is then occupied by a higher energy outer shell electron. When this electron makes its transition, energy is released in the form of a photon (in this case, an x-ray) which can be detected above the sample. The energy of the photon is of course equal to the energy gap that the electron transitioned through and is unique to a specific element. Thus the elements identity is provided by the frequency of the resulting x-ray. An example spectrum is shown in Figure 3.5. The x-axis is the emitted photon energy and software analysis provides the elemental identifi cation of the gaussian peaks. The y-axis represents counts of emitted photons at each energy and therefore the magnitude of the peak provides some information about the content of the element in the sample material.  4  Introduction to Proteins  Proteins are ubiquitous in nature. They fill a variety of roles from transporting material and controlling functions in cells to providing structural architecture with materials such as hair, nails 30  kCts C  8-  6-  4-  2-  0  Li  uruIrrI,,,II—I-----r-——  0  2  4  6  I  8  I  keV  Figure 3.5: Trial data from EDX experiment showing elemental content of GTC bundle. and tendons. Their diverse biological function is facilitated through various combinations of 20 different building blocks, the amino acids. It is the sequence of amino acids into polymeric chains that controls the properties and three-dimensional structures that the protein displays. The amino acids share a common repeating backbone, see Figure 4.1, which provides the linear basis for the protein. The backbone carbons are known as the carbonyl- and a-carbons. The  Figure 4.1: Protein amino acids are all similar, differing in the attached side chain R. carbonyl carbon is, of course, attached to the oxygen atom via a double bond. The a-carbons root the amino acid side chain to the backbone. If they exist, the subsequent carbons are normally labeled /3, y and so on. However, not all amino acids are made up of linear carbon chains and some have alternative naming conventions. The bond between the carbonyl carbon and the nitrogen atom is called the peptide bond and links adjacent amino acid residues together. This bond is unique in that it has partial double bond  31  characteristics forming a resonance with the carbonyl valency, C°. Because of this, the peptide unit, pictured in Figure 4.2, is normally partially planar. The group of atoms forming the peptide unit is restricted by this bond and usually acts as a rigid structure. Rotation about the peptide bond is defined by an angle  .  The trans form is energetically favourable in most cases as there  H  /  H  C—  C)  /NC\  /NC\  (a)  (b)  Figure 4.2: The peptide unit; a) the trans form with c  =  1800; b) the cis form with w  =  00.  is less repulsion between non-bonded atoms. However, the amino acid residue proline, having a cyclic side chain bonded to the nitrogen atom as well as the alpha carbon, allows a stability that makes the cis form of comparable occurrence. The angles the N  —  C and C  —  and  define torsional rotation about  C° bonds, respectively.  Since NMR is sensitive to different molecular configurations it is ideal for studying proteins as the nuclei from different amino acids will exhibit different chemical shifts. Other interactions can also provide additional information, for example, the dipolar interaction can in some cases help to elucidate the three dimensional structure.  4.1  Protein Secondary Structure  The primary structure of proteins refers to the covalent structure defined by the amino acid se quence.  There exists however, some freedom in the manner in which the covalent bonds are  configured. At room temperature, bond lengths can vary by ±0.05A and bond angles by The angles  and  +50  [6].  have some rotational freedom and assume different orientations dependent on  the residue type. In large macromolecules such as proteins, these allowances can all contribute to a greatly flexible overall shape. Certain amino acids or combinations of amino acids can provide flex ibility in the chain, or restrict motion. There are however, energetically preferential conformations that exist due to non-covalent interactions of molecules, either adjacent or distant, which govern what is known as the secondary structure of the protein. The various configurations of amino acids are invariably tied to the resulting protein secondary structure, often referred to as folding.  32  4.1.1  Random Coil  Random coil secondary structure refers to a dynamically changing configuration. There is rapid reorientation of the protein as the structure relies primarily on the intrinsic conformational prop erties of the amino acid residues. There is little or no association between distant parts of the polypeptide chain. The torsional angles  and  freely rotate through —180° to + 180°, although  the peptide bond w is restricted to approximately —20° to +100.  4.1.2  Alpha Helix  The alpha helix is the most well known and easily identified of the secondary structures. The backbone forms a helix with 3.6 residues per turn and a translation of 1.5 torsion angles  and  ‘J’  A  per residue. The  are approximately —60° and —50°, respectively. The backbone atoms pack  closely to form van der Waals interactions to favourably reduce the energy of the configuration. In addition, the carbonyl oxygen of each residue forms a hydrogen bond with the backbone-NH of the fourth residue along the chain, see Figure 4.3(a).  (b) (a) Figure 4.3: (a) The alpha helix structure, hydrogen bonds (dashed lines) between carbonyl oxygen and amides; (b) the single beta strand and beta sheet, showing hydrogen bonding between adjacent beta strands via the peptide unit. Image taken from [6]. The side chains project outward from the backbone and tilt slightly toward the amino end.  33  4.1.3  Beta Strand  The next most regular conformation is the beta strand, in which the protein is almost fully extended. This could be considered a type of helix with 2 residues per turn and a translation of  3.4A per  residue. The beta strand is not energetically stable on its own, but must be incorporated into a beta sheet, which can be parallel or anti-parallel, see Figure 4.3(b). In the sheet, hydrogen bonds are formed between the peptide groups of adjacent beta strands. Beta sheets differ greatly from alpha helices; alpha helices can be considered basically one dimensional chains and the interactions occur between residues on the same peptide. In beta sheets, interactions occur between residues on different peptides.  5  Hagfish Slime Threads  Pacific Hagfish (Eptatretus stouti) are jawless, deep sea marine dwellers that have an interesting defense mechanism. When agitated the hagfish releases a combination of protein threads and vesicles composed of glyco-proteins, called mucins. These components interact with the surrounding seawater to produce a viscous slime that clogs the gills of predators, see Figure 5.1. The slime  Figure 5.1: Pacific Hagfish slime; an effective defense mechanism. Photo courtesy of D. Fudge, P. Guerette. threads are of particular interest owing to their incredible mechanical properties. Mechanical studies [13] have shown the threads to have low initial stiffness (E  =  6.4 MPa) and high elasticity  (up to strains of 0.34), as well as high tensile strength (180 MPa) and toughness (130 3 MJ/m ) . The mechanical properties of the IFs are compared to some other biomaterials and high performance fibres in Table 5.1. The slime threads are also an excellent candidate for the study of intermediate filaments [7, 24, 25]; they offer an exposed view of the mechanics of IFs in living cells. The composition of the 34  Fibre Type Hagfish Thread  Modulus (MPa) 6.4  Tensile Strength (MPa) 180  Spider Silk Silkworm Silk  10000 5000 130000  1800 600 3600  200000  3000  Keviar 49 Steel  Failure Strain 220  (%)  Toughness (MJ/m ) 2 130  30 12  3 2  130 50 50  123  Table 5.1: Mechanical properties of some biomaterials and high performance synthetic materials, adapted from [8, 13].  (%)  Amino Acid Gly Ser Thr Ala Leu  a 15.9 10.3 9.0 7.5  Composition 7 14.6 11.9 7.5 7.8  total 15.2 11.1 8.2  Val Glu Gln Ile Arg Tyr Asp  5.9 7.6 4.0 4.8 5.6 4.7 4.0 3.7  8.3 6.6 6.5 5.3 4.3 4.3 3.7 4.0  7.6 7.1 7.1 5.3 5.1 5.0 4.5 3.9 3.9  Lys Met Asn  3.6 2.2 3.3  3.2 4.5 3.3  3.4 3.3 3.3  Pro  3.3  1.5  2.4  Phe  2.3  1.8  2.1  His  2.0 0.3  0.8 0.0  1.4 0.2  0.0  0.2  0.1  Trp Cys  Table 5.2: Amino acid composition of hagfish IF polypeptides. threads is believed to be tightly packed and oriented intermediate filaments (IFs), which are in turn made up of pairs of unlike polypeptides; a and  .  The amino acid sequences of a and -y have  been deduced [24], and the amino acid content of the dual helix is listed in Table 5.2. A model of the IFs has been proposed to explain the mechanical characteristics [14].  The  model is keratin-like with a stiff central rod domain contained between flexible terminal ends and punctuated with non-helical linker regions which may provide additional flexibility. A simplified model is shown in Figure 5.2.  X-ray diffraction data [13] has shown evidence of an a-helical  conformation, and the central rod domain is believed to be a coiled-coil structure. The terminal ends, like the linker regions, are thought to be randomly structured. The X-ray diffraction results, displayed in Figure 5.3, also show that the protein undergoes an irreversible transition from a-helix to /3-sheet under strain. The proposed effect of strain on this model is visualized in Figure 5.4. The change in structure is reflected in the stress-strain characteristics of the IFs. When the filaments 35  Terminal Ends  Central Rod Figure 5.2: A schematic model of the polypeptide composing the hagfish slime gland thread cell (GTC). Image taken from [13].  =  to  (a)  Figure 5.3: X-ray diffraction results for a) unstrained b) high strain hagfish IFs. Images taken from [13].  0_v  c 5a  ‘Jr 0 6t  —$J’  a  130  MPa  r 1.6  Figure 5.4: The proposed nature of the transition from -he1ix to /3-strand under strain. Image taken from [13]. are stressed past the point of elastic deformation, the transition to a /3-sheet conformation imparts additional stiffness. This transition behaviour explains why the failure strain is so much higher  36  C.  4’ Q,O  i  0.2  O3  O4  0.5  0.6  Strain LIL  Strain (SU)  (b)  (a)  Figure 5.5: Stress strain curves for hagfish IFs a) c-he1ical, elastic region b) deformation into plastic, /3-sheet region. Images taken from [13]. than the yield strain of the IFs.  5.1  Sample Preparation  Hagfish were captured with assistance of the Bamfield Marine Station in the Pacific Ocean near Barkley Sound. The fish were stored in a 200 L aquarium of chilled seawater. To collect slime, hagfish were anesthetized in a bucket with a buffered anesthetic (250 mg/L tetramethyl silane, MS-222; 500 mg/L sodium bicarbonate) in seawater until unresponsive. The fish were placed on a dissection tray and the skin was rinsed with de-ionized (milli-Q) water and blotted dry. Slime ejection was induced by mild electrical stiumlation (8 V, 80 Hz) near the glands. The slime was collected with a plastic spatula and transferred to a buffer solution (0.9 M sodium citrate) via a 50 m filter to separate thread cells from mucins. A protease inhibitor cocktail (Sigma Aldrich P2714) was added to prevent protein degradation. The sample preparation techniques were slightly modified from [13] and samples were prepared by P. Guerette.  5.2  Structure and Mechanical Properties  General structural information can be obtained from quite simple NMR experiments. As alluded to in Section 3.4, magnetization transfer in a CP experiment will only occur between nuclei which are close in space. Furthermore, the CP pulse will only be effective if there is not significant relative motion between a proton and a carbon nucleus. Molecular motion disrupting the dipolar interaction will prevent efficient magnetization transfer between protons and carbon nuclei. Because of this, a 37  comparison of the results from direct polarization (DP) and CF experiments can suggest whether or not there may be mobility in the sample under investigation. DP and CF experiments were performed on a Varian 400MHz (9.3T) spectrometer with an HXY MAS probe. Measurements from the hagfish IFs indicate a significant amount of motion in the backbone of the protein. A direct polarization experiment, in which the  pulse is applied  directly to the 13 C nuclei, shows mobility in the carbonyl peak. Figure 5.6 displays the results from a DP experiment performed at 20°C. The spectrum can be divided into four main regions;  0 250  200  150  100  50  0  -50  [ppm] Figure 5.6: Direct Polarization results for hagfish IFs at 20°C. Arrows indicate citrate peaks. the carbonyl region (C=O) is the furthest downfield from appear in a range between  ‘-  150— 250 ppm; the a-carbons normally  40— 80 ppm; the 3-carbons are generally found from  10— 40 ppm;  the last region is the aromatic region which appears between the carbonyl and a-carbon range. Unfortunately the aromatic carbons in the hagfish IFs were not readily apparent in DP spectra, masked by a large background signal. Other carbons (y, 5 etc.) can occur in the a or  ranges  and there are some exceptions, such as the Thr 3-carbon which appears around 80 ppm. The sharp peaks in the spectrum, indicated by the arrows, are signals from citrate carbons, rapidly tumbling in the buffer solution. The background signal comes from material outside of the coil, such as the end caps sealing the sample holder. The absence of a powder pattern in the carbonyl region suggest that there is significant motion. However, there is also evidence of a broad feature beneath the sharp carbonyl peak, suggesting the presence of some rigid structures in the backbone. This is confirmed in Figure 5.7, a CF spectrum under the same conditions. The 38  I  I  I  I  I  I  200  150  100  I  0 250  50  0  -50  [ppm] Figure 5.7: Cross polarized experimental results for hagflsh IFs at 20°C. background signal, coming from outside the coil and the citrate peaks from solution vanish in the CP spectrum. The broad portion of the carbonyl region cross polarizes well, thus remaining visible in both spectra. The highly mobile sharp peak has disappeared in the CP spectrum, rapid motion removing the possibility of magnetization transfer for these 3 ‘ nuclei. These results suggest that C there are different regions in the polypeptide; in some, there is high flexibility in the backbone, while others retain rigidity. These regions may contribute to the elastic and strength characteristics of the IFs. Mobility in the peptide chain is also temperature dependent. Through analysis of the direct polarization spectra, the timescale of motion in different regions of the chain can be inferred from the size and shape of the various peaks. Direct polarization spectra were obtained at various temperatures (Figure 5.8).  The carbonyl region shows a decrease in the sharp component as  temperature drops. This could be attributed to restricted mobility, as the lack of rapid motion would result in dramatic broadening of the carbonyl line due to its large chemical shift anisotropy. The broad component becomes slightly more intense but as it is spread over such a large range, the increase is difficult to see. A qualitative inspection of the carbonyl region in the CP and DP results indicates that most of the carbonyl carbons are in relatively rigid backbone conformations. A small fraction, perhaps 10% based on the relative sizes of the sharp and broad peaks, can be attributed to mobile carbonyl carbons at room temperature. In the  -  and side chain carbon regions, the situation is more complicated. 39  The chemical  0 250  200  150  100  50  0  -50  [ppm] Figure 5.8: 20°C, 5°C,  Direct Polarization results for hagfish IFs at varying temperature. 15°C.  Temp  =  —  shift anisotropy is not as large for these nuclei and therefore broadening due to this interaction will not be as prominent as with the C=O carbons. Furthermore, whereas the carbonyl carbon isotropic values are quite close together for the various residues in the chain, most in a range of 10 ppm, the  -  and side chain carbons span a larger range, closer to 40 ppm. The large number  of these carbons, all with slightly different chemical environments, combine and overlap to give a large broad conglomeration of peaks. In general, the a-carbons appear to behave similar to the carbonyl carbons, the peak height dropping with the temperature. This may also be a result of sharper peaks broadening, but because of the large range of overlapping peaks and relatively small chemical shift anisotropy, it just appears that the size of the peak is decreasing. The side chain carbons, mainly /3-carbons, appear to exhibit the reverse effect; the peak becoming larger as temperature decreases. Since it is unlikely to have the motion increase and result in sharper peaks as the temperature drops, another explanation is required. If the side chain carbons are in a fast motion regime, see Figure 2.11, then the T 1 times will become longer as r gets shorter. It is possible that at higher temperature, the side chain carbons are not being allowed to fully relax due to a very long T . This is a result of a delay between subsequent experiment scans that is not 1 adequately long, and gives rise to a situation in which the perturbing  pulse does not project all  of the magnetization into the transverse plane. The effect is suppression of the signal from these carbons at higher temperatures. As the temperature decreases, so does T 1 allowing full relaxation  40  to equilibrium magnetization. Incidentally, this effect may also be the cause of the o-carbon peak behaviour, although in the opposite sense. The a-carbon T s will increase with the decrease in 1 temperature, becoming too long to allow full relaxation at lower temperatures. The loss of mobility can be characterized well in the carbonyl region, since the broad and sharp portion of the signal can be easily separated. The integral of the sharp peak was plotted against the experimental temperature to give an impression of the temperature dependence. The results, shown in Figure 5.9, indicate that the mobility of the carbonyl carbons is largely temperature dependent and is reduced as the temperature decreases. 1.2 -  ci)  1•  I  N  cci  0.8  0  z -  0.6 I  0.4 cci ci)  °-  0.2 I I  -25  -20  -15  -10  I  -5 0 Temp [C]  5  10  15  20  Figure 5.9: Temperature dependence of mobile C=O peak in DP spectra of hagfish IFs. The DP and CP results give some indication that the protein backbone in hagfish IFs is divided into regions of higher mobility and regions of greater stiffness. This notion of varying degrees of flexibility supports hypotheses of previous work [13, 14] regarding the structure of the hagfish IF.  5.3  Nuclear Relaxation in Hagflsh IF Proteins  In an effort to further characterize the structural composition of the IFs, relaxation experiments were implemented. The pulse sequence used was developed by Torchia [35], and incorporates ‘ C 3 signal enhancement via cross-polarization. A schematic of the pulse sequence is shown in Figure 5.10. The first portion of the sequence is the same as the simple cross-polarization experiment employed in Section 5.2, resulting in the ‘ C magnetization on the —y-axis. The first 13 3 C  pulse  rotates the magnetization into the —z-axis, where it is allowed to relax back along the longitudinal axis due to the influence of the static field B 0 for a time, r. Next, the final  41  pulse returns the  _______  H 1  7r  CP  .  J H  Tr  HTRH  Figure 5.10: T 1 inversion recovery experiment employing cross-polarization pulse to study longitu C nuclei. Note the pulses are generally not the same duration on both 3 dinal relaxation of the ‘ channels. remaining longitudinal magnetization into the xy-plane where it provides the signal for acquisition. The pulse sequence is run many times with various delays,  T.  The resulting spectra can be analysed  and the intensity of the peaks is related to the delay time, decaying exponentially with a dependence on T : 1 1(r)  =  I e 0 ’,  (5.1)  o represents the intensity of the initial measure (i.e. that with the shortest delay, r). 1 Experiments were performed on a Varian 400MHz (9.3T) spectrometer in a MAS probe spinning at 6600Hz. Results on a hydrated sample of hagfish IFs are displayed for various temperatures in Table 5.3. It should be noted that since these results were obtained using a CP T 1 experiment, only signal from rigid carbons was received. Carbons in rapid motion environments will not contribute. The side chain carbons may experience fast, confined motions that still allow CP, but it is assumed that the other results refer only to the rigid components of the IFs. It should be noted that the broad carbonyl peak, from carbons in rigid structures, has become a sharp peak with spinning sidebands as a result of MAS (see Section 3.2). The regions analysed were the carbonyl peak, two aromatic peaks believed to be tyrosine ç- and 6-carbons, the a-carbons and other side chain carbons (/3 etc.). These regions are identified on the 20°C spectrum with the shortest delay, r (thereby providing the highest signal intensity), in Figure 5.11. Due to the poor signal to noise ratio (SNR) of the aromatic carbons, the T 1 values are only to be considered as order of magnitude estimates. The carbonyl spinning sidebands (C=0 ) were 85 included in the calculation of the carbonyl 1 T s . The carbonyl carbons for the most part fit a single exponential (Equation 5.1) well, see Figure 5.12a. However, this is not the case for the a-carbons  42  T (°C) 20  1 (s) T % 100  Carbonyl 9.3 ± 0.6  %  %  100  4.5 + 3.9  100  1.8 ± 0.4  5  100  11.4 ± 0.5  100  5.3 ± 2.9  100  3.6 ± 0.8  -5  100  11.1 ± 0.5  100  5.1 ± 1.8  100  4.5 ± 0.8  -20  91  14.2 ± 0.6 0.5±0.2  100  5.0 ± 2.5  71 29  8.6 ± 2.1 0.4+0.2  9  %  Alpha  %  74 26 77 23 73 27 77 23  5.8 ± 0.9 0.5 ± 0.2 7.2 ± 0.7 0.5 ± 0.2 8.2 ± 0.9 0.9 ± 0.2 8.7 ± 0.5 0.5±0.1  69 31 70 30 64 36  Other 0.4 ± 0.1 2.9 ± 0.9 0.4 ± 0.1 3.6 ± 0.8 0.4 + 0.1 3.0 + 0.5  66  0.4±0.1  34  3.8±0.7  Table 5.3: 1 T relaxation times for hagfish IFs. A single number indicates a one component expo nential fit; two numbers represent a two component fit.  0  250  200  150  100 [ppm]  50  -50  0  Figure 5.11: Spectrum from T 1 inversion recovery experiment with r  =  ims, Temp  =  20°C.  and other side chain carbons. For the spins in these positions, the spin-lattice relaxation appears to be caused by mechanisms which operate at different rates. A model with a single exponential is not sufficient and results in a fit with non-random residuals, a more general model is needed:  1(T)  =  IoAe + IoBe.  (5.2)  Equation 5.2 accounts for a situation in which not all spins are relaxing at the same rate. If there were simply two different components, the contribution to the total intensity of the signal from the A component, I, would represent the fraction of the total population of spins relaxing at a rate The remainder of the spins would be represented by signal I and relaxing at  .  Unfortunately,  it is not possible to discern how many different rates may be present. A two-component model  43  I  I  I  I  Data One Component Fit  +  COEt  0  0 0  2  4  6  8 Delay [s]  10  12  14  16  0  2  4  6  I  I  10  12  14  16  (b)  (a) I  8 Delay [s]  I  I  I  Data One Component Fit Two Component Fit  I  I  ;2  1’4  I  Data  0 0  I  +  00  16  Delay [s]  2  4  6  8 Delay [s]  10  1’2  +  1’4  16  (d)  (c)  Figure 5.12: T 1 experimental data for (a) carbonyl, (b) a-carbons, (c) other side chain carbons at Temp = 20°C; (d) carbonyl data requires a two component fit at Temp = —20°C. may fit the results of a wide distribution of relaxation rates [34]. However, due to the nature of exponential functions, the two component fit can provide a reasonable estimate of the breadth of the distribution of relaxation rates. Furthermore, the prefactors in Equation 5.2 will represent the relative amounts of spins relaxing at the respective rates. If the prefactor for the shorter T 1 is larger, it means that more of the spins are relaxing at faster rates, but no further information should be inferred regarding the nature of the distribution. The percentage of the signal relaxing at each rate is displayed before the relaxation time in Table 5.3. At low temperatures (—20°C), a single component model begins to fail for the carbonyl signal (Figure 5.12d). This may be a symptom of colder temperatures further freezing out of motion in the backbone. It is possible that at this low temperature, the cold temperatures have restricted the mobile portions of the backbone to a point where they appear in the CP spectrum. The data suggests that the rigid parts of the backbone are not homogeneous.  There is a  division of the rates of signal relaxation indicating that there are at least two different regions.  44  For simplicity, the components can be considered limit guidelines for the possible distribution of relaxation times; the shorter relaxation times will be referred to as the fast limit component and the longer times the slow limit component. The tyrosine aromatic carbon T s exhibited the largest uncertainties as the information available 1 in the signal was lost in noise. This is due to the minimal occurrence of tyrosine in the hagfish IFs (3.85%) and compounded by the low natural abundance of 13 C nuclei. In many cases, there was no apparent indication that a two component model would fit the data any better than the single component model (see Figure 5.13). The relative uncertainties in relaxation times ranged from roughly 30-90%. I  I  I  I  I  Data One Component Fit Two Component Fit  I  I  I  I  I  I  Data One Component Fit Two Component Fit  + —  +  o o  16  1’2  Delay [s]  1’4  +  16  Delay [s]  (b)  (a)  Figure 5.13: The Tyr -peak T 1 results for Temp  =  20°C experiment.  The carbonyl carbon relaxation times are not dramatically affected by the temperature. This result is concordant with the notion that the peak is associated with only carbonyl carbons in the rigid components. The remaining results show that the rigid component signals are characterized by at least two, and possibly more, different relaxation rates for both backbone o-carbons and the side chain carbons. The distribution of relaxation rates suggests a distribution of different regimes in the rigid environments in the hagfish IF. These different regimes must possess varying degrees of flexibility to allow the variation in relaxation rates. For the backbone carbons, the temperature dependence of T 1 indicates that the sample is in the slow regime to the right of the T 1 minimum, (see Section 2.8). In this regime, a shorter T 1 value implies that the spins are rotating or vibrating faster, thus are incorporated in a part of the structure with greater flexibility. One interesting feature is that the a-carbon signal portrays a situation in which most of the spins are relaxing at a slower rate, whereas the side chain carbons have the minority of the population with a longer  45  . This is intuitive since the 3- and other ‘side chain carbons generally do have a greater degree 1 T  of flexibility than those involved in the peptide bonding on the protein backbone. These T 1 results can be accounted for in the model proposed by Fudge et al [13, 14]. 1 relaxation measurements proved difficult for the hagflsh IFs due to long relaxation times T  and low sensitivity without cross-polarization. In an attempt to characterize the structure in mo bile regions, the direct polarization results from the previous section (5.2) were further analysed. These results indirectly allowed estimates of correlation times for the mobile components, using techniques discussed in Section 2.8. Furthermore, because the single DP spectra was relatively quick to perform, data at a greater number of temperatures could be extracted. The T 1 experi ments performed required a long time to complete (l5Ohrs) and due to time constraints were only performed at the temperatures in Table 5.3. The linewidth of a signal may be used to characterize the degree of motion of the nuclei associated with it. This is due to the fact that some of the spread in spin precession frequency stems from the random reorientation of spins in their immediate chemical environment. This reorientation causes relaxation as discussed in Section 2.8. A simulation of the line broadening caused by the modulation of the chemical shift anisotropy provides an expected lineshape based on a correlation time,  Tc.  The contribution to the lineshape from a specific chemical shift frequency  depends on the anisotropy z and the asymmetry,  =  the angles 0 and  ij:  8—1+sin (3cos 9 2 cos2),  (5.3)  describe the orientation of the principle axis system of the nucleus with respect  to the static field. These angles are assumed to change randomly and instantaneously at intervals of an exponentially distributed random duration TD, on the order of r,  TD  —-rlogz,  (5.4)  where z is a random number with 0 < z < 1. The spin is assumed to contribute to the signal at for TD at which point there is a jump to the next random orientation (0, b). The phase accumulated over these time periods is numerically integrated using a “brute force” calculation. From the phase the FID signal is simulated for multiple initial orientations, and Fourier transformed to provide an estimate of the lineshape for the carbonyl carbons.  46  The simulated signal is processed slightly to account for field inhomogeneity. Broadening will occur due to the fact that identical spins may experience a slightly different field based on their position within the superconducting magnet, as it is not an infinite cylinder.  The amount of  broadening was estimated using the citrate peaks in the DP spectra. These peaks represent signal from an inviscid solution, which would be very sharp in a completely homogeneous field due to fast motional average in the liquid. The exponential broadening factor, BR, applied to the simulation was chosen to match the observed citrate linewidth. The broadening is implemented by a decaying exponential envelope on the signal S at point n in the FID:  Sn  =  Sne  (5.5)  The source code for the simulation can be found in Appendix A. The simulations were qualitatively compared to the direct polarization results from the experi ments in Section 5.2, see Figure 5.14. The simulated lineshape was overlayed on the sharp carbonyl  0 250  200  150  100 [ppm]  50  0  -50  Figure 5.14: A simulated lineshape overlayed on a DP spectrum collected at Temp correlation time of r = 0.06is acheives a reasonable fit.  =  20°C. A  peak of the DP spectra, and the simulation correlation time was adjusted until the simulated peak seemed to match the observed carbonyl peak. The broad part of the spectrum was ignored and the simulated peak was taken to stand atop the underlying broad signal due to rigid structure. The results of the simulations are presented in Table 5.4, and displayed graphically in Figure 5.15. It should be noted that this is not a direct measure or calculation of the correlation time, the simulation merely provides an order of magnitude estimation of r. The simulation results were fit  47  Temp (°C) 20 15 10 5 -5 -10 -15 -25 Table 5.4: Simulated  T  r (us) 0.06 0.08 0.10 0.15 0.20 0.30 0.80 1.00  results for the mobile carbonyl carbons.  to the well known Arrhenius equation:  ln(r)  Ea ,  =  (5.6)  where R is the gas constant (8.3145 J/mol K), T is the temperature in Kelvin and Ea denotes the activation energy in J/mol. The activation energy in this case refers to a characteristic energy barrier between states that describe the motion of the protein backbone. For the simulation results, the value of Ea was found to be 40.3 kJ/mol.  c.5  I  I  I  I  o  I  I  I  Simulated Data Arrhenius Fit  -0.5 3’  I  •  -  -1  ‘N •“N  -1.5 -2 -2.5 3  I  I  I  I  I  I  245 250 255 260 265 270 275 280 285 290 295 Temperature [K]  Figure 5.15: Simulated r temperature dependence results displaying Arrhenius fit with Ea kJ/mol.  =  40.3  NMR studies of similar proteins have found correlation times ranging from ones to hundreds of nanoseconds. For example, a study of hydrated spider silk [38] reported rapidly moving backbone correlation times of r  10 ns. Hydrated elastin filaments exhibited correlation times on the order  of tens of ns [28]. The simulation results for the hagfish IFs are of a similar order of magnitude  48  for temperatures above 0°C, but rapidly become much larger as the temperature gets colder, see Figure 5.15. The results of the simulation provide a reasonable estimate of correlation times and correctly display an increase in r as temperature is reduced. The simulation follows an Arrhenius law behaviour with a characteristic energy of 40.3 kJ/mol. A feature of the hagfish biopolymer is that the flexible terminal ends contain a higher percentage of glycine than the central rod domain; approximately 30% in the ends compared to less than 2% in the central rod. It would be interesting to investigate the mobility of the glycine Cas compared to other a-carbons, as the glycines primarily represent the terminal regions. Unfortunately, the resolution in the spectrum was not adequate to facilitate such an investigation.  6  Resilin: A Resilient Rubber-Like Protein  Resilin provides a means of efficient energy storage in many insects [11]. It belongs to a family of elastic proteins including elastin and spider silks, and combines low stiffness and high strain. Resilin is normally found in parts of the cuticle of insects and is involved in roles from flight [36, 15] to generation of sound [5]. The basic function is mechanical storage of elastic potential energy, usually by means of a deflection, extension, compression or even twisting of an elastic structure containing the resilin protein. The strain is induced by a power muscle and is sometimes held by a latch system until release. Previous studies of naturally occurring resilin protein [9, 37], have established that the material consists of an amorphous network of randomly coiled polypeptide chains with stable chemical cross-links. A resilin-like protein has been tentatively identified in the gene of fruit flies (Drosophila melanogaster) [4]. The soluble recombinant protein, expressed in E. coli from the gene has been shown to cast into a solid rubber-like material via rapid photochemical crosslinking [10]. The study further shows that the resilience of the crosslinked recombinant resilin exceeds that of synthetic polybutadiene and chiorobutyl rubbers, high performance materials used in tire linings. The mechanical properties, along with the ability to rapidly cast samples with light may make it a prime candidate for in situ use in biomedical and industrial applications. The recombinant resilin (rec-1) was sequenced from the first exon of the Drosophila CG15920 gene. The sequence contains 17 repeats of the putative elastic motif GGRPSDSYGAPGGGN. The ubiq uitous 4 residue YGAP repeat is believed to be an important component in the resilin sequence, the site at which dityrosine crosslinks are formed. The rec- 1 sequence is shown in Figure 6.1. A second resilin sample was created from a consensus sequence from Anopheles gambiae, 49  MHHHHHHPEPPVNSYLPPSDSYGAPGQSGPGGRPSDSYGAPGGGNGGRPSDSYGAP GQGQGQGQGQGGYAGKPSDSYGAPGGGDGNGGRPSSSYGAPGGGNGGRPSDTYGAP GGGNGGRPSDTYGAPGGGGNGNGGRPSSSYGAPGQGQGNGNGGRPSSSYGAPGGGN GGRPSDTYGAPGGGNGGRPSDTYGAPGGGNNGGRPSSSYGAPGGGNGGRPSDTYGA PGGGNGNGSGGRPSSSYGAPGQGQGGFGGRPSDSYGAPGQNQKPSDSYGAPGSGNG NGGRPSSSYGAPGSCPCGRPSDSYCPPASG  Figure 6.1: Amino acid sequence of recombinant resilin, rec- 1. Residue Ala Asp Glu Phe Gly His Lys Met Asn Pro Gin Arg Ser Thr Vai Tyr Leu  rec-1 (%) 6.1 4.2 0.3 0.3 34.8 1.9 0.6 0.3 6.1 13.9 3.9 4.8 13.9 1.6 0.3 6.5 0.3  an-16 (%) 18.2 0.0 0.0 0.0 9.1 0.0 0.0 0.0 0.0 18.2 18.2 0.0 18.2 9.1 0.0 9.1 0.0  Table 6.1: Amino Acid content of resilin samples. Residues not listed are not present in either sequence. AQTPSSQYGAP, repeated 16 times. This sequence (an-16) has a smaller separation of YGAP re peats, see Figure 6.2. The relative abundances of the amino acid residues in each sequence are provided in Tabie 6.1. AQTPSSQYGAPAQTPSSQYGAPAQTPSSQYGAPAQTPSSQYGAP AQTPSSQYGAPAQTPSSQYGAPAQTPSSQYGAPAQTPSSQYGAP AQTPSSQYGAPAQTPSSQYGAPAQTPSSQYGAPAQTPSSQYGAP AQTPSSQYGAPAQTPSSQYGAPAQTPSSQYGAPAQTPSSQYGAP Figure 6.2: Amino acid sequence of an-16 resilin. The crosslinking in natural resiiin occurs between adjacent tyrosine residues forming di- and trityrosine adducts [2]. In the recombinant resiiin, roughly 21% of the tyrosines are converted to dityrosines (see Figure 6.3) under irradiation mediated by Ru(bpy). Samples of reci-resilin and an-16 sequence were analysed on a Varian 400MHz with an HX probe and a homemade 5mm horizontal coil. DP spectra are shown in Figure 6.4.  50  c=O HO  //\ —  /  —CH 2 CH  /NH 2 C—CH  OH  HN c=O  /  Figure 6.3: Dityrosine complex formed via photo-crosslinking. The crosslink site is shown here at the €-carbon but may also occur at the 6-carbon.  0  0  250  200  150  100 [ppm]  50  0  -50  250  200  150  100 [ppm]  50  0  -50  (b)  (a)  Figure 6.4: DP experimental spectra (a) rec-1 resilin (b) an-16 resilin. The broad peak centered at l2Oppm is due to probe background.  6.1  Chemical Shift Assignment of Recombinant Resilins  In contrast to the hagfish IF biopolymer, the resilin 13 C spectra are well resolved and allow iden tification of different carbons in the amino acid residues. The chemical shifts for backbone and /3-carbons of the residues in the amino acid sequence Figure 6.1 were predicted from a database of shifts. The prediction calculations were based on amino acid sequence and secondary structure, with corrections for nearest neighbour effects [39]. A value for each residue carbonyl, a- and /3carbon was calculated for each of 3 different conformations; a-helix, /3-sheet and a structurally dynamic model denoted “random coil”. The predicted values were then compared to the observed chemical shifts and peaks were assigned based on agreement with calculated values as well as rel ative size of the peak corresponding to residue content in the chain (Table 6.1). A high degree of confidence was possible for some peaks, while other peak assignments could not be made positively.  51  Other chemical shifts (i.e. for y-, s-carbons etc.) were referenced from the Biological Magnetic Resonance Data Bank [31]. The assigned spectra are presented in Figure 6.5.  0  0 200  180  160  140  120  100  80  [ppm] (a)  70  60  50  40  30  20  10  0  [ppm]  (b)  Figure 6.5: rec-1 resilin DP spectra peak assignment (a) carbonyl and aromatic region (b) c- and /3-carbon region. The peaks without labels were more difficult to assign owing to poor agreement with predicted values or overlap with other possible species. In Figure 6.5a, only the Gly carbonyl peak was positively assigned. It was easy to assign because of the relative high abundance of Gly in the sequence. Unfortunately, since the carbonyl peaks are all centered around a short range (‘-470 to 180 ppm) it was difficult to assign other peaks with any degree of confidence. The carbonyl peak with the highest shift at -.180 ppm could be Ala or Pro (or a combination of both). The other carbonyl peaks, having lower chemical shift predictions are not as probable. Referring to Figure 6.5b, A has a small shoulder on the downfield side. There is also a peak just downfield of A at -19.5 ppm. It is most likely these signals are alanine peaks as well, as no other  /3  species appears lower than 20 ppm. There are three different occurrences of Ala in the  sequence, GAP, YAG and PAS, appearing in a ratio 17:1:1. These varied sequences may give rise to slightly different shifts. Furthermore, Ala is one of the residues close to the putative cross-link site YGAP. It is possible that these factors provide for a second Ala peak at .‘20 ppm. There is suggestion of a peak just upfield of the P. This peak is not likely from Ala, since the shift is nearly 6 ppm higher than the assigned A. It is possible that the peak is noise, however it does appear to be significant compared to the surrounding noise level. It is most likely that it is a second P peak. Pro appears in many different sets of neighbouring residues (see Figure 6.1) and is one of the residues in the YGAP repeat. Furthermore, the peptide bond cis conformation is more likely when the subsequent residue is Pro (1:4 probability of being cis instead of trans compared to 52  1:1000 [6]). These facts could possibly explain an extra peak from the Pro 7-carbon. The P peak also has a shoulder on its upfield side; probably a P conformer, as the only residues with remotely nearby chemical shifts are Gin and His /3-carbons, which do not constitute an appropriate fraction of the protein, see Table 6.1. There are two definite peaks downfield of the P peak, which are presumed to be Gln and Arg 3s, respectively, based on predicted chemical shift values and relative content. Between the Arg /3 peak and the P there is indication of a small peak which could be either a /3-carbon from a Pro, Arg or Gin in a different residue sequence or combinations of the three. The peak just downfield of the P at .i32 ppm has many possible assignments. It could arise from the /3-carbon of another confomer of Pro, the closest peak with a substantial number of residues in the chain. Alternatively, the /3-carbons for Val, Met and Lys are predicted at this chemical shift, however the combined percentage of these residues in the chain is just 1.2%, which would not result in such a large peak. In the a-carbon region, the peak between G and D’ 3 is likely due to the a-carbon of Gly in an alternate sequence as there are no other nearby predicted shifts. The Gly a-carbon had two predicted shifts based on the adjacent residues. The sequence SGP accounted for roughly 3% of the Gly and resulted in a predicted shift of 43.1 ppm, while other sequences with Gly resulted in a 45.1 ppm predicted shift. These shifts are separated by 2 ppm, agreeing well with the separation observed in the spectrum. Much like the /3-carbon, the A peak appears to have a small shoulder on the left side, possibly from an Ala in an alternate sequence. The other unknown peaks in the a region are in a conglomeration between the large A and S/Yc. These peaks result from the a-carbons from Asn, Arg, Asp, Gln, Leu and His. The Leu and His contributions are small due to low concentrations in the protein. Based on predicted shifts, the 4 peaks from right to left are most likely Asn, Arg, Asp and Gin, respectively. The an-16 sample had fewer peaks to assign thanks to the simpler amino sequence, but the resolution was not as fine as with the rec-1 resilin. Similar to the rec-1 carbonyl peaks, Gc was the only positively identified species, see Figure 6.6a. Predicted chemical shift, relative peak size and comparison with the rec-l spectrum allowed identification of the dy peak. Again, the peak at 180ppm is believed to be an Ala/Pro carbonyl. Referring to Figure 6.6b the A’ has a shoulder that may be attributed to alternate sequences, PAQ and GAP, or the inclusion of the Ala in the YGAP repeat. The peak between A’ 3 and  Q’3  is likely  the Pro 7-carbon, as the chemical shift is in good agreement with reported values and lines up  53  0 0 200  180  160  140  120  100  80  [ppm]  70  60  50  40  30  20  10  0  [ppm]  (b)  (a)  Figure 6.6: an-16 resilin DP spectra peak assignment (a) carbonyl and aromatic region (b) /3-carbon region.  -  and  well with the P peak in the rec-1 spectrum, see Figure 6.7b. The two peaks between the Y and  t3 Q  are probably due to Pro /3-carbons in slightly different environments. There are two sequences  involving Pro; TPS and APA, as well as the aforementioned cis/trans conformers, which may lead to different chemical shifts. In the o-carbon region of an-16, there are two large peaks that are between the A and P peaks. The downfield peak is likely the combination of Tyr and Ser a-carbon signals, which aligns well in Figure 6.7b. The upfieid peak must originate from the Gin o-carbons. The A peak appears to have a small downfield shoulder, possibly also attributed to alternate sequence environments. The aromatic regions should provide some indication of the effects of the dityrosine bonds, as the aromatic carbons of the tyrosine are the closest to the bond location, which can occur at any one of the Tyr c- or 6-carbons. However, Figures 6.5a and 6.6a do not exhibit any compelling evidence of dityrosine bonds in the sample. In the rec-1 sample, Figure 6.5a, the signal from the Tyr c-carbons (the furthest upfield peak) appear in a single sharp peak. There is no apparent splitting or change in the isotropic chemical shift due to the presence of dityrosine bonding. The peaks in the center of the aromatic region are believed to be the 3-carbons (around 132 ppm) and the 7-carbon (around 129 ppm) signals. The apparent 2:1 ratio of the 6:7 peak sizes correctly accounts for the abundance of these species. There is also suggestion of two other small peaks, upfield from the 6 and between the 6 and y peaks. These small signals may result from His c-carbon (138 ppm) and 7-carbon (131 ppm), respectively. However, these peaks are still present in the an16 spectrum, which does not contain any His, see Figure 6.7a. It is possible that these extra peaks arise from a changed chemical environment due to dityrosine bonding, or from alternate sequence 54  environments. It is strange however that a similar effect is not seen in the 6-carbon signal. The 6and 7-carbon signals are very similar between the rec-1 and an-16 spectra. In the rec-1 spectrum, signal from the Tyr q-carbon (furthest downfield, next to the carbonyl region) appears as a single peak. The peak downfield of the  peak in the rec-1 spectrum could  possibly be the Arg (-carbon peak, occurring at 159 ppm with an appropriate magnitude relative to the Y peak. The Arg  peak is absent from the an-16 spectrum, as expected. The Y peak  has a slight downfield shoulder that may be attributed to either dityrosine bonding or alternate sequences around the tyrosine. The an-16 spectrum is more informative to look at due to the fact that the aromatic signals are provided solely by tyrosine. Referring to Figure 6.7a, the 6-carbon peak has a slight shoulder on it and the 6/7-carbon peaks are broader but there are two peaks in close to the same positions as the rec-1 Tyr 6/7 peaks. The excess broadening may be a result of poorer SNR in the an-16 spectrum.  0  0 200  180  160  140  120  100  80  70  [ppm]  60  50  40  30  20  10  0  [ppm]  (a)  (b)  Figure 6.7: red and an-16 DP spectra overlay (a) carbonyl and aromatic region (b) c- and 3-carbon region.  6.2  Secondary Structure of Recombinant Resilin  The confidently assigned peaks were used to provide a quantitative measure of the possible sec ondary structure of the proteins. The difference between the observed and predicted chemical shifts, =  —  55  bs, 69  (6.1)  was calculated for each possible conformation. The deviations d, defined:  d  =  ), 5 (  —  (6.2)  were plotted along the chemical shift scale for the residues under evaluation. (ö) represents the average of all the differences for the definite peaks for a particular conformation. Figures 6.8a and 6.8b show the deviations from predicted chemical shifts for each of the 3 conformations. The deviations were used instead of the absolute differences /ö as absolute referencing was not possible. This is simply because a chemical shift standard could not be inserted into the sample holder with the resilin samples. 4  I  3  .  I  +  ÷  I  3  I  x  +  ÷  _1. a 2  •  )<X  3 0  20  I  x +  x  +  x  +  -  I  I  Random Coil Alpha Helix Beta Sheet  ..  .  X  x  I  0  0•  -2  I  x  ;  .0. .  -1  +  I  x  E  1•  0  I  +  x  x  +  I  +  2  +  x  +  E  a > a) 0  I  Random Coil Alpha Helix Beta Sheet  2 0  I  + ++  +  -3 I  I  I  I  I  40 60 80 100 120 140 Residue Chemical Shift [ppm]  I  160  + I  4 180  0  20  I  I  I  I  I  I  40 60 80 100 120 140 Residue Chemical Shift [ppm]  I  160  180  (b)  (a)  Figure 6.8: Deviation from observed chemical shift (a) rec-1 resilin, N N=8.  =  13 (b) an-16 resilin,  The standard deviation o- for each conformation was calculated from the N high confidence peak results:  >  (  -  ())2  The standard deviation results are summarized in Table 6.2.  (6.3) The standard deviation for the  Random Coil configuration is shown to be almost an order of magnitude lower than either the ce-helix or 3-sheet, suggesting that the proteins do not form stable secondary structure, but rather the protein backbone averages rapidly over many different conformations. These results suggest that the recombinant resilin samples exhibit random coil structure, similar to the conformations discovered by Weis-Fogh et al [37].  56  rec-1 Variance [ppml 0.23 1.52 1.83  Conformation Random Coil Alpha Helix Beta Sheet  anl6 Variance [ppml 0.16 1.47 1.95  Table 6.2: Simulated chemical shift variance.  Relaxation Measurements  6.3  The T 1 relaxation times were also measured in the resilin samples. The results further indicate a material with a high degree of molecular mobility. The experiments were carried out on a Varian 400MHz spectrometer with a HX probe and a homemade 0.5cm (inner diameter) copper coil. The pulse sequence used employed selective phase cycling to eliminate the background artifacts (Figure 6.9). A side effect of the background elimination combined with delay times was the loss of some SNR, as seen in Figure 6.10.  ‘H  ir  7r  7r  Figure 6.9: T, experiment employing background suppression via phase modulation.  0 200  0 150  100  50  200  [ppm]  100  50  [ppm] (b)  (a)  Figure 6.10: T, spectra with r  150  =  0.Ols and Temp  57  =  4°C a) rec-1 resilin b) an-16 resilin.  0  Peak  Species  C=O  all C=O Tyr S Tyr  P  Pro a  *  Tyr, Ser a  o A’  Asn, Arg Asp, Gin a Ala a  G  Gly a  Temp [°C} 4 -8 4 -8 4 -8 4 -8 4 -8 4 -8 4 -8 4 -8  T 1 [s] 1.72 ± 0.05 1.87 + 0.08 0.47 + 0.02 0.48 + 0.05 0.37 ± 0.04 0.35 ± 0.02 0.24 ± 0.02 0.25 ± 0.02 0.31 + 0.01 0.38 + 0.02 0.30 + 0.01 0.38 ± 0.03 0.28 + 0.02 0.30 + 0.02 0.21 + 0.01 0.22 + 0.01  T  Fast 0.96 0.82 0.106 0.105 0.14 0.15 0.28 0.25 0.18 0.14 0.19 0.14 0.20 0.18 0.12 0.11  [nsj Slow 2.6 3.7 8.2 8.3 6.4 6.0 3.7 3.9 5.2 6.6 4.9 6.5 4.7 5.0 7.4 7.8  Table 6.3: rec-1 relaxation times and corresponding correlation times r. Temperature dependence trend indicates that backbone and aromatic carbons are in the slow regime. The identifiable peaks, those denoted in Figure 6.10, were used in the T 1 calculations. All of the peaks fit a single exponential decay well, though some of the smaller peaks had larger uncertainties due to poorer SNR. The T 1 values were subsequently used to determine the correlation times r, using the relations in Section 2.8. Again, the carbonyl carbons were assumed to relax primarily under the chemical shift anisotropy (Equation 2.71). The other carbons were assumed to relax due to dipolar interaction with nearby protons (Equation 2.66). The results are summarized in Tables 6.3 and 6.4. Consideration of the amide proton (NH) in the relaxation of ‘ C nuclei had negligible 3 effect on the resulting correlation time. The glycine a-carbons were assumed to relax under the influence of the dipolar interaction with 2 nearby protons, instead of just 1. The experiments were performed at 4 and -8°C to identify whether the protein backbone carbons were in the fast or slow regime. The backbone carbons should move slower as temperature is reduced, resulting in a longer r. Thus, it is apparent from Tables 6.3 and 6.4, that all of the nuclei observed are in the slow  regime, which is common for large molecules. The fast regime would see the various parts of the molecule tumbling faster at lower temperature. The 3-carbons were excluded from T 1 analysis as the correlation times from the more freely mobile side-chain carbons do not provide much insight into the dynamics of the protein backbone. The backbone carbon correlation times are all quite fast (2-8 ns). This further supports the notion  58  Peak  Species  C=O  All C=O Tyr ó Tyr  €  T  Thr a  f Q  Tyr, Ser a  A  Ala a  Gln a  Temp [°C} 4 -8 4 -8 4 -8 4 -8 4 -8 4 -8 4 -8  T 1 [s] 1.81 + 0.07 2.11 ± 0.05 0.46 ± 0.04 0.51 + 0.04 0.29 + 0.02 0.31 ± 0.01 0.17 ± 0.03 0.20 + 0.03 0.22 + 0.02 0.22 ± 0.01 0.33 ± 0.01 0.36 ± 0.01 0.30 ± 0.02 0.35 ± 0.01  r  Fast 0.86 0.67 0.11 0.097 0.20 0.18 0.73 0.43 0.34 0.26 0.16 0.15 0.19 0.15  [ns] Slow 2.9 3.7 8.0 9.0 4.7 5.2 2.0 2.7 3.2 3.4 5.5 6.0 4.9 6.0  Table 6.4: an-16 relaxation times and corresponding correlation times r. that the resilin is composed of a highly flexible protein chain, providing the elastic properties of the material. The correlation times found for the aromatic Y carbons were the longest reported. This is interesting because these are carbons close to, or involved in the dityrosine crosslinks. It is possible that the crosslinks provide extra stability that restricts the motion of these aromatic tyrosine carbons. However, the c-carbons did not prove to have significantly longer rs. It might also be expected that the aromatic carbons would display two-component behaviour due to 20 involvement in dityrosine bonding, but this is not seen either. The correlation times of the backbone carbons compare well between the two samples. One might expect the larger separation of YGAP binding sites would allow for greater flexibility, and therefore faster correlation times in the rec 1 molecule. However this is not the case, the rec-1 backbone correlation times report a slightly slower upper limit;  rs  from 2-8 ns vs. 2-6 ns. This difference between samples is small and may  be partially attributed to experimental error.  7  Incorporation of Metal Ions into Hagfish IF: Preliminary Work  Many proteins bind metal ions in a variety of ways, for a multitude of purposes. It has been demonstrated that formation of IFs is affected by ligand metal concentrations [20]. The cohesive properties of the slime in water have been shown to be dependent on the presence of calcium [12].  Ca + , and a calcium It is possible that the IF component properties are dependent on 2  binding mechanism has been purported (P. Guerette, private communication). It was suggested 59  that the hagfish biopolymer may contain 3,4-dihydroxy-L-phenolalanine (L-DOPA), frequently seen in marine bioadhesion proteins [26, 33, 40]. DOPA is converted from the amino acid tyrosine and +, Cu 2 + or Ca 2 +, see Figure 7.1. In an 2 provides a binding site for divalent metals such as A1 Ca was investigated. + attempt to support or refute this claim, the ability of the protein to bind 2  /  /  OH O=CCa 2  /  —  HN  —/ HN c=O  c=O  /  /  Figure 7.1: 3,4-dihydroxy-L-phenolalanine (L-DOPA). (a) DOPA is much like the amino acid tyrosine but has a second hydroxyl group on the aromatic ring; (b) a divalent metal (in this case j may form an ionic bond with the oxygen atoms. 2 Ca To accomplish this, the hagfish IFs were treated with an ionic solution. The procedure for this is outlined in Section 7.1. The metal ion incorporation, if present, could be characterized by an NMR experiment which is sensitive to nuclear separation. Rotational-echo double-resonance (REDOR) and REDOR-like experiments (REAPDOR [17], SEDOR [22]) are techniques used to measure the dipolar coupling and therefore could determine the internuclear distance and indicate the location of binding. Such an experiment is discussed in Section 7.2.  A simulation of the  experiment given the purported binding site was also performed for comparison with results. The success of the experiment depends on the ability to maintain the signal for an adequate amount of time, discussed in Section 7.2.1, as well as the ability of the hagfish IFs to actually bind the ions. The latter point is addressed by EDX in Section 7.3.  7.1  Sample Preparation  + in 2 Samples of the hagfish IF bundles were subjected to a bath in a concentrated solution of Ca an attempt to promote ligand binding. Care  was taken to provide a setting in which exposure to  pollutant ions was minimal. The IFs were taken from the citrate buffer and stored at -4°C when not in use. A solution of 10 mM Ca 2 was produced by adding 5 mg of CaCO 3 to 2 mL of 0.12 M HC1 solution. The solution was then neutralized using 0.12 M NaOH solution, bringing the pH to approximately 8 and the final volume to 5 mL. The concentration of dissolved CaCO 3 is dependent on the solvent pH. 60  Adding CaCO 3 to a strong acid allowed for improved dissolution of the compound and the release of CO 2 gas, thereby mitigating precipitation of CaCO 3 as the solution was brought back to a more neutral pH. Excess solid CaCO 3 was removed by centrifugation and pipetting. Approximately + solution and allowed to sit for 24 hrs, 2 2 mg of IFs were added to 5 mL of the 10 mM Ca periodically agitating the sample to ensure adequate mixing.  After exposure, the sample was  rinsed by repeatedly pipetting off solution, adding nanopure H 0 to dilute the concentration of 2 + and centrifuging the new dilute solution. This was done 10-20 times to reduce the free Ca 2 Ca + 2 ion concentration to lessthan 10— 12 times the amount expected to bind assuming all of the tyrosines were converted to DOPAs. Ca used was chosen to be a 10-fold excess of the available binding sites + The concentration of 2 in the hagfish IF. Since the purported binding site is DOPA converted from tyrosine, this is simply the number of tyrosine residues in a given mass of the hagfish IF. Standards were prepared by adding IF samples to the nanopure H 0 and subjecting them to the 2 Ca solutions were also prepared with CaCl + same rinsing procedure. 5 mM 2 2 (much more soluble in water) in nanopure H 0 and additional samples were treated in this solution. The samples were 2 dried overnight in a vacuum chamber on glass microscope slides before being subjected to energy dispersive x-ray spectroscopy to determine elemental content.  7.2  Using REAPDOR to Determine Metal Binding Site  If the samples could be prepared reliably, the next step would be to determine the location that the metals were binding. This could be done using rotational echo, adiabatic passage double resonance (REAPDOR) NMR, an experiment developed by Gullion [16]. The REAPDOR experiment isolates the dipolar coupling interaction between a spin-  nucleus and a spin  1 nucleus with a large  quadrupolar coupling. By comparing the estimated nuclear separation at the possible binding sites in the protein with that obtained experimentally, the location or locations binding the metal could be uncovered. The REAPDOR pulse sequence (Figure 7.2) essentially allows the observation of magnetization dephased solely under the dipolar interaction, using selective ir pulses every half rotor cycle, TR/2. In the absence of pulses, the anisotropic interactions are averaged to zero by MAS. The addition of perfect  it  pulses on the I channel every half rotor cycle ensures there is no contribution from the  isotropic chemical shift Hamiltonian. The I channel pulses, however, result in a non-zero average  61  for the anisotropic terms over a single rotor cycle, TR. This undesired effect is corrected by omitting a  pulse at the center of the pulse sequence, refocusing the dephasing from these interactions at  it  the time of signal acquisition. Finally, since the dipolar interaction is dependent on both the I and S spins, an inverting pulse on the S channel causes the refocusing of the dipolar dephasing to be undone. The pulse is termed the recoupling pulse and allows the observation of the dipolar dephased signal. Application of the sequence without the S channel recoupling pulse provides a reference signal which accounts for T 2 relaxation effects. By comparing a dipolar dephased signal to the reference signal, a measure of the dipolar coupling can be obtained. To understand this, the  xyxyxyxy I  xyxyxyxy  H 111111111  IIIIIIIII H  S I  I  I  I  I  I  I  I  I  I  I  0  1OTR  Figure 7.2: A REAPDOR pulse sequence. The x and y are hard on the S channel is an adiabatic passage recoupling pulse.  it  pulses at  inervals. The pulse  pertinent interactions must be traced over the course of the pulse sequence. First, the Hamiltonians must be written in terms of PAF components. The Hamiltonian of the I-S system with I  =  and 5> 1 has the terms:  (7.1)  Isa+Ha+Hd+HQ+Hf+H,  respectively denoting the chemical shift for the I and S spins, the dipolar coupling, the quadrupolar coupling and the rf pulses on the I and S spins. In the rotating frame, the terms have the form:  S (3cos 1 —w O —1— isin 2 2 Ocos2)  f1c’sa cSsa  =  ‘s6 (3 cos 2O  —  1  ij  —  2 9 cos 2) sin  S(13c0526)IS I 7  Hd HQ  —  I  V’s =  wQ (3cos 2 O —1— 71Qsin OQcos2Q) 2  The quadrupolar frequency  VQ  =  [  —  S(S+ 1)  î].  (7.2)  wq/2ir, can be represented in terms of the quadrupolar coupling  62  constant  x  =  qQ/h: 2 e VQ =  2S(2S  (7.3)  1)  Each term in the Hamiltonians (Equation 7.2) has some complicated time dependence of the orien tation angles 8 and  j,  brought on by MAS of the sample, see Section 3.2. The time dependence  of the coefficients for each interaction can be represented as a function with terms that oscillate at the MAS rotor frequency  WR  and  g(t)  j: 2  gi cos(wRt  +  71)  +  g2  cos(2wRt +  72),  (7.4)  where the s are angles representing initial molecular orientations, and the gs contain the inter action constants displayed in Equation 7.2. The g(t) functions are oscillatory with a period of TR. This periodicity results in rotational  echoes which are vital to the function of the sequence, noting: fTRg(t)dt =  0 fTR  /  g(t)dt  = —  /  g(t)dt.  (7.5)  J  Jo  The functions g(t) must be compared with the tensor form of the Hamiltonians to determine the coefficients g, in terms of the PAF components. The dipolar Hamiltonian for example, =  7I7Sh  (1  —  2 Od) 3 cos  I&  =  —21 D(t) S, .  .  (7.6)  ris  where D(t) is dependent on g(t) and the initial orientation of the tensor PAF with respect to the static field. To determine D(t), the rotor frame tensor, DR(t) must be projected into the lab frame. The rotor frame tensor is related to the PAF tensor by the appropriate Euler transformation  DR  (7.7)  =  —  DPAF  =  0 0  63  0 —  0  0 0  d  ,  (7.8)  where d is the dipolar coupling constant for the IS pair,  d=  (79)  rIs  The important component is the lab frame z-component, obtained from the projection of DR onto the lab frame z-axis: r  L)z  where b  _R —  hO  nR  R  7.1  (sin 0 m cos WRt, sin m 0 sin WRt, cos Om) is parallel to the static field. Comparing the  left and right sides of Equation 7.6:  —2D  d (i  —  2 Od) 3cos  .  (7.11)  Finally, the lab frame Hamiltonian can be written in terms of the dipolar tensor PAF components and the initial orientation angles c, /3 and :  2 /3cos(2Rt + 27)] Hd = [V’cisin2/3cos(wRt + ‘y) + dsin  (7.12)  Average Hamiltonian theory can be applied to the pulse sequence, noting that g(t) changes sign every half rotor period and the  7t  pulses induce a sign change from the affected spin operator.  The first sequence, to obtain the control signal, is run without the recoupling pulse. The resulting average Hamiltonians are  ,  flcsa and HQ. When the recoupling pulse is applied to obtain the  dipolar dephased signal, the chemical shift and quadrupolar Hamiltonians are averaged to 0 by MAS, while the dipolar Hamiltonian average is unaffected. This is due to the fact that pulses on both channels affect the sign of the dipolar Hamiltonian, which has an IS dependence, while the other interactions depend only on  I,  or  Ideally the recoupling pulse will invert all of the S spins in the sample. However, when the S spin has a large quadrupolar coupling this is not the case, and the recoupling pulse must be the adiabatic passage pulse. With the application of a hard r pulse, only a fraction of the spins with frequencies near the rf pulse will be allowed to undergo state transition, see Figure 7.3. As the rotor spins during the recoupling pulse, the spins experience a range of frequencies due to the time dependence on the quadrupolar interaction. If the frequency of the spin passes through the , then it is allowed to undergo a state transition. The duration of the pulse is 0 Larmor frequency w  64  Lu U, ‘I  0 C  0 .1-’  CD  0  wo  Figure 7.3: The adiabatic passage pulse is required to invert an adequate population of S spins. selected such that an optimal number of spins precess at the Larmor frequency only once during the recoupling pulse. This optimal duration has been shown to be TR/3 [18]. The adiabatic passage pulse has further power requirements. In order for state transitions to occur, the passage of the nuclear interaction frequency through the Larmor frequency must happen slowly enough to allow the transitions to happen. This requirement is described by the adiabaticity parameter c. The adiabatic passage requirement depends on the rotor frequency and the magnitude of the quadrupolar coupling:  =  1/RVQ  A strong rf pulse may have a power of v resolution is  yR  =  =  > 1.  (7.13)  100kHz and a typical spinning rate for suitable  5kHz. With these conditions, the REAPDOR sequence could be successfully  applied to a system which has a quadrupolar coupling frequency VQ up to 2MHz. Recently reported values for u [3, 23, 29] ranged from 0.1 to 0.7 MHz, well below the required limit. The REAPDOR experiment is repeated numerous times, increasing the number of cycles be tween time 0 (at\the initial  pulse) and acquisition. For each number of cycles the reference signal,  S is compared to the dipolar dephased signal, Sr obtained with the recoupling pulse present. The resulting signal ratio (conventionally displayed as AS/S  1  —  Sr/S) is plotted against the experi  ment duration, which is equivalent to the number of rotor cycles times the rotor period;  T =  NTR.  The modulation of the signal ratio with respect to r is dependent upon the magnitude of the dipolar coupling d. An example of a REAPDOR curve is shown in Figure 7.4, where the abscissa  65  is plotted as the dimensionless parameter ,\  =  rd. The success of the REAPDOR experiment is  1.2 1 0.8 •  S  I,  0.6 0.4 0.2  0  0.5  1  1.5  I  I  1  I  2  2.5  3  3.5  4  Figure 7.4: An example of a REAPDOR experimental curve. contingent on the presence of adequate signal at the end of the rotor cycles. Here, dephasing of transverse magnetization is a limiting factor. T 2 relaxation measurements provide a timescale on which the transverse magnetization decays. 7.2.1  2 Relaxation in Hagfish IFs T  A requirement for the REAPDOR experiment is that the number of cycles be adequate to see a modulation due to the dipolar coupling. To determine feasibility of the REAPDOR experiments, a measure of T 2 relaxation times in the hagfish IFs was performed. The T 2 experiment was a spin echo experiment (Figure 7.5) first developed by Hahn [19]. The T 2 experiment consists of an  c 3 i  7T•  Figure 7.5: Hahn spin echo experiment with cross-polarization. The delays r 1 and T2 are very similar, but the acquisition may start sooner than r after the ir pulse to ensure the full echo is captured.  66  Peak 2 [ms] T  C=O 6.11 + 0.09  4.72 + 0.27  3.96 + 0.14  Other 3.72 + 0.14  Table 7.1: T 2 relaxation times. initial cross-polarization pulse to put the 13 C magnetization in the xy-plane followed by a period of free evolution (decoupling protons to enhance SNR and resolution), r . During the evolution, the 1 transverse magnetization will begin to dephase, owing to the difference in precession frequencies due to chemical shift and dipolar interactions. After the delay, there is a  it  pulse on the 13 C channel  flipping the transverse magnetization. This does not affect the precession frequency of the spins and as a result, the “dephasing” effect is reversed and the transverse magnetization refocuses, see Figure 7.6. This is known as the spin echo and it peaks at a time equal to r 1 after the  (a)  (b)  (c)  it  pulse.  (d)  Figure 7.6: The spin echo. Vectors represent transverse magnetization in a frame rotating at the Larmor frequency ceo; (a) Initial transverse magnetization following pulse; (b) after time r the magnetization has dephased due to spins precessing at frequencies slightly different from the Larmor frequency, w = wo+&.’; (c) a it pulse is applied, inverting magnetization; (d) magnetization refocuses at time r after the it pulse. Over longer and longer delays, r  =  , the spin echo magnitude will eventually die out. The 1 2r  rate at which it does so is characterized by T , measured in the same manner as T 2 1 relaxation times in Section 5.3: 1(r)  =  Ioe.  (7.14)  The T 2 values were measured for the hagflsh IFs on a Varian 400MHz spectrometer with an HXY 4mm MAS probe spinning at 5kHz. A sample spectrum from the 7’2 experiment is shown in Figure 7.7. The resulting T 2 values for peaks identified in the spectrum are summarized in Table 7.1. The tyrosine &-carbon is the putative binding site. To determine if the T 2 relaxation of 4.72ms for this species is adequate, a computer simulation of the REAPDOR program was written.  67  0 250  200  150  100  50  0  [ppm]  Figure 7.7: Spin Echo experimental spectrum. 7.2.2  VR  =  5kHz  REAPDOR Simulation  A simulation of the REAPDOR experiment was written, following the algorithm put forth by Hughes and Gullion [21]. The simulation evolves the density operator, p according to the Liouville von Neumann equation (Equation 2.21) throughout the pulse sequence and obtains the resulting REAPDOR signal, AS/S. The code was written to simulate the dipolar dephasing curve obtained from the DOPA-Ca ligand, Figure 7.1. I  The dipolar evolution of the I spin magnetization is I  I  I  I  0.8  I  I  •••••••••••••  •••  0.6  tS S  0.4  0.2  0 0  2  4  6  8  I  I  I  10  12  14  T [ms]  Figure 7.8: REAPDOR Simulation for DOPA-Ca binding: yR = 5kHz, S= The arrow indicates the T 2 limit for the tyrosine ç-carbon.  d  =  57Hz,  x  =  50kHz,  .  calculated by evaluating Tr (I+p(T)). Each I-S spin pair, at different orientations contribute a dipolar dephased signal  sd(a,  j3, r). The ensemble signal is computed as a powder sum of signals  over all angles a, 3: .  S  —  —  J fc sd(a, 3, r) sin /3dad/3 jfasin/dad/3  68  .  ( 7 15  The form of  Sd  depends on the spin number S. For a spin S  ,  the dipolar dephased signal is  [18] =  where wd  =  [cos(wr)  +  cos(3wdr)  +  Cos(5wdT)  + cos(7wdT)],  (7.16)  2/d sin 23 sin a. The solution is quite involved and will be omitted in this work,  suffice to say the resulting integral contains Bessel functions [18,  =  4  301:  () + 4 ()J_ 114 [J (3)J_i/ / 1 J ( 3)  114 (5vA) 4 (5v’A) J_ +Ji/  114 (7v’) J—i/ 4 (7v)]. +J  (7.17)  The experimental REAPDOR curve can be compared to a curve using Equation 7.17 to deter mine the dipolar coupling constant and thus confirm the binding location of the calcium ions. The T 2 result for the proposed binding site, 4.72ms, is indicated on the simulation curve 7.8. Experimental data would be available for the tyrosine -carbon up to this point. After the T 2 cutoff, the SNR would start to become poor. Although more data would be better, the cutoff is high enough to allow comparison between simulated and experimental results.  7.3  Energy Dispersive X-Ray Spectroscopy  Energy dispersive x-ray spectroscopy (EDX) was employed to determine if calcium could be in corporated into the hagfish IFs. The EDX experiments were carried out on a variable pressure Hitachi S-3000N Scanning Electron Microscope (SEM) with light element EDX at 20 Pa. Electron micrographs of the samples (Figure 7.9) were analysed to identify regions of the protein free of vis ible impurities. Suitable surfaces were selected for point focused EDX measurements with a beam exposure duration of 200s. Because the SEM did not have vacuum conditions inside, there was some electron beam deviation due to defiections by atmospheric ions inside the chamber. These deviations are infrequent and errant electrons should strike within a 20 tm diameter of the desired focus point. The EDX experiments provided some positive results although they were not easily reproduced due to difficulty in controlling variables in sample preparation. The control samples repeatedly showed a negative result, lacking any sign of Ca in the EDX spectra. However, some control samples were contaminated with Ca and other heavy metals (see Figure 7.lOb), illustrating the need for extremely clean handling conditions of the samples during preparation.  69  Figure 7.9: Trial SEM micrograph of GTC bundle with nearby CaCO 3 contaminant. Both the CaCO 2 exposed samples exhibited positive and negative results. The 3 and CaC1 positive results were not reliably reproducable. It appears that the ability for the protein to bind metals is dependent on solution pH, but the degree to which is not known. Unfortunately, the NMR active isotope 43 Ca poses a potential problem for the experiment due to low natural abundance (0.135%). Because of this, a costly, isotopically enriched treatment compound would be needed and in order to carry out the REAPDOR experiment with limited supply, the sample preparation must result in successful incorporation of Ca into the protein every time. This was not achieved in the course of this study. It is clearly evident that despite careful preparation methods, contamination with heavy atoms is frequent, as shown in Figures 7.lOb, 7.llb and 7.12b. This contamination could arise at any step in the preparation or handling of the samples. Exposure to open air was kept to a minimum, but impossible to avoid completely. The use of metal tools was avoided and glass test tubes were cleaned with methanol and rinsed thoroughly with nanopure water before containing samples or solutions. With the CaCO 3 preparation there is some possibility of contamination with Cl— and Na ions from the HCI/NaOH solutions. These ions should not interfere with the purported binding site as they have incorrect valency. The spectra displayed in this Section are just a few of the many attempts, but summarize the breadth of the results obtained during the study. Initial preparations were made without monitoring the solution pH carefully and the procedure was revised many times for subsequent trials. Unfortunately, the techniques used were not adequate to acquire the desired confidence levels. The lack of Ca in the treated samples Figures 7.llc and 7.12c must be addressed before  70  Counts  C  1000  500  I  —r  0  2  4  6  8  key  6  8  key  (a) Counts  K  SI  1000  0 500  0  2  4  (b)  Figure 7.10: EDX spectra for control samples a) pure b) contaminated. attempting the REAPDOR experiment. Solution pH and temperature or UV exposure of the sample before treatment may affect the ability of the sample to bind calcium. Before a reasonable result can be obtained in this line of research, the effect of these variables on the Ca-binding potential must be carefully analysed.  71  Counts 2000  1500  1000  0  500  I,,  0  4  2  8  8  key  8  keV  (a) Counts  C 4000  3000  2000  1000  TI TI 0  (b) Counts  C  1000  500 0  s CI  Al  1ti1L  r 0  2  4  1 6  1  (c)  Figure 7.11: EDX spectra for samples treated with CaCO 3 a) positive results b) contaminated c) no apparent Ca presence. 72  Counts  C 4000  3000  2000  1000  L 0  2  4  6  8  key  (a) Counts  2000  1000  key  (b) Counts 3000  2000  1000  6  8  key  (c)  Figure 7.12: EDX spectra for samples treated with CaC1 2 a) positive results b) contaminated c) no apparent Ca presence. 73  8  Concluding Remarks  A variety of NMR techniques were employed to probe the structure and mechanics of two potentially useful biological materials. Proteins forming materials with mechanical properties rivalling and exceeding those of synthetic materials may eventually replace them. Understanding the facets of the protein structure is an imperative step along the road to achieving this goal. Hagfish gland thread cell protein forms intermediate filament threads that are strong and highly extensible when hydrated. Direct polarization and cross-polarization experiments were used to ex pose the underlying two-component structure of the protein backbone. This dichotomous compo sition agrees with the predicted model of the IF structure. Signal from a rigid central rod domain appears in cross-polarized spectra while the dynamic terminal regions fail to cross-polarize well. The next step would be to definitively assign the dynamic behaviour in the chain to the terminal re gions, perhaps using the high concentration of glycine in these domains. It would also be of interest if one could extend these measurements to observe the filaments in an orientationally depenedent state, or to look at the effects of the protein dynamics while the filaments are under strain. To accomplish this, the problem of naturally dilute 13 C nuclei must be addressed, either by isotopic labelling (very difficult given the size and maturation rate of the organism) or the employment of smaller coils in the NMR probe. Hagfish threads also provide a convenient model of intermediate filaments, normally difficult to study in vitro. There is evidence of interaction with metal ions that seem to play a role in the formation and structural properties of the slime as a whole, and may be important to the IFs themselves. Lineshape simulations were performed to characterize the degree of the molecular motion in the flexible parts of the chain. These measurements provide reasonable estimates of the dynamic nature of the elastic regions, compared with results from similar protein structures. Recombinant resilin casts were identified as highly elastic materials, composed of protein with an extremely mobile backbone adopting random coil conformational properties. The molecular dynamics reflect the observed macroscopic mechanics of the material. These results suggest that the recombinant resilin has a structural composition similar to the natural resilin studied in the 1960s by Weis-Fogh. The notion of an amorphous network of flexible random coil polypeptides is entirely congruent with the well resolved spectra and the remarkably short correlation times displayed by the resilin samples. Because this protein is rapidly cast from a solution into a solid state under photo-crosslinking, it may find a wealth of application in biomedical or commercial 74  pursuits. The recombinant resilins exhibited a highly mobile backbone structure compared to the hagfish IFs. Backbone carbon correlation times taken from experimental relaxation values were always much faster in the resilin (2 to 8 ns), compared the hagfish IFs (60 ns for the most mobile compo nents). This fact is intuitive as the hagfish IF is a much tougher material and the primary feature of the resilin is extreme elasticity. Elastin, a highly elastic natural protein is a similar mechanically robust material. Previous studies have identified elastin as a network of mobile polypeptide chains with cross-link regions, similar to the resilin model. The relative mobility and structural order of all three materials can be seen in Figure 8.1. From these results it is immediately evident that  A_JLiL  B  C  200 :150 100 50  0  -50  [ppm] Figure 8.1: DP spectra comparison of elastin (C) with rec-1 resilin (A) and hagfish IF (B) spectra. (C) was taken from [32] and displays spectra for strained (dotted) and unstrained (solid) elastin. the resilin material has a much more mobile nature in the protein chain than both the hagfish IF and the elastin proteins. The much sharper lineshapes in the resilin spectra reflect the greater degree of molecular motion. The elastin and hagfish IFs exhibit similar linewidths owing to regions 75  with similar correlation times. Table 8.1 summarizes the dynamic quantities of the three different materials. NMR of the dynamics in elastin networks show a correlation time of approximately Material Resilin Elastin Hagfish IF  Correlation Time [ns] < 8 40 60  Table 8.1: Summary of dynamic characteristics for structural proteins. 40 ns [28], putting elastin at an intermediate flexibility between the highly mobile resilin and the tougher hagflsh IF. 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Robertson, S. A. Jewhurst, and J. H. Waite. Probing the adhesive footprints of mytilus californianus byssus. J. Biol. Chem., 281(16):11090—11096, 2006.  80  A  Lineshape Simulation Code  1* program to calculate spectrum of a CSA undergoing random flips, with a s correlation time and an average angular jump  #include <math.h> #include <stdio h> #include <stdlib h> .  .  /* for for for for for  .Olus .lus lus 2us 5us  did did did did did  NPC=1024, NPC=1024, NPC=1024, NPC=1024, NPC1024,  BR400, BR400, BR=400, BR=400, NR400,  NSIM100 NSIM1000 NSIM=10000 NSIM=10000 NSIMI00000 */  II number of sites to simulate 100000 for static, try 1000 for rapid flipping #define NSIM 10000  7/ correlation time in sec #define TAUC 0.8e-6 /7 jump size has an exponential distribution, this is correlation angle #define DTH 15 #define #define #define #define  DT 2e—6 /1 dwell time of data NP 2048 II number of points in fid. NPC 2048 II number of points to actually calc in fid BR 400.*DT*M_PI /7 broadening in points  7/ CSA parameters based on polyglycine data #define DELTA —75.66*100. 523*2*M_PI #define ETA -0.8267 #define ISO 0.0 void evolve_to_next 0; float dur , curr_freq,phase , thi ,phi; main0{ float spec [2*NP] ,ct,sti,fid[2*NP]; mt i,j ,next=0,last=0; for (i=0;i<2*NP;i+-i-) spec[i]=0.; for(j=0;j<NSIM;j++){  II get the initial angle thi phi  = =  (float) randomQ*MPI/RANDMAX; (float) random0*M_PI/RAND_MAX;  sti=sin(thi); ct=cos(thi); ct=ct*ct; curr_freq = DELTA/2.*(3*ct—1+ETA*(1.—ct)*cos(2*phi));  81  phase = 0; dur = -log((float) randomO/RAND_MAX)*TAUC; for( i=0 ; i<NPC ; i++ ){ spec[2*i] + cos(phase)*sti; spec[2*i+iJ += sin(phase)*sti; evolve_to_next  0;  } // keep the user informed: next = (int) j/(NSIM/iOi.); if (next > last) { fprintf(stderr, “\rY.i/iOO” ,next); fflush(stdout); II last=next;  } } fprintf(stderr, ?I\nII); /1 now do ft and output.  //  store fid before broaden. for(i=0; i<2*NP; i++) fid[i]=spec[i];  II broaden: for (i=O;i<ISTP;i++){ spec[2*i] *= exp(—(float)i*BR); spec[2*i+i] *= exp(—(float)i*BR); } spec[0] /=2.;  fouri(spec—i,NP,—i); // unscramble for(i=0; i<NP;i++){ thispec[i] spec [i] spec [i+NP]; spec [i+NP] =thi;  } for(i=0 ; i<NP; i++) printf(”hf %f °hf °hf °hf\n°,i/DT/NP/iOO.523,spec[2*i], spec [2*i+i] ,fid[2*i] ,fid[2*i+i]);  } void evolve_to_nextQ{ float time_remain=DT; float thn,phn,gam,squig; float cg,st,ct,sg,sp,cp,cs,ss; do{ if (dur >time_remain){ phase + curr_freq*DT;  82  dur DT; return; -=  } else{ phase += curr_freq*dur; time_remain dur; dur = -log((float) randomO/RAND_MAX)*TAUC; // do the jump, set the new curr_freq squig = (float)randomO/RAND_MAX*M_PI*2; II could be in any direction -=  II exponentially distributed gamma gain  =  —log((float) randomO/RAND_MAX)*DTH*M_PI/180.;  II get the new angles cg=cos(gam); sg=sin(gain); st=sin(thi); ct=cos(thi); sp=sin (phi); cp=cos(phi); ss=sin(squig); cs=cos(squig); phn = atan2(cg*st*sp—sg*(cs*ct*sp+ss*cp), cg*st*cp—sg*(cs*ct*cp—ss*sp)); ct=sg*cs*st+cg*ct; if (ct > 1 II ct < —1) fprintf(stderr,”ct is: °hf\n’,ct); thn = acos(ct);  thithn; phi=phn;  II  fprintf(stderr,”\n°hf 7,f °hf ‘/,f\n” ,thn,phn,squig,gam);  ct=ct*ct; curr_freq  =  DELTA/2.*(3*ct—1.+ETA*(1.—ct)*cos(2*phi));  } } while(O==O);  }  83  

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