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Solid state NMR investigations of protein based biomaterials: spider silk, recombinant spider silk proteins,… Katz, David Samuel 2010

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Solid State NMR Investigations of Protein Based Biomaterials Spider Silk, Recombinant Spider Silk Proteins, and Electrospun Recombinant Spider Silk Proteins by David Samuel Katz B.A. Reed College, 2006 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in The Faculty of Graduate Studies (Physics) The University of British Columbia (Vancouver) October 2010 © David S. Katz 2010 Abstract 13C Nuclear Magnetic Resonance was employed to investigate the structure of spider dragline silk, powdered recombinant major ampulate spidroin 1 (MaSp1) and 2 (MaSp2) that were produced in the milk of genetically engineered goats, and electrospun MaSp1. Cross polariza- tion spectra were used to assign secondary structures to the protein residues, and longitudinal relaxation measurements were used to investigate the molecular thermal motion. The crystalline regions of spider silk were found to exhibit nanosecond scale thermal mo- tion, subject to very rigid motional limits. The recombinant MaSp1 and MaSp2 were found to have very similar structures that exhibited abundant β sheet crystalline regions. Elec- trospun MaSp1 however appears to be highly disordered and is perhaps best characterized as denatured. These results are in contrast to previous findings of spider silk proteins in non-fiber states, where no appreciable crystalline component was observed, and appears to be inconsistent with previous Fourier transform infrared spectroscopy of similarly prepared samples. Reconsideration of the FTIR data however raises concerns about the interpreta- tion of those data, possibly explaining the disagreement. This work suggests that the lack of regular structure found in the electrospun MaSp1 is the cause of the very poor mechanical properties previously measured for this material. ii Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Nuclear Magnetic Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Zeeman Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 The NMR Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Classical Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Density Matrix Representation . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Rotating Frame Transformation . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.6 Advanced NMR Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.6.1 Chemical Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.6.2 Dipolar Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.7 Microscopic Description of Relaxation . . . . . . . . . . . . . . . . . . . . . . 16 2.7.1 Dipolar Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.1 Heteronuclear Decoupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Magic Angle Spinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3 Cross Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Electrospinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4 Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 iii 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.2 Secondary Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.1 α-Helix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2.2 β-Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.3 Silk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.3.1 Spider Silk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.3.2 Transgenic Spider Silk . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.3.2.1 FTIR Results of the Transgenic MaSp1 and MaSp2 . . . . . 39 5 Experimental Materials, Methods, and Results . . . . . . . . . . . . . . . . 42 5.1 Samples Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.2 Cross Polarization Experiments and Chemical Shift . . . . . . . . . . . . . . 43 5.3 Relaxation Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.4 Characterization of Secondary Structures . . . . . . . . . . . . . . . . . . . . 46 5.4.1 Alanine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.4.2 Glycine α Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.4.3 Glutamine α/β/γ Carbons . . . . . . . . . . . . . . . . . . . . . . . . 50 6 Spider Silk NMR Results and Analysis . . . . . . . . . . . . . . . . . . . . . 52 6.1 Alanine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 6.2 Glycine α Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.3 Glutamine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 7 Recombinant Mammalian Silk . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.1 MaSp1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.1.1 Alanine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.1.2 Glycine α Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7.1.3 Glutamine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7.1.4 Discussion of MaSp1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 7.2 MaSp2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 7.2.1 Alanine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 7.2.2 Glycine α Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 7.2.3 Glutamine and Serine α Carbons . . . . . . . . . . . . . . . . . . . . 69 7.2.4 Proline α and Serine β Carbons . . . . . . . . . . . . . . . . . . . . . 70 7.2.5 Glutamine β/γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 7.2.6 MaSp2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 7.3 Electrospun MaSp1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 iv 7.3.1 Alanine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 7.3.2 Glycine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 7.3.3 Glutamine β/γ Carbons . . . . . . . . . . . . . . . . . . . . . . . . . 75 7.3.4 Electrospun MaSp1 Conclusions . . . . . . . . . . . . . . . . . . . . . 76 8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 v List of Tables 4.1 Torsion angles for various secondary structures. . . . . . . . . . . . . . . . . 32 4.2 Mechanical properties of various man made materials and dragline silk. . . . 35 4.3 Breakdown by amino acid of N. clavipes dragline silk, MaSp1, and MaSp2. . 38 4.4 Mechanical properties of natural spider silk and various electrospun silks made from MaSp1 and MaSp2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.5 Secondary structure assignments from FTIR wavenumbers. . . . . . . . . . . 39 4.6 Reported wavenumbers from Figure 4.6 and estimates of actual wavenumbers which found using image analysis software. . . . . . . . . . . . . . . . . . . . 40 5.1 Chemical shifts for spider silk, MaSp1, MaSp2, and electrospun MaSp1. . . . 47 5.2 Known chemical shifts for amino acids important in spider silk and various secondary structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.3 Relaxation parameters for alanine α carbons. . . . . . . . . . . . . . . . . . . 48 5.4 Relaxation parameters for alanine β carbons. . . . . . . . . . . . . . . . . . . 49 5.5 Relaxation parameters for glycine α carbons. . . . . . . . . . . . . . . . . . . 50 5.6 Relaxation parameters for glutamine β/γ carbons. . . . . . . . . . . . . . . . 51 vi List of Figures 2.1 The precession of a magnetic moment about a static magnetic field. . . . . . 4 2.2 The energy levels of a 1 2 spin system. . . . . . . . . . . . . . . . . . . . . . . 5 2.3 A sample free induction decay. . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 The rotating frame transformation. . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 The dipolar interaction between two spins. . . . . . . . . . . . . . . . . . . . 15 3.1 A schematic of magic angle spinning. . . . . . . . . . . . . . . . . . . . . . . 24 3.2 A cross polarization pulse sequence. . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Components of an electrospinning apparatus. . . . . . . . . . . . . . . . . . . 29 4.1 A connection of two unspecified amino acids. . . . . . . . . . . . . . . . . . . 31 4.2 The structure of the β strand and β sheets. . . . . . . . . . . . . . . . . . . 33 4.3 The sequence of the MaSp1 protein. . . . . . . . . . . . . . . . . . . . . . . . 35 4.4 The sequence of the MaSp2 protein. . . . . . . . . . . . . . . . . . . . . . . . 36 4.5 A possible structure of spider dragline silk . . . . . . . . . . . . . . . . . . . 37 4.6 Analysis of MaSp1 FTIR results. . . . . . . . . . . . . . . . . . . . . . . . . 41 5.1 T1 experiment pulse sequence employing cross-polarization to study the lon- gitudinal relaxation of the 13C nuclei. . . . . . . . . . . . . . . . . . . . . . . 44 5.2 The cross polarization spectra for electrospun MaSp1, MaSp1, MaSp2, and spider silk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 6.1 The relaxation curve of the alanine α carbons in spider silk. . . . . . . . . . 53 6.2 Plot of correlation time versus 1 T1 for the alanine α carbon. . . . . . . . . . . 54 6.3 Single, double, and stretched exponential fits to the spider silk alanine β carbon relaxation data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.4 Single, double, and stretched exponential fits to the spider silk alanine α carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6.5 Plot of correlation time versus 1 T1 for the glycine α carbon. . . . . . . . . . . 57 vii 6.6 Multiple spectra from the spider silk room temperature T1 relaxation experi- ment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6.7 Single, double, and stretched exponential fits to the spider silk glutamine β/γ carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 7.1 Single, double, and stretched exponential fits to the MaSp1 alanine α carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 7.2 Single, double, and stretched exponential fits to the MaSp1 alanine β carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7.3 Single, double, and stretched exponential fits to the MaSp1 glycine α-C re- laxation data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.4 Multiple spectra from the MaSp1 T1 relaxation experiment. . . . . . . . . . . 64 7.5 Single, double, and stretched exponential fits to the MaSp1 glycine β/γ carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 7.6 Spectra of lyophilized gland silk (B) and lyophilized denatured silk (D), com- pared to MaSp1 (A) and MaSp2 (C) and electrospun MaSp1. Lyophilized spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 7.7 Single, double, and stretched exponential fits to the MaSp2 alanine α carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 7.8 Single, double, and stretched exponential fits to the MaSp2 alanine β carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 7.9 Single, double, and stretched exponential fits to the MaSp2 glycine α carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.10 The relaxation curve of the glutamine α carbons (and possibly serine α car- bons) in MaSp2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 7.11 The relaxation curve of the proline α carbons in MaSp2. . . . . . . . . . . . 71 7.12 Single, double, and stretched exponential fits to the MaSp2 glutamine β/γ carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 7.13 Single, double, and stretched exponential fits to the electrospun MaSp1 ala- nine α carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . 73 7.14 Single, double, and stretched exponential fits to the electrospun MaSp1 ala- nine β carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . 74 7.15 Single, double, and stretched exponential fits to the electrospun MaSp1 glycine α carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 7.16 Single, double, and stretched exponential fits to the electrospun MaSp1 glu- tamine β/γ carbon relaxation data. . . . . . . . . . . . . . . . . . . . . . . . 76 viii Acknowledgments While a thesis may only have one author, it is not an individual effort. Without the people behind me this work would never have been written. More than anyone, I owe thanks to my adviser, Carl Michal, who's patience with me may go down as an official miracle if he is ever (and deservedly) canonized. His insight into every aspect of this thesis was instrumental and I could not have hoped to have a better friend and mentor throughout this process. My peers helped me along this process as well. Jenny Chien-Hsin, who helped me work through the initial learning curve of NMR theory; Tom Depew, who taught me pretty much everything regarding how to actually run a spectrometer; Andy Reddin, who was always willing to lend me a pencil1, and a very special thanks to Clark Lemke, who gave me the motivation to graduate. I would also like to thank Ronald Dong; having a brilliant scientist sitting next to me defi- nitely helped me overcome more than one conceptual hurdle. Thank you Stephen Reinsberg for helping me convert on 4th and long. I would also like to thank my collaborators from the Advanced Fibrous Material Laboratory. Frank Ko made sure that this thesis got off the ground. It is a rare man that would trust a first year masters student from a different department after a single meeting with material as incredibly hard to acquire as Nexia's MaSp1 and MaSp2 powder. Adrienne Chang provided the most useful hour that a high school summer intern could possibly give when he taught me electrospinning and spun what would be my primary sample. I would also like to thank Heejay Yang, Victor Leung, and Steve Yeoh of the AFML. I would like to thank all of my friends; James and associates, Zac, Mike, my friends from Hillel, the crew at Ceili's, and the heathens (Reedies). You all made my life enjoyable over the past few years. Kaylie, your love and support has helped to keep me sane through these hard years. Thank you. Finally a huge thanks to my family for really helping me through all of this, my mom and dad for offering to drive me home from campus on cold and wet nights, my brother and sister in-law for motivation, my niece Rubi for so many hugs, and my nephew Avi for not kicking me in the head as hard as he can... too often. 1Willing and borrow may be slightly inaccurate, A more accurate acknowledgment would be thank you for not locking your desk at night. ix Chapter 1 Introduction The orb-weaving spider, Nephila clavipes produces a dragline silk that has a higher tensile strength than steel, and has a higher break energy than synthetic high performance fibers. Until recently the possibility of mass production of spider silk has been impossible due to the cannibalistic nature of spiders. Advances in genetic engineering have allowed for the production of the spider silk proteins without the need for spiders. Producing high performance fibers from these proteins is a challenge in its own right. This challenge is two fold. The first is the generation of fibers that have a similar protein secondary structure to those produced by spiders. The second challenge is finding a method of creating fibers with an aspect ratio comparable to the fibers produced by spiders. One method for creating fibers uses a process called electrospinning which violently whips a charged jet of polymer solution into nanofibers. This method had been known to produce fibers with extremely large aspect ratios, unfortunately the mechanical properties of silk fibers created by this method do not compare with those produced in nature. Solid state NMR is a useful technique for the study of both the spider silk proteins and the electrospun fibers to find out how these fibers are different from those produced by a spider. Because NMR allows us to probe the local nuclear environment, we are able to use it to look at characteristics such as molecular orientation, dynamics, and conformation. One important measurement that can be taken in NMR is finding the longitudinal relaxation time. This relaxation time is caused by fluctuations in the magnetic interactions between nuclei that are a result of thermal motion. Knowing the dominant interaction can yield the frequency of the thermal fluctuations, or the correlation time. These measurements thus 1 can be used to characterize molecular motion, to differentiate structural regions, and to find order parameters that describe motional restrictions. In similar materials, it is possible to use changes in relaxation time to see if there are changes in the order parameter, which can help tell us which system has more structure. This thesis begins with an introduction to NMR in Chapter 2. Chapter 3 will present some of the experimental tools used in NMR, including a derivation relating thermal motion to the longitudinal relaxation time and a brief introduction to the process of electrospinning. Chapter 4 will be devoted to introducing protein structure, the current understanding of spider silk, and some of the past work on recombinant spider silk proteins. Chapter 5 provides an overview of the specific experimental techniques used, the materials being studied, how they will be analyzed, and the presentation of the experimental results. Chapter 6 covers the analysis of the NMR experiments on spider silk and Chapter 7 covers the analysis of results from the NMR experiments on the recombinant proteins in both powder and electrospun fiber form. Chapter 8 concludes the thesis and suggests several possible avenues of future research. 2 Chapter 2 Nuclear Magnetic Resonance Nuclear magnetic resonance (NMR) is a phenomenon that is exhibited by nuclear species with an intrinsic nuclear magnetic moment. This occurs as a result of the nucleus containing an odd number of baryons. It is possible to study these nuclei and their chemical environment by aligning these moments in a magnetic field and observing their response to radio frequency pulses. Levitt [1] provides a broad, less mathematically oriented overview of NMR and can act as an excellent introduction to the field for an undergraduate interested in NMR or for researchers from less analytical fields. A more mathematically rigorous treatment of the material can be found in Abragam [2] or Slichter [3]. The book by Duer [4] provides an excellent middle ground that manages to cover the subject with mathematical rigor without ever losing the perspective of experimental application and should be the first source for any experimentalist with a solid mathematical background interested in NMR. Much of this chapter is drawn from various treatments of the subject by these authors. 2.1 Zeeman Interaction The starting point in understanding NMR is understanding the effect that a static magnetic field, Bo has on a nucleus. The nucleus interacts with magnetic fields via its magnetic moment, which is given as µ = γI, (2.1) 3 Figure 2.1: The precession of a magnetic moment about a static magnetic field. where µ is the magnetic moment and I is the nuclear spin angular momentum. γ is the gyromagnetic ratio of the nucleus and is unique for each nuclear species. An external field has the effect of exerting a torque on the nucleus. The torque is given as the time derivative of the nuclear spin T = dI dt . (2.2) We can further note by elementary physics that the torque will be the cross product of the external field and the magnetic moment, which gives T = µ×Bo. (2.3) After some rearranging, the above three equations can be combined to give the classical equation of motion for a nuclear spin; dµ dt = γµ×Bo. (2.4) The solution to this equation shows that the magnetic moment precesses about the magnetic field, as shown in Figure 2.1. The rate of precession is called the Larmor frequency, and is equal to 4 Figure 2.2: The energy levels of a 1 2 spin system. ω = γB0. (2.5) The quantum mechanical description of this system is found by writing the Hamiltonian of the system in terms of quantum mechanical spin operators. For example, ~I becomes ~Î. The Hamiltonian for the Zeeman field, ĤZ , is therefore ĤZ = −Bo · µ̂. (2.6) By convention, the static magnetic field is assigned to the z-axis. This convention is intuitive with the fact that most NMR magnets use a vertical field. Substituting in the relation for the magnetic moment we get ĤZ = γ~BoÎz (2.7) The case of the ±1 2 spin system is the most trivial, as it only has two states, shown in Figure 2.2, and one of the most common in NMR experiments of biological systems, as it applies to both 13C and protons. Using the possible spin values of ±1 2 for Îz in Equation (2.7) we get the possible energies of a nucleus in this system, which are; E±1/2 = ±1 2 γ~Bo. (2.8) In this case, the energy separation between the two states can be shown to be: ∆E = ~γB0 = −~ωo. (2.9) As NMR experiments typically deal with extremely large numbers of particles, we can apply statistical mechanics in all cases relevant to this work. A collection of interacting nuclei, 5 known as a spin ensemble, with the Zeeman energy states given above will have a thermal equilibrium population distribution given by the Boltzmann distribution; p±1/2 = exp−E±1/2/kBT Z , (2.10) where p± is the probability of a nucleus being in state up (+) or down (−), kB is the Boltzmann constant, T is the temperature and Z is the partition function given by the equation; Z = ∑ m exp−Em/kBT . (2.11) 2.2 The NMR Experiment The typical NMR experiment observes the response of a system of nuclei after it is subjected to a radio frequency (rf) magnetic pulse. The pulse is created in a coil surrounding the sample by having an AC current applied to it. For there to be a noticeable effect from the rf pulse, the frequency of the pulse must be on or close to resonance; the Larmor frequency. This requirement is extremely fortunate, as it allows for easy isolation of different species of nuclei. The classical formula for spins in magnetic fields can be altered into a description of the total magnetization of a sample: dM dt = γM×B. (2.12) This is known as the Bloch equation, and is the classical representation of a nuclear spin system. This equation, which is in fact a set of three equations, describing the time dependent change of the magnetization along the X, Y, and Z axes, provides a simple, intuitive, and classical description of the magnetization sidestepping completely any involvement from quantum mechanics. This formulation of the Bloch equation neglects relaxation. After the initial RF pulse, the oscillating magnetization induces a voltage in the RF coil. This voltage produces a signal known as the free induction decay (FID) of the magnetization of the system. An example of an FID can be seen in Figure 2.3 These signals are mixed down by a quadrature receiver with the rf-pulse frequency ωrf . This mixing down of the frequency reduces the demand on the electronics and the amount of 6 Figure 2.3: A free induction decay of a sample in a poorly shimmed magnet courtesy of GyroMagician from the Wikipedia commons. data needed. The range of frequencies observed in the sample are dependent on various environmental factors of the nuclear spins, such as electronic structure and spin couplings (these will be detailed in a later section). The frequency range of Ω0 = ω0 − ωrf is typically a few hundred kHz at most. After quadrature detection, the FID consists of two signals of the form sR(T ) ∝ ∑ j cos(Ωjt) exp −t/T j2 (2.13) sI(T ) ∝ ∑ j sin(Ωjt) exp −t/T j2 (2.14) These signals are superpositions of signals with various frequencies represented by Ωj. These signals can be combined into a single complex time dependent function s(t), with sR repre- senting the real component, and sI representing the imaginary component1. This yields the function s(t) = sR(t)+isI(t). Doing this distinguishes the frequencies that are faster than the transmitter frequency from those slower than the transmitter frequency. The time domain signal can be transferred to a frequency space by conducting a Fourier transformation S(Ω) = ˆ ∞ 0 s(t) exp−iΩt dt. (2.15) This yields S(Ω) = ∑ j 1 T j2 (1/T j2 ) 2 + (Ω− Ωj)2 − i Ω− Ωj (1/T j2 ) 2 + (Ω− Ωj)2 (2.16) 1Although this is more of convention, there is no reason that sR could not be the imaginary component other than the notation could get confusing 7 The real component is the absorption and the imaginary is the dispersion component of the Lorentzian peak. The rate of the decay affects the peak width, where slower decay sharpens the peak. 2.3 Classical Relaxation Relaxation is the process in which an excited system moves back to thermal equilibrium or a stable local minima energy configuration. In NMR, the system referred to in relaxation is the net magnetization. Practically speaking, relaxation is measured by the time taken for the magnetization to revert to thermal equilibrium after a resonant RF pulse. There are two parameters that characterize the timescales for nuclear excitation to relax back into thermal equilibrium. The first is the longitudinal relaxation, T1. The second is the transverse relaxation, T2. The relaxation of magnetization can be described classically by adding relaxation terms to the Bloch Equations, which can then be expressed as; Mx(t) = Mx(0) cos(ωot)e −t T2 (2.17) My(t) = Mx(0) sin(ωot)e −t T2 (2.18) Mz(t) = M0 + (Mz(0)−Mo)e −t T1 , (2.19) where M0 is the equilibrium magnetization. Using this, the Bloch Equations become; dM dt = γM×B−R(M−M0), (2.20) where R = ( 1 T2 0 0 0 1 T2 0 0 0 1 T1 ) . (2.21) These relaxation times T1 and T2 are linked to deeper quantum mechanical processes that are discussed in a later section. 2.4 Density Matrix Representation The density matrix representation is a simple way to represent the state of a sample that is often more convenient than using an ensemble of single quantum states. Representing 8 a collection of spins, where each has a probability of being in state ψ by a superposition state Ψ requires one to account for each spin individually. This can quickly degenerate into extremely messy summation manipulations. The expectation value for some operator  in the spin ensemble must be summed over all possible states: <  >=< Ψ|Â|Ψ >= ∑ ψ pψ < ψ|Â|ψ > (2.22) Representing the spin states in terms of basis states simplifies the above spin ensemble with possible states ψ = ∑ i cψiφi (2.23) where φi are the basis states. This expands the expectation value to: <  >= ∑ ψ pψ ∑ i,j c∗ψicψj < φi|Â|φj > (2.24) This approach is advantageous because the matrix elements of  in this basis are independent of the specific state of Ψ. If we define the state dependent coefficients ∑ ψ pψc ∗ ψicψj as the components ρji of another matrix, we can see that the expectation value of  becomes <  >= ∑ i,j ρjiAij (2.25) where Aij are the matrix elements of the operator Â. ρji are the matrix elements of what is called the density matrix, ρ. The density matrix corresponds to an operator who's elements can be shown to be ρ̂ = ∑ i pi|φi >< φi|. (2.26) At thermal equilibrium, the density matrix takes the form ρ̂ = 1 Z exp−Ĥ/kT (2.27) where the partition function is Z = Tr(exp−Ĥ/kT ) (2.28) For example, we can use this to find an approximation of the thermal equilibrium density matrix for the Zeeman interaction. Recalling that the Hamiltonian for this interaction is Ĥ = −γ~ÎzB0 = ~ω0Îz (2.29) 9 We can then approximate the density matrix to first order as; ρ̂eq = 1 Z ( 1 + ~ω0 kT Îz ) , (2.30) which can be treated as; ρ̂eq = 1 Z ~ω0 kT Îz, because the 1 does not lead to any observables. This is a valid approximation for the field strengths and temperatures used in typical NMR experiments. The equation describing the evolution of the system is the Liouville-von Neumann equation, which is derived from the Schrodinger equation and is: dρ̂ dt = −i[Ĥ, ρ̂]. (2.31) The solution to this is; ρ̂(t) = Û(t, 0)ρ̂(0)Û †(t, 0), (2.32) where ρ̂(0) is the initial density operator and Û(t, 0) is the time evolution operator. The time evolution operator is also called the propagator and is defined for the general time-dependent Hamiltonians as; Û(t, 0) = µ̂T exp− i ~ ´ t 0 Ĥ(t ′)dt′ , (2.33) where T̂ is the Dyson time ordering operator. 2.5 Rotating Frame Transformation The involvement of oscillating components of spin operators in static magnetic fields mean that NMR experiments are almost always simplified by working within the rotating frame. The rotating frame rotates at the applied rf-frequency about the z-axis of the lab frame as defined to be in the direction of the magnetic field. The frame transformation is a linear transformation of the lab frame using the rotation operator R̂ = exp−iφÎz (2.34) 10 Figure 2.4: The rotating frame (x′, y′, z′): A frame taken to precess around the static field, B0 at with a frequency of ωrf . In the rotating frame the spins evolve according to the effective field which includes a −ωrf ẑ term arising from the frame transformation. which can be used to generate a rotating frame Hamiltonian which takes the form; ĤR = R̂−1ĤR̂− ωrf Îz. (2.35) In an NMR experiment, the pulses are applied on or near resonance, meaning that ωrf ≈ ωo. The frame rotates at the Larmor frequency, which means that from this perspective the spin vector does not rotate around the Z axis. This means that the terms associated with the Zeeman terms are effectively greatly reduced. Furthermore, the effective field Beff is that of the pulse B1 in the rotating frame, shown in Figure 2.4. 2.6 Advanced NMR Interactions There are a wide variety of interactions that affect an NMR active sample. These interactions are driven by various electromagnetic fields that the various sample nuclei are exposed to. The simplest one is the interaction with the Zeeman field. More complicated ones are a result of shielding from the electron clouds and various nuclear magnetic couplings. Two of these interactions are relevant for context of this work. 11 2.6.1 Chemical Shift When a magnetic field is applied to an atom, the electronic structure does not sit on the sidelines. This field has a purtabitory effect that alters ever so slightly the effective magnetic field at the nucleus. The strength of the change in the field is determined by the chemical environment of the atom, specifically the the strength, location, distance, and type of bonds it shares with its neighbors. This phenomenon is known as chemical shielding. The chemical shielding of a nucleus changes the local magnetic field. This in turn changes the frequency of the nuclear precession. This phenomenon is known as chemical shift and the study of it is one of the primary methods of characterization in this thesis. The chemical shielding is described by the chemical shielding tensor, σcs (to be referred to as σ for this section only). The non coordinate specific elements of this second rank tensor describe the three components of the magnetic field generated when a magnetic field is applied. The Hamiltonian will be: Ĥ = Ĥo + Ĥcs = γ(̂I ·Bo − Î · σ ·Bo). (2.36) In the case of the field aligned along z, the resulting field will be given by Equation (2.37). As will be shown, the x and y components can be ignored if σ  1. This approximation is called the secular approximation, and can be shown with the use of average Hamiltonian theory. This approximation can also be seen to be true by looking at the first order change in magnitude to the magnetic field. The magnetic field as a result of the shielding will be: B = (−Bzσzx,−Bzσzy, Bz(1− σzz)). (2.37) The magnitude of the magnetic field will therefore be: B2 = B2z (σ 2 zx + σ 2 zy + (1 + σzz) 2) = B2z (σ 2 zx + σ 2 zy + σ 2 zz − 2σzz + 1). (2.38) Assuming that each component of the chemical shielding tensor is much smaller than one (the change in frequency by chemical shift is measured in parts per million of the Larmor frequency), then to the first order, the magnitude of the magnetic field is: B ≈ Bz(1− σzz). (2.39) For this reason, we can ignore the transverse components. From here we can rewrite the 12 Hamiltonian as: Ĥo + Ĥcs = γ(1− σzz)BoÎz = ωo(1− σzz)Îz. (2.40) By inspection we can see that the chemical shift frequency is: [5] ωcs = −ωoσzz. (2.41) We can take this further by noting that σzz = b T o σbo, (2.42) where bo is the unit vector in the direction of the magnetic field. Equation (2.42) holds true regardless of the choice of coordinate system. Furthermore, because the term σzz is on the diagonal, the only relevant components of the shielding tensor after transformation would have to be symmetric. This means that it is possible to choose a coordinate system that would diagonalize the shielding tensor. In this coordinate system the magnetic field direction is specified by polar and azimuthal angles θ and φ. bPASo = (sin θ cosφ, sin θ sinφ, cos θ), (2.43) The chemical shift frequency contribution can be written in terms of the PAF components: ωcs = −ωo(σPASxx (sin θ cosφ)2 + σPASyy (sin θ sinφ)2 + σPASzz cos2 θ). (2.44) By making the following substitutions: σPASxx = σ PAS x + σiso (2.45) σPASyy = σ PAS y + σiso (2.46) σPASzz = σ PAS z + σiso, (2.47) where the anisotropic components of the diagonal are σPASα and the isotropic component is: σiso = 1 3 (σPASxx + σ PAS yy + σ PAS zz ), (2.48) the chemical shift frequency can be reduced to: ωcs = ωiso + ωaniso = −ωoσiso − 1 2 δ(3 cos2 θ − 1− η sin2 θ cos(2φ)). (2.49) 13 The two new parameters are the asymmetry parameter: η = σy − σx σz = ωy − ωx ωz (2.50) and the anisotropy parameter: δ = ωz = −ωoσz. (2.51) The total frequency of the sample will be equal to the chemical shift frequency plus the Larmor frequency. The chemical shift is not however, measured in absolute terms because of the dependence on the strength of the external magnetic field, but in the relative terms of parts per million. The orientation dependence of the chemical shift does not present a problem in liquids NMR because the random motion averages out the anisotropy. However, in solids molecular motion is not fast enough to do this and as a result in the typical solid, a spectrum of all orientations will appear, and as a result the spectrum will experience line broadening. The solution to this will be dealt with later when we work with magic angle spinning. 2.6.2 Dipolar Coupling In a collection of nuclei, the nuclear magnetic moments of the spins interact with each other through the dipolar interaction. In effect the local field of each spin creates a local magnetic field which interacts with the surrounding spins. This interaction is classically analogous to the interaction of bar magnets close to each other. In liquids, this phenomenon is averaged to its isotropic value of 0 through molecular tumbling. However, in a solid this is not the case and dipolar coupling can be one of the major causes of solid state line broadening. The range of this interaction is effectively very short, with its range dropping off as that of a magnetic dipole; 1 r3 . In addition, the orientation of the molecule is of key importance as seen in Figure 2.5. The classical energy between two magnetic dipoles µ1 and µ2 is given by: U = ( µ1 · µ2 r3 − 3(µ1 · r)(µ2 · r) r5 ) µ0 4pi . (2.52) We can use this to find the analogous quantummechanical Hamiltonian by using the quantum 14 φθ r z x y I S B0 Figure 2.5: The dipolar interaction between two spins I and S; as a result of the coupling of the magnetic fields that are produced by their dipole moments. θ and φ are the polar and azimuthal angles of the interaction vector r with respect to the static field, B0. moment of µ̂1 = γ1~Î and µ̂1 = γ2~Ŝ in the above equation. This yields: Ĥdd = −µ0 4pi γIγS~( Î · Ŝ r3 − 3(̂I · r)(Ŝ · r) r3 ). (2.53) This can be rewritten in spherical coordinates with expanded scalar products as: Ĥdd = d(A+B + C +D + E + F ), (2.54) with A = ÎzŜz(3 cos 2 θ − 1) (2.55) B = −1 4 [Î+Ŝ− + Î−Ŝ+](3 cos2 θ − 1) (2.56) C = 3 2 [ÎZŜ+ + Î+Ŝz] sin θ cos θ exp −iφ (2.57) D = 3 2 [ÎZŜ− + Î−Ŝz] sin θ cos θ expiφ (2.58) E = 3 4 [Î+Ŝ+] sin 2 θ exp−2iφ (2.59) F = 3 4 [Î−Ŝ−] sin2 θ exp2iφ, (2.60) where the I± and S± represent the raising and lowering operators acting on the spins I and 15 S and d is the dipolar coupling constant defined as d = −µo 4pi γIγS~ r3 . (2.61) Dipolar couplings can be split into two logical subgroups; dipolar couplings between like spins, known as homonuclear couplings, and between different spins, heteronuclear dipolar couplings. The Hamiltonian for both kinds of dipolar couplings are simplified in the rotating frame. This happens because the Zeeman interaction is so much larger than the dipolar interactions that to first order, only the components that commute with Ĥz matter. The simplified Hamiltonians become Ĥhomodd = −d · 1 2 (3 cos2 θ − 1)[3ÎzŜz − I · S] (2.62) Ĥheterodd = −d(3 cos2 θ − 1)ÎzŜz. (2.63) 2.7 Microscopic Description of Relaxation While the Bloch Equations are useful for providing insight into the consequences of relax- ation, they provide very little understanding of the physical causes of relaxation. To acquire this, a deeper understanding into the mechanisms of relaxation must be understood. The relaxation of a spin 1 2 nucleus is caused by fluctuations in the various NMR interactions experienced by the nuclei such as chemical shift anisotropy and dipolar couplings. These fluctuations are caused by thermal motion, whose frequency, range of motion and type of fluctuation determine the rate of relaxation. The two above interactions are both orientation dependent and so any motion of the nuclei results in a contribution of time dependence to the interaction. The time dependence of the local fields is described by a correlation function. This correlation function describes how much the local magnetic field will evolve from time t to time t+ τ and can be represented by the ensemble average: G(τ) = B(t)B(t+ τ), (2.64) where the overbar represents the average over time t within the system. G(τ) represents the the likelihood that the magnetic field will be the same at some later point in time. For random motions, it is expected that G(τ) will monotonically decay to 0. The quantum mechanical Hamiltonian describing the Zeeman field and a second arbitrary 16 interaction, α is given by: Ĥ = Ĥz + Ĥα. (2.65) The second Hamiltonian is responsible for the random fluctuation that lead to relaxation. The density operator is then described in the rotating frame by the Liouville von Neumann equation: dρ̂ dt = −i[Ĥα, ρ̂]. (2.66) From this, we can solve for the time dependence of ρ̂(t) through integration and use of the Magnus expansion ρ̂(t) = ρ̂(0)− i ˆ t 0 [Ĥα(t′), ρ̂(0)]dt′ − ˆ t 0 dt′ ˆ t′ 0 [Ĥα(t′), [Ĥα(t′′), ρ̂(0)]]dt′′ + ... (2.67) A small t is shown so that the second order description is enough to describe the density operator. The first order term drops out because the average is 0 because random fluctuations make all orientations equally likely. We can describe the Hamiltonian Ĥα as a summation of the form: Ĥα = ∑ m FmT̂me iωt, (2.68) where the T̂m are the spin operators and the exponential factor is a result of the rotating frame transformation on the spin operators. The Fm are the orientation dependent part of Hα, which fluctuate due to thermal motion. We define the correlation function to be: G(τ)mm′ = Fm(t)F † m′(t+ τ). (2.69) Experimentally, the correlation function is well represented by an exponential function, while it is not limited to this form in theory, in general practice it is asumed to be: G(τ) = Ce− τ τc . (2.70) The value of the constant C is determined by the type of interaction(s) dominating the relaxation process, and the value τc is the correlation time, which represents the timescale of the intermolecular motion. Noting that in practice: Fm(t) = F † m(−t), (2.71) 17 and substituting in the function for Ĥα from Equation (2.68) into Equation (2.67) we get ρ̂(t)− ρ̂(0) = [T̂m, [T̂ †m, ρ̂(0)]] ˆ t 0 dt′ ˆ t′ 0 Gmm′(t ′ − t′′)ei(ωmt′−ωm′ t′′)dt′′, (2.72) Often the only significant contributions to d̂ρ dt are when m = m′. Making a variable change of: τ = t′ − t′′. (2.73) we get: ˆ t 0 dt′ ˆ t′ 0 Gmm′(t ′ − t′′)ei(ωmt′−ωm′ t′′)dt′′ = ˆ t 0 (t− τ)Gmmeiωmτdτ. (2.74) At this point, we introduce the spectral density J(ω) which is the Fourier transform of the correlation function. It represents the allowable frequencies for energy transmission and characterizes the energy spectrum associated with thermal motion. Assuming an exponential growth function, the Fourier transform results in a Lorentzian: J(ω) = C ˆ ∞ −∞ e− τ τc e−iωτdτ = C 2τc 1 + (τcω)2 . (2.75) We then note that with regards to Equation (2.74) that the timescale t is much greater than τ . This also implies that the contributions outside of the bounds of the integral are negligible, and the bounds can be extended to get: ˆ t 0 (t− τ)Gmmeiωmτdτ = ˆ ∞ 0 tGmme iωmτdτ = tJmm(ωm). (2.76) Noting that ρ̂(t)−ρ̂(0) t = d ˆρ(t) dt because t is small enough that the density operator undergoes small changes, we get the master equation: dρ̂ dt = [T̂m, [T̂ † m, ρ̂]]Jmm(ωm) (2.77) We can determine the evolution of any physical observable using: d dt < Q̂ >= Tr(Q dρ̂ dt ) = ∑ m Tr(Q̂[T̂m, [T̂ † m, ρ̂])Jmm(ωm). (2.78) 18 By substituting in ρ̂ = ρ̂ − ρ̂eq to account for the initial thermal equilibrium value of the density operator we get: d dt < Q̂ >= ∑ m Jmm(ωm)(< [[Q̂, T̂m], T̂ † m] > − < [[Q̂, T̂m], T̂ †m] >eq). (2.79) We can use the above to derive the longitudinal relaxation time, T1, by inserting the observ- able of the longitudinal magnetization of Îz. We can then use the master equation to relate the T1 to the correlation time. 2.7.1 Dipolar Relaxation The primary mechanism of relaxation relevant to this work is dipolar coupling. By reworking the dipolar Hamiltonian from Equation (2.53) into a form suitable for relaxation in terms of Fm and T̂m we can apply the results of the previous section. Fm are the spatial functions that fluctuate randomly which results in an exponential correlation function. The functions for Fm are: F0 = √ 3 2 (cos2 θ − 1) (2.80) F±1 = ∓3 sin θ cos θ exp±iφ (2.81) F±2 = 3 2 sin2 θ exp±2iφ . (2.82) The spin operators for T̂m are the spherical tensors: T̂0 = 1√ 6 (3ÎzŜz − Î · Ŝ) (2.83) T̂±1 = ∓1 2 (αŜz + ÎzŜ±) (2.84) T̂±2 = 1 2 αŜ±. (2.85) From this we get the dipolar Hamiltonian in the form of: Ĥd = −µ0 4pi γIγs~ r3IS +2∑ −2 Fm(θ, φ)T̂m(Î , Ŝ), (2.86) where I and S represent different spins. The derivation that follows only applies to systems where both spins are 1 2 which within the context of this thesis of only using hydrogen and 19 carbon, is true. It is worth noting that in relaxation studies, the non secular terms from the dipolar Hamiltonian Equations (2.56-2.60) are important. Using this Hamiltonian with the observables Îz and Ŝz the longitudinal magnetization with Equation 2.86 one obtains two coupled expressions of the form: d dt 〈Îz〉 = −RI(〈Îz〉 − 〈Îz〉eq)−RIS(〈Ŝz〉 − 〈Ŝz〉eq) (2.87) d dt 〈Ŝz〉 = −RIS(〈Îz〉 − 〈Îz〉eq)−RS(〈Ŝz〉 − 〈Ŝz〉eq). (2.88) The Rα represent rates. The longitudinal relaxation time for I is T1 = 1RI . The term RIS represents cross relaxation between the I and S spins. The relationships between Rα and the correlation time τc are: RI = 1 10 (µ0 4pi ) γ2Iγ2S~2 r6IS τc ( 3 1 + (ωIτc)2 + 1 1 + ((ωI − ωS)τc)2 + 6 1 + ((ωI + ωS)τc)2 ) (2.89) RIS = 1 10 (µ0 4pi ) γ2Iγ2S~2 r6IS τc ( 1 1 + ((ωI − ωS)τc)2 + 6 1 + ((ωI + ωS)τc)2 ) . (2.90) While this result only describes uniform isotropic motion, it is possible to gain a general understanding of the motion by looking at the magnetic field dependence of the T1. As can be seen from Equation (2.89) when τcωI  1, representing the fast motion regime where a short τc implies fast motion, Equation (2.89) becomes: RI ≈ (µ0 4pi ) γ2Iγ2S~2 r6IS τc. (2.91) Likewise, in the slow motion limit where τcωI  1, we see Equation (2.89) become: RI = 1 10 (µ0 4pi ) γ2Iγ2S~2 r6IS 1 τc ( 3 ω2I + 1 (ωI − ωS)2 + 6 (ωI + ωS)2 ) . (2.92) Because RI is 1T1 , and ωx = −γxB0, and the fact that in most cases the correct prefactor will be unknown, we have T fast1 ∝ 1 τc (2.93) T slow1 ∝ τcB20 . (2.94) So for motion in the fast regime the relaxation time scales independently of the magnetic 20 field, and inverse to the correlation time, while for the slow limit the relaxation time scales proportionally to the correlation time and to the magnetic field squared. Even if motion is not in either limit, we can further refine this by noting that a stronger relationship to the magnetic field means that the correlation time is longer. The spectral density used above represents an ideal case where there is a single correlation time undergoing isotropic motion. In reality this is quite rare with macromolecules. In large molecules such as the ones that are the subject of this thesis, there is more likely to exist a distribution of correlation times. How the correlation times are distributed has a significant effect on the spectral density. One of the most successful spectral density distributions used to interpret relaxation experiments in solids is the Davidson-Cole distribution. This distribution density is given by [6] : ρ(τ, η, σ) = sin(σpi) pi ( 1 τ/η − 1 )σ , (2.95) where ρ is the correlation time distribution, τ is the correlation time, η determines the distribution center, and σ determines the distribution width and ranges from 0 to 1, with a value of 1 resulting in a width of 0. This distribution has a spectral density of: JDC(ω, τ, σ) = 2 ω sin(σ arctan(ωτ)) (1 + ω2τ 2)σ/2 (2.96) A second and simpler option to use a mean correlation time. The advantage of this is that it can be treated as a single correlation time which reverts back to Equation (2.89) reducing the number of unknowns by 1. This makes it easier to solve for the correlation time. However, as a result of this approximation, there is a significant loss of information. The first piece of information lost is the width of the correlation time distribution. It will not be known if the motion is confined to a single correlation time for the entire system, or a very wide range that could extend well over an order magnitude. The second piece of information lost is how far from the actual center of the distribution the average correlation time is. This is because the Davidson Cole distribution is asymmetric, so the mean does not actually correspond to the distribution 'center' parameter η discussed in Equation 2.95. However even with this averaged assumption, this still has not taken into account motional restrictions. For a single correlation time undergoing anisotropic motion, the spectral density 21 can be represented through a model free approach by the function [7]: J(ω) = 2 5 ( S2τM 1 + (τMω)2 + (1− S2)τ 1 + (τω)2 ) , (2.97) with τ−1 = τ−1M + τ −1 c , (2.98) where τM represents the overall molecular tumbling, τc represents the internal molecular vibrations, and S is a generalized order parameter which measures the degree of spatial restriction of the motion and ranges from 0 (no restrictions) to 1 (completely restricted). For cases where the overall motion is relatively slow compared to the internal motion such that τM  τc Equation (2.97) reduces to J(ω) = 2 5 ( S2τM 1 + (τMω)2 + (1− S2)τc 1 + (τcω)2 ) . (2.99) Furthermore, if the overall molecular motion is relatively static and the intermolecular motion is fast such that following conditions, τMω  1, τcω  1, and S2τMω2  (1−S2)τc 1+(τcω)2 , hold true then Equation (2.99) can be further reduced into J(ω) = 2 5 (1− S2)τc 1 + (τcω)2 . (2.100) This result, along with that for the mean relaxation time, means that we can replace the spec- tral density and T1 of Equation (2.89) to develop a rough idea of the scale of the correlation time and order parameter within a protein. 22 Chapter 3 Experimental Techniques One advantage of NMR is that there are literally hundreds of various tools and techniques to probe the molecular structures of matter and improve spectrum resolution. These range from various pulse sequences, magnetic field corrections (a process called shimming), to spinning the sample extremely fast. The following contains the NMR techniques relevant to this thesis. In addition, a process used to make nanofibers known as electrospinning will be described at the end of the section. 3.1 Heteronuclear Decoupling Dilute spins near abundant spins such as the proximity of the dilute 13C to the highly abundant 1H in organic materials causes a broadening of spectral lines. This can reduced through heteronuclear decoupling, a technique that applies high power rf irradiation to the abundant spin channel during acquisition of the target observation channel. The high power irradiation causes the abundant spins to undergo transitions at a rate determined by the rf amplitude. Protons then have a time averaged dipolar coupling contribution of zero because the spin quantum number oscillates between ±1 2 . This time averaging of the proton spin states eliminates the dipolar contribution to the 13C [8]. 23 Figure 3.1: A schematic of magic angle spinning. 3.2 Magic Angle Spinning Magic angle spinning (MAS) is a routine, simple, and extremely effective technique used in solid-state NMR experiments that effectively removes broadening from chemical shift anisotropy as well as helping in the removal of heteronuclear dipolar couplings. It is also effective for reducing the effects of quadrupolar coupling and at high enough spinning fre- quencies, it is effective for removing homonuclear dipolar couplings. An observant reader will notice that the the majority of the interactions that MAS affects are ones that do not affect liquid NMR. This is because MAS in some ways mimics the rapid isotropic tumbling of the molecules in a solution. This tumbling averages the molecular orientation dependence of the transition frequencies to zero. Magic angle spinning replicates this phenomenon by rotating the sample along an axis at a magic angle that averages out isotropic effects. As noted in the previous chapter, there are many molecular orientation dependent interactions of the form 3 cos2 θ− 1, where θ is the angle of the orientation of the interaction tensor. In a powder sample, θ takes on all possible values because all molecular orientations are represented in a random distribution. If the sample is spun around an angular axis, θR off of the applied field, then θ will vary with time as the molecules rotate around the axis. The average orientation dependence of the interaction will then be < 3 cos2 θ − 1 >= 1 2 (3 cos2 θR − 1)(3 cos2 β − 1) (3.1) 24 π 2 CP CPC 13 H1 Figure 3.2: A cross polarization pulse sequence. The first block represents a pi 2 pulse. The blocks labeled CP the cross polarization pulses. where β = θR − θ. Because θ is time dependent, so is β. However, the angle of rotation can be chosen as an experimental parameter. When θR is set to be 54.74o, then the strength of the interaction will be averaged to zero. A schematic of a MAS system can be seen in Figure 3.1 [4]. 3.3 Cross Polarization Cross polarization (CP) sequences are a crucial part of techniques used to study biological materials. An important element in probing these materials via NMR often lies in performing NMR experiments on the carbon atoms. The NMR active component, 13C, has a natural abundance of slightly above 1.1 percent making the signal to noise ratio very low. One way to increase the signal to noise is to increase the amount of 13C within the sample by doping it with 13C enriched material. However, this is often not possible or practical. An easier way to increase the signal to noise is to use a cross polarizing pulse sequence. In a CP sequence, the energy gap for 13C within the sample is made to be the same as that of 1H. This allows magnetization to be transferred from the abundant nuclei to the dilute nuclei that are being observed. Cross polarization is not limited to 1H/13C nuclei, any abundant nucleus with a high γ and short T1 in close proximity to the dilute target could be used. 25 The pulse sequence used is shown in Figure 3.2, and begins with a pi 2 pulse to the 1H to create -y axis magnetization in the 1H rotating frame. After this, an RF cross polarization (CP) pulse is applied. This pulse is resonant and directed along the -y axis which locks the spins onto the axis. The effect of this is the creation of a quantum environment similar to that of the Zeeman static field. The energy gap for this new state is ∆EH = ~γHBH where BH is the strength of the RF magnetic field applied in the pulse. Simultaneously to this pulse, a CP pulse is applied to the carbon nuclei. The resulting energy gap for the 13C is ∆EC = ~γCBH . Under the condition BH = γC γH BC (3.2) we get ∆EC = ∆EH . (3.3) This matching of the energy level separation of the rotating frame spin states is called Hartman-Hann matching. This condition allows a transfer of magnetization from the protons to the 13C nuclei. This transfer is mediated through mutual spin flips via the heteronuclear dipolar interaction between the protons and carbon nuclei. The Hamiltonian for this system is Ĥ = ĤZ + ĤHH + ĤHC + ĤCC + Ĥ x pulse. (3.4) However, because the 13C is so dilute, we can ignore its homonuclear dipolar interaction. Moving into the rotating frame, the Zeeman interaction term vanishes as well. It can be shown that in the rotating frame, the Hamiltonian becomes Ĥrot = ĤHH + ĤHC + Ĥ x pulse,rot (3.5) where Ĥxpulse,rot = ω H 1 ∑ i ÎHiz + ω C 1 Ŝ C x (3.6) where the subscript i represents the ith proton associated with a 13C and ωH/C1 = γH/CBH/C . The next step from here is to do a further frame transformation into what is termed the toggling frame or interaction representation. The toggling frame is an extension by analogy of the rotating frame where the applied pulse in the rotating frame is removed through a second rotation transformation. This works in the same way that adopting a frame rotating around the Zeeman axis at the Larmor frequency, the toggling frame rotates about the applied field in the rotating frame. This requires the creation of a doubly rotating frame for 26 both the protons and carbon nuclei, and is created by applying the rotation R̂ = exp−iωH ∑ i Iix expiωC Ŝx (3.7) to the rotating frame Hamiltonian, which gives the toggling frame representation Ĥ tog = R̂−1ĤrotR̂− ω ∑ i Îix − ωCŜx.. (3.8) The extra Îix and Ŝx terms cancel perfectly with the pulse terms from the rotating frame Hamiltonian. This allows the toggling frame Hamiltonian to be rewritten as Ĥ tog = Ĥ togHH + Ĥ tog HC (3.9) where Ĥ togHH = − 1 2 ∑ i<j CHHij (Îi · Îj − 3ÎixÎjx) (3.10) and Ĥ togHC = − ∑ i CHCi [( ∑ i ÎizŜz + ∑ i ÎiyŜy) cos(ωH − ωC)t + ( ∑ i ÎiyŜz ∑ i ÎizŜy) sin(ωH − ωC)t] (3.11) with coefficients C being CHHij = 1 2 µo 4pi γ2H r3ij (cos2 θij − 1) (3.12) CHCi = 1 2 µo 4pi γHγC r3ij (cos2 θi − 1). (3.13) In the above coefficients, ri represents the internuclear distance between the iTh proton and the carbon nucleus. θi represents the polar angle between the vector ri and the applied field. Likewise, rij represents internuclear distances between protons i and j and θij represents the polar angle between the vector rij and the applied field. While the homonuclear coupling between protons affects the redistribution of magnetization, it does not represent a significant interaction for cross- polarization. The heteronuclear coupling plays the dominant role, but because of the Hartman-Hahn condition of ωH ≈ ωC , the time dependence is removed from the heteronuclear Hamiltonian. The terms of the 27 resulting Hamiltonian are of the form ÎzŜz and ÎyŜy. The latter term can be represented as Î+Ŝ−+ Î−Ŝ+ which is the B term from the dipolar coupling interaction that promotes mutual spin flips between the I and S spins. Because the energy level separation is the same for both species under the Hartman-Hahn condition, there is no net change of magnetization or loss of energy when there is an exchange of magnetization from the protons to the carbon nuclei. The result of this is that the carbon and protons equilibriate to equal magnetizations, and because the carbon population is negligible compared to that of the protons, the equilibrium magnetization is approximately that of the proton. Initial intuition should leave one skeptical of this result, after all the population of the dilute 13C is still quite small, and all that has happened is that the percentage of NMR active carbons that are in the high energy state is equal to that of the excited protons. Or more succinctly, wouldn't a direct polarization carbon spectrum accomplish the same result? The reason for this technique comes down to the constants. The γ factor for protons is approximately a factor of 4 greater than that of carbon meaning that they are much more likely to be polarized in thermal equilibrium. There is also a secondary advantage that the T1 for protons is generally much shorter than that of carbon. This allows the experiment to be repeated more frequently, resulting in an increase in the signal to noise ratio [9]. 3.4 Electrospinning Electrospinning is a novel technique capable of producing nanoscale fibers from polymers that has recently come into vogue in engineering research. Unlike most techniques for nano- materials, electrospinning has been used since the early twentieth century. The origins of the technique date back hundreds of years to an ancillary phenomenon; electrospraying. A book published in 1628 by William Gilbert detailed a phenomenon where water with a voltage source in a capillary in proximity of a grounded source would have a cone of water form at the tip that would eject small droplets towards the voltage source. The technique of electro- spinning itself did not come around until 1902 when it was found that using the techniques of electrospraying using a viscous polymer solution instead of water results in the ejection of a single jet instead of of droplets. The electrospinning technique, shown in Figure 3.3, involves generating a high electric po- tential between a polymer solution in a reservoir, typically a glass syringe or pipette with a capillary or needle at the tip and a conducting collection plate. As the voltage increases 28 Figure 3.3: Components of an electrospinning apparatus. Image from Gandhi [10]. from 0, the droplet at the tip of the needle or capillary begins to deform into a cone pointing towards the plate. At a critical voltage the electronic force overcomes the surface tension of the cone and a jet is produced. The diameter of this jet decreases under electrohydrodynamic forces, and undergoes a destabilization that results in a rapid whipping motion which results in extensive stretching on it's path to the plate. The stretching process results in a rapid evaporation of the solvent due to the incredibly high aspect ratio of the jet, which leads to a further diameter reduction. The dried fibers are deposited in a random configuration on the collection plate (although methods of aligning fibers do exist) resulting in a thin mat of nanofibers. The fiber diameter and the thickness of the scaffolds can be controlled by varying a wide variety of parameters including, but not limited to, the solution concentration, the distance between the needle and the plate, and the voltage [10]. 29 Chapter 4 Proteins Virtually every physical aspect of living organisms are either affected or determined by proteins. While nucleic acids such as DNA and RNA may be the blueprints for life, proteins are the materials that build it and the engines that run it. The role of proteins is as diverse as life itself. They fill the administrative roles in organisms such as transporting materials and controlling cellular functions, they provide structural roles such as hair, nails, tendons, and muscle. They also serve as the material for novel biological functions, such as silks, hagfish slime, and pheromone detectors. 4.1 Introduction The diverse properties of proteins are facilitated through 20 amino acids, the building blocks of proteins. These 20 amino acids form linear polymeric chains that form the secondary and tertiary structure and thus dictate the properties and function of the proteins. Amino acids share a common backbone with two polymerization sites, resulting in the forma- tion of strictly linear molecules. This backbone contains two carbons, known as the carbonyl, which serves as one of the polymerization sites, and the α carbon. What makes the amino acids different is a side chain which is bonded to the α carbon, as shown in Figure 4.1, and in the case of proline is also bonded to the nitrogen as well. With the exception of glycine, all of the 20 common amino acids contain additional carbons on their side chains. These are labeled as β, γ, δ, , ζ where the closest carbon to the α will be the β carbon, and so on. 30 Figure 4.1: A connection of two unspecified amino acids. Amino acids are differentiated by their sidechains (R). Image from Depew [8]. Some amino acids have non linear side chains. In this case a different naming convention is used. The peptide bond is the bond between the carbonyl carbon and the nitrogen of the following amino acid and serves to link amino acids together. This is a unique bond because of its partial double characteristic that has a resonance with the carbonyl valency CO. This results in the peptide unit being planar. This restricts the atoms forming the peptide unit, and acts as a rigid structure. In most cases, the most favorable state is trans where the bond rotation is ω = 180. However, in some cases particularly in that of bonds with the proline residue, the most favorable energy state is that of the cis conformation, where the bond rotation is ω = 0. 4.2 Secondary Structure The primary structure of a protein is the covalent structure defined by the amino acid se- quence. In proteins, certain combinations of amino acids can allow flexibility of the chain, while other combinations can restrict motion resulting in rigid sections. This happens be- cause there is some freedom in the manner in which the covalent bonds are configured. At room temperature bond lengths and bond angles can vary by ±0.05 and ±5o respectively. However, energetically favorable conformations exist due to non-covalent interactions as well. These conformations, shown in Table 4.1, govern what is known as the secondary structure of proteins. This level of structure can have a dramatic effect on the characteristics and behavior of the protein, more than the specific sequence itself in some cases. Computational 31 Structure φ(◦) ψ(◦) ω(◦) right handed α helix -57 -47 180 310 helix -49 -26 180 31 helix -80 150 180 anti parallel β-sheet -139 135 -178 parallel βsheet -119 113 180 Table 4.1: Torsion angles for various secondary structures [11]. simulations of protein folding are made in an attempt to find the exact secondary structures that proteins favor. NMR is extremely sensitive to molecular configurations. This makes it a perfect tool for studying proteins. Not only will each carbon have a well defined peak (ideally), but the chemical shift can be used to help find the torsion angles associated with the amino acids, which can be used to get a clear picture of what secondary structures are present in the protein. 4.2.1 α-Helix Helices are the most common secondary structure. There are a wide variety of them, catego- rized by their residues per turn. The α-helix is considered to be the most common. This helix is a right handed spiral in which every backbone carbonyl group receives an extra hydrogen bond donated from a backbone N-H group four residues later in the sequence. Each amino acid residue makes a turn of 100o and a translation of 1.5Å. This means that each full turn contains 3.6 residues and translates 5.4 Å. The dynamics of α-helices are low frequency 1- dimensional oscillations in an accordion like manner[12]. This helix is often observed to have a characteristic three phase deformation under mechanical duress. During the first phase the helix is stretched uniformly resulting in a short and stiff deformation. In the second phase, the turns break and rupture the hydrogen bonds resulting in a decrease in modulus. During the final phase, the stiff covalent bonds are stretched until the helix rips [13]. 4.2.2 β-Sheets While the α-helix may be the most common conformation it is does not play an important role in major ampullate spider silk. The second most common protein secondary structure is the β sheet, shown in Figure 4.2. β sheets plays a crucial role in the physical properties 32 Figure 4.2: The single β strand and the β sheet, showing hydrogen bonding between adjacent β strands via the peptide unit. Image from Creighton [12]. of silks, and will be of import for much of this thesis. The basic unit of the β-sheet is the β strand, with the polypeptide almost extended fully, this can be considered a special helix with 2 residues per turn, and a 3.4 Å per residue translation. On its own, the β strand is not energetically stable. To maintain structural integrity, it must be incorporated into a β sheet, where hydrogen bonds form between peptide groups on adjacent β-strands. These adjacent strands can align to be either parallel or anti-parallel. The latter are thought to be a more stable structure, however, this may also depend on which amino acids are present in the strands. Adjacent side chains from the same strands protrude from opposite sides of the sheet, and do not interact. However, side chains do have significant interactions with the backbone and side chains from nearby strands. This two dimensional structure means that in β sheets the interactions occur between residues on distant parts of the protein, which is a stark contrast to that of α helices where interactions occur between neighboring residues [12]. 4.3 Silk For thousands of years, silks have been a symbol of wealth, power, and status. The techniques for processing the thin fibers extruded by the silk worm were first mastered in Asia, and for 33 many years this knowledge was a source of great economic power over the nations of Europe. Even today silk clothing represents the pinnacle of decadence and luxury. The softness of silk is only part of this equation. Due to the aspect ratio and strength of these fibers, clothing made from them was able to have a finer weave and be both stronger and thinner than any other material. In fact, historical evidence suggests that one of the reasons for the Mongols great success in their westward conquests was due to the silk vests that the horsemen wore under the armor. These vests were able to protect them better than armor from piercing wounds, such as arrows. While there would still be a wound, often the arrow would not actually penetrate the silk resulting in a less deep wound, and allow its removal to be a far gentler process [14]. Silk from the classical silkworm (most often Bombyx mori) is not the only silk there is. Other species produce silks, including every kind of the over 30 000 varieties of spider. Spider silk is of particular significance because of its remarkable properties and will be the focused on in the next section. Despite this great variance in kinds of silks, many of them share several features including; an unrivaled combination of mechanical properties, the existence of a water soluble state, being made primarily out of proteins, and the durability of the finished product. With regards to the second point, it must be noted that the finished silk itself is not water soluble under normal conditions, and in fact is quite resistant to most forms of acid and organic solvents. The water soluble state exists prior to the spinning of the silk, and requires a great deal of treatment for the silk fibers to be made into a water soluble product. 4.3.1 Spider Silk While many silks have remarkable mechanical properties, the properties of spider silk greatly surpass those of textile silks. Millions of years of predatory evolution has evolved spider silk into a material with mechanical properties comparable to advanced synthetic materials. Spider silk is tougher than steel and Kevlar. What makes spider silk so durable is that it is exhibits a combination of a high strength, modulus, and extendability. This combination means that the amount of energy required to break spider silk is comparable to, and in most cases surpasses, some of the most successful man made materials, as can be seen in Table 4.2. In addition to its impressive mechanical characteristics, spider silk can exhibit a phenomenon known as supercontraction. When exposed to water, spider silk can contract by up to 50%, this phenomenon allows the morning dew to keep spider webs tight [15]. Supercontraction 34 Material Strength Modulus Extendability Toughness (GPa) (GPa) (% of length) (MJ/m3) High-tensile steel 1.5 200 0.8 6 Kevlar 47 27 3.6 130 Nylon 0.95 4 18 80 Dragline Silk (Nephila) 1.1 20 30 170 Table 4.2: Mechanical properties of various man made materials and dragline silk [16]. Figure 4.3: The sequence of the MaSp1 protein. The repeating amino acid sequences have been arranged from amino-terminal end to the end of the repeating segment, which is 69 amino acids from the carboxyl terminus. The units have been arranged for maximum identity. The dashes are deletions. Image from Xu and Lewis [17]. has been observed in synthetic materials, however, this has only occurred at extremely high temperatures or with the use of caustic solvents. A complete understanding of where the properties of spider silk come from is still a partial mystery. The accepted model is that its properties originate from the proteins themselves, but it is the secondary structures that allow for them. Nephila clavipes dragline silk is composed of two proteins, Spidroin I (MaSp1) and Spidroin II (MaSp2) whose sequences are shown in Figures 4.3 and 4.4. SpI is dominated by runs of 5-7 residues of polyalanine with generally five -Gly-Gly-X- sets separating them, where X is predominantly Gln, Tyr, and Leu. It is thought that the polyalanine sets participate in β-sheet formation. Sp2 has runs of polyalanine with length of 35 Figure 4.4: The sequence of the MaSp2 protein. The repeating amino acid sequences have been arranged from the amino terminal through the highly conserved region, followed by the less conserved region and divergent COOH-terminal tail. The dashes are deletions. Image from Hinman and Lewis [18]. 6-10 residues. A significant feature of Sp2 are several proline containing pentapeptides such as; -Gly-Tyr-Gly-Pro-Gly-, Gly-Pro-Gly-Gly-Tyr-, and -Gly-Pro-Gly-Gln-Gln-. The proline in these pentapeptides forces an abrupt kink in the polymer backbone. It is thought that this makes it difficult for β-sheet crystals to form out of these segments of MaSp2, thus if an attempt were made to construct β sheet crystals out of MaSp2, the proline would disrupt their structural integrity effectively turning the crystals into disordered matrices [19]. The breakdown by amino acid contribution of both MaSp1 and MaSp2 are shown in Table 4.3. While β sheets do form from components of the proteins, the sequence itself does not have an intrinsic tendency to do so. The fact that β sheets form at all is thought to be a result of external conditions, not some inherent property of the protein [20, 19, 21]. It is thought that as the protein solution is drawn through the spinneret, it is exposed to a greater-than-critical shear rate, whose magnitude is dependent on the concentration, some of the β strands are stabilized by forming hydrogen bonds and β sheets. These sheets stack into 3-dimensional crystals called β-sheet crystals. It is these crystals that give spider silk much of its strength [19]. Much of the the non crystalline region is believed to take the form of 31 helices [5]. This phase connects the β crystals together and becomes highly entangled with each other forming hydrogen bonds. This region gives silk a rubbery property, resulting in the silk having a high modulus and extendability. This model is shown in Figure 4.5. It is believed that it is this combination of these two regions that gives spider silk its remarkable mechanical properties. 36 Figure 4.5: A possible structure of spider dragline silk proposed by van Beek with (A) a skin-core organization, with a multitude of fibrillar substructures and covered by a hard skin, forms the fiber The molecular structure consists of sheet regions, containing alanine (red lines) and glycine (blue lines) with the green boxes being the crystalline domains. These regions are interleaved with a predominantly 31 helical (blue curls) amorphous region, which do not contain alanine. All chains tend to be parallel. (B and C) Side and top projections of a repetitive model peptide with dihedral angles to show the approximate 3-fold symmetry of the 31 helical structure. Image from van Beek et al. [5]. 37 Silk Sequenced Protein Amino Acid major dragline [22] MaSp1 [17] Sp2 [18] glycine 45.8 49.5 29.63 alanine 22.2 29.4 21.3 glutamine 10.9 10.6 11.9 leucine 1.5 3.4 1.0 tyrsine 4.3 3.2 4.8 serine 7.4 1.8 10.1 arginine 1.7 0.3 1.3 proline 3.5 0 13.9 aspargine 1.2 0.5 0.6 valine 0.8 0.8 2.1 histidine 0 0 0 phenylalanine 0.3 0 0.3 lysine 0.3 0 0 isoleucine 0.1 0.2 1.1 cysteine 0 0 .3 methionine 0 0 0 Table 4.3: Breakdown by amino acid of N. clavipes dragline silk, MaSp1, and MaSp2. Measurements have determined that 28% of the glycine and 82% [23] of the alanines take the form of β sheets. In total β sheets make less than 40% of spider silk [15]. 4.3.2 Transgenic Spider Silk In 1999, Nexia Biotechnologies Inc., a Quebec biotechnology company developed a novel approach for the synthetic production of spider silk. The were able to produce recombi- nant spider silk, dubbed Biosteel, using BELE (Breed Early Lactate Early) goats that were treated using pronuclear micro injections and nuclear transfer technologies [24]. Nexia has successfully generated both MaSp1 and MaSp2 in their transgenic goat milk. The milk has had yields of up to 2 grams of protein per liter and the proteins can be isolated and purified to homogeneity [10]. Unfortunately, despite the ability to produce the spider silk proteins artificially, researchers have been unable to produce fibers with comparable mechanical properties to those produced by spiders. For example, the mechanical properties of silk nanofibers produced via electro- spinning by M. Gandhi had moduli and tensile strengths over two orders of magnitude below that of naturally produced spider silk, and at best, two thirds of the maximum elongation 38 Silk type Strength Modulus (MPa) Extendability (MPa) (MPa) (% of length) Dragline Silk 1100 20000 30 3:1 MaSp1:MaSp2 7.4±0.36 104±15 14.0±0.1 1:1 MaSp1:MaSp2 5.0±1.2 77±4 12.6±0.2 1:3 MaSp1:MaSp2 2.4±0.8 21.3±5.2 22.2±1.2 1:0 MaSp1:MaSp2 9.6±2.0 123±25 14.3±0.2 1:0 MaSp1:MaSp2+1%CNT 40.7±6.3 1004±53 7.39±1.4 Table 4.4: Mechanical properties of natural spider silk [16] and various electrospun silks made from MaSp1 and MaSp2 [10]. Structure Amide 1 frequency (cm−1) anti parallel β sheets/aggregated strands 1675-1695 310 helix 1660-1670 α helix 1648-1660 unordered 1640-1648 β sheet 1625-1640 aggregated strands 1610-1628 Table 4.5: Secondary structure assignments from FTIR wavenumbers [25]. as shown in Table 4.4. This dark cloud does have a silver lining however. By adding carbon nanotubes into the fibers during spinning process, the modulus and strength were greatly increased. These improvements however, came at the cost of decreasing the elongation by close to 50%. 4.3.2.1 FTIR Results of the Transgenic MaSp1 and MaSp2 FTIR experiments conducted on electrospun silk and the lyophilized MaSp1 and MaSp2 powders by Gandhi [10] found that the electrospun MaSp1 contained around 40% β sheets, the MaSp1 and MaSp2 powders respectively contain around 12% and 3-4% β sheets. These results were found by analyzing the intensity of the FTIR peak from the amide 1 range whose wavenumber was 1630cm−1, which corresponds to β sheets structure, and calculating the percent of the signal that they represented by comparing the area under the peak to the area under the helical regions. A selection of secondary structures and corresponding wave numbers are shown in Table 4.5. However, close examination of the FTIR data in Gandhi's work raises some questions. Gandhi states that the peaks for β sheets appears at 1630cm−1, shown in Figure 4.6, but 39 Reported value (cm−1) Analyzed value (cm−1) 1650 1650 1630 1610 1545 1540 1520 1500 1270 1290 1230 1230 Table 4.6: Reported wavenumbers from Figure 4.6 and estimates of actual wavenumbers which found using image analysis software (Adobe Illustrator). it appears that some of the lines are not actually where they are said to be. This can be seen by noting that the separation between the lines at 1650 cm−1and 1630 cm−1 is barely half of the separation between the lines at 1630 cm−1 and 1540 cm−1 when it should be less than a quarter. Furthermore, scaling the distance between the 1530 cm−1 and 1630 cm−1 peaks by ten results in a line that is nearly 400 wavenumbers long. Attaching a scale to the data (there were no x axis tics initially, reveals that several of the peaks are located at different wavenumbers, as shown in Table 4.6. Assuming this is correct, this implies that the dominant structure observed at the line 1630cm−1 is not β sheets, but is instead aggre- gated strands, a structure that is consistent with denatured proteins. Furthermore, in the range of where β sheets actually occur, there is a minimum in the electrospun silk suggesting that β sheets are not a dominant structure in the material. What this implies is that the electrospun MaSp1 proteins do not form a regular secondary structure. Also, while there is no peak in the MaSp1 powder at 1630, there is significantly more signal in that region than the electrospun fibers, meaning that the presence of β sheets is likely. Interestingly however, there is a small peak in the β sheet regime in both the MaSp2 powder and fibers. It should also be added that while the actual structures may be different than reported, the composition of the secondary structure that was calculated from these peaks is also suspect as several critical reviews of FTIR have been skeptical of the use of FTIR in determining secondary exact proportions [25, 26]. 40 20 cm-1 X10 20 cm-120 cm-1 90 cm-1 20 cm-1 400 cm-1 Figure 4.6: Analysis of Gandhi's MaSp1 FTIR results. The 20 cm−1 seperation is more than half the length of the 90 cm−1 seperation, and that when scaled by a 10, it results in a length of 400 cm−1. Note that the tic along the x axis were added to the image as they were not included in the original. The distance from the 1650 cm−1 line to the boundary at 1800 cm−1 was used as the reference for these tics. 41 Chapter 5 Experimental Materials, Methods, and Results In this chapter we describe samples and their preperation, the NMR experiments and meth- ods of analysis, and present the raw results from them. 5.1 Samples Preparation Four different protein samples were analyzed using NMR; spider (N. Clavipes) silk, MaSp1, MaSp2, and electrospun MaSp1. The sample masses were 34.9mg of spider silk, 42mg of MaSp1, 44mg of MaSp2, and 7mg of electrospun MaSp1. The MaSp1 and MaSp2 were provided to the Advanced Fibrous Materials Laboratory at UBC by Nexia Biotechnologies Inc. The proteins were produced using genetically engineered goats who produced the protein via lactation (milk) using a process created by Lazaris et al. [24] and were provided as lyophilized powders and used without further processing. The electrospun MaSp1 was electrospun in a custom built electrospinning set up, with min- imal metal parts that caustic solutions could cause damage to. The polymer solution was made from 8% MaSp1 powder in 99% formic acid and electrospun from a Fischer 1ml glass pipette, which had a copper wire connected to a power supply, charged it to 20 kV, inserted into the solution. The solution was spun at an angle of 45 degrees below the horizontal with the pipette tip 12cm from the grounded plate. The sample did not initially spin and instead 42 sputtered. Higher voltage resulted in arcing. To compensate for this the concentration was increased by 2% to 10% where it spun into fibers. 5.2 Cross Polarization Experiments and Chemical Shift Cross polarization magic angle spinning experiments were performed on a Varian 400 MHz (9.4T) NMR spectrometer with an HXY MAS probe on the four samples. The samples were packed into a zirconia rotor and then spun at 5kHz. The goal of the cross polarization experiments were to find chemical shift assignments for the amino acid carbons so secondary structures could be assigned. 4000 scans were taken for each, except for spider silk, which was 2000. The spectra were referenced to adamantane spectra taken either before or after the experi- ments to obtain the chemical shifts of each peak. These chemical shifts were then compared to the values from Table 5.2 to both determine what amino acid carbon the peak represented and the range of structures that they represent. The measured chemical shifts for each sam- ple are listed in Table 5.1. The secondary structure associated with these chemical shifts will be discussed in detail in the future sections. One issue with cross polarization experiments is that the intensities are not quantitative. Very rigid structures tend to cross polarize well and can show signal intensities approaching the theoretical maximum. More mobile structures tend to cross polarize less well due to partial averaging of the C-H dipolar couplings that are necessary for cross polarization, such partial averaging can result in reduced intensities for peaks arising from less rigid structures [4]. 5.3 Relaxation Measurements 13C relaxation times were measured using a cross polarized pulse sequence shown in Fig- ure 5.1. This pulse sequence was developed by Torchia [27], and amplifies the 13C signal using cross polarization. The first part of the sequence is the same as a simple cross- polarization experiment employed in Section 5.2 where 13C magnetizes directly along the y-axis. Then, a pi 2 pulse rotates the magnetization alternately to the z or -z axis, where it 43 π 2 π 2 π 2 CP CPC 13 H1 D2 Figure 5.1: T1 experiment pulse sequence employing cross-polarization to study the longitu- dinal relaxation of the 13C nuclei. relaxes back to equilibrium along the longitudinal axis for a time of D2. After this delay time, a third pi 2 pulse returns any remaining magnetization to the xy-plane where it pro- vides the acquisition signal. This sequence is run multiple times with a variety of D2's, that ranged, depending on which sample, from 1ms to 100s. The range that all fits covered was D2=(0.1s,0.2s,0.5s,1s,2s,5s,10s,20s,50s). Other times were used as well, but this range was found to be critical. These spectra were analyzed by either integrating across the peak to find the peak intensity using a custom NMR analysis program called XNMR. The error is determined by the sample noise times the square root of the number of data points that the peak was integrated over. The intensities of the peaks decay with increasing delay time. The exact dependence on D2 is dependent on the underlying molecular motions that cause relaxation. For a simple system with only a single, or very tight distribution of motional correlation times the function will look like I(D2) = I0e −D2 T1 (5.1) For systems that have two distinct sets of motion, typically indicative of two structures, the intensity decay will take the form of a double exponential which will be 44 I(D2) = Ifast0 e −D2 T fast 1 + Islow0 e −D2 Tslow1 , (5.2) where T fast1 and I fast 1 are the relaxation time and initial intensity of the fast relaxing systems, and T slow1 and I slow 0 are the relaxation time and initial intensity of the slower relaxing system. An important point of clarification must be made here that the fast and slow terminology is not connected to the speed of the molecular motion, as the two motions could be on either side of the fast/slow regime of the correlation time. For systems that have a distribution of relaxation times, the curve will often relax in a stretched exponential. The stretched exponential represents the William-Watts distribution, an assymetric distribution that from an experimental perspective, is nearly indistinguishable from the Davidson-Cole distribution [28]. The distribution of relaxation times in the William- Watts distribution is ρ( T1 T ∗1 ) = − 1 piT1 ∞∑ k=0 (−1)k k! sin(piβk)Γ(βk + 1) T1 T ∗1 βk , (5.3) where β is related to the distribution width of relaxation times and ranges from 0, rep- resenting a large distribution, and 1, which represents a single relaxation time. T ∗1 is the distribution center for β = 1. For values of β less than one, the distribution maximum point is dependent on both T ∗1 and β parameters. The stretched exponential yields a relaxation function of the form: I(D2) = I0e − ( D2 T∗1 )β . (5.4) The mean relaxation time for a stretched exponential is given by: < T1 >= T ∗1 β Γ ( 1 β ) . (5.5) Selection amongst fits to a single exponential, stretched exponential, and double exponential decays is done based on the test of additional fits: Fχ = χ2(m)− χ2(m+ 1) χ2(m+ 1)/(N −m− 1) (5.6) 45  0 10 20 30 40 50 60 70 In te ns ity Chemical Shift (ppm) Electrospun MaSp1 Spider Silk MaSp1 MaSp2 β,γ Aα Qα P α Gα Q β A S α* S β Figure 5.2: The cross polarization spectra for electrospun MaSp1, MaSp1, MaSp2, and spider silk. The proline residues carbons between 20ppm, and 40ppm are unlabeled because of the overlap with other residues, and the fact that only MaSp2 contains a significant amount of proline. where χ2 is the goodness of fit, N is the number of data points, and m is the number of parameters used in the fit. Fχ represents the probability of the fit being an improvement, which must be above a threshold value for the fit to have a 95% confidence for the higher parameter fit to be accepted. This threshold value is dependent on the degrees of freedom in the two fits and can was found in a reference table [29]. In addition to these relaxation experiments, an additional experiment was performed on the spider silk, measuring the relaxation time at 40◦C. This measurement was conducted to increase the thermal motion thus lowering the correlation time, allowing a glimpse of whether the protein motions were in the fast or slow regime. Lastly, it is important to note that with the exception of the carbonyl, all of the backbone and side chain carbons are assumed to primarily relax through the dipolar interaction due to covalently bonded hydrogen. 5.4 Characterization of Secondary Structures The characterization of the secondary structure is done through careful analysis of the dif- ferent backbone and side chain carbons peaks in the NMR spectrum. After the molecular 46 13C chemical shift (in ppm) Residue Dragline MaSp1 MaSp2 Electrospun DN silk1 Gland silk1 Silk MaSp1 Alanine α Carbon 49.2 49.6 49.2 52.3 52.4 51.7 Alanine β Carbon 20.5 21.1 20.8 15.8-16.8 17.2 16.1 ∆CSαβala 28.7 28.5 28.4 35.5-36.5 35 35.6 Glycine α Carbon 42.8 43.4 42.9 42.4 Glutamine β, γ Carbon 29-33, 25 28-33, 25 28-31, 25 28-33 Glutamine α Carbon 54.1 Proline αCarbon 60.5 60.8 Serine β Carbon 60.7 Serine α Carbon 54.5 Table 5.1: Chemical shifts for spider silk, MaSp1, MaSp2, and electrospun MaSp1. 1Taken from [20]. structure, which amino acid the carbon is in, and what position it occupies in the amino acid (C=O, α,β,etc,) the secondary structure makes the largest contribution to chemical shift. This allows the chemical shifts from the cross polarization spectra in Figure 5.2, and listed in Table 5.1, to be compared to known chemical shifts of carbons in known secondary structures, which can be seen in Table 5.2. For spider silk and MaSp1 the three amino acids, glycine, alanine, and glutamine, make up almost 90% of the residues as can be seen in Table 4.3. In MaSp2 proline and serine are also abundant, making them important to study as well. The 13C spectra consist of peaks due to all of the carbon nuclei in all of the amino acids. Each amino acid has two backbone carbons, Cα and carbonyl. Because of severe overlap amongst the various carbonyl carbons, no attempt as been made to draw structural information from the carbonyl peaks 5.4.1 Alanine The alanine residue has a chemical shift range of around 4.5 ppm, starting at 48.2-49.3 ppm for β sheets to 52.3-52.8 ppm for α helices. It is unfortunate that the 31 helix chemical shift is 48.9 ppm, right in the middle of the β sheet range making it difficult to separate the two from the chemical shift data. Because spider silk alanine is almost entirely β sheets, comparisons to the relaxation data should be able to help show the presence of β sheets. The relaxation parameters of all the samples' alanine α carbons can be found in Table 5.3. The alanine β carbon is a CH3 group known as a methyl group. The alanine β carbon 47 13C chemical shift (in ppm) Residue Major Silk α-helix β-sheet r. coil 31-helix β-turn Ala Cα 49,49.2,50 52.3-52.8 48.2-49.3 50.5 48.9 50.8-51.7 Ala Cβ 17.5,21,23.3 14.8-16.0 19.9-20.7 17.1 17.4 16.5-17.4 ∆CSαβala 31.5, 36.3-38 27.5-29.4 33.4 31.5 33.4-35.2 Gln Cβ 32 25.6-26.3 29.0-29.3 27.4 26.9 Gln Cγ 33.2 29.7-29.8 51.0-51.4 52.2 51.2-51.7 Gln Cα 52.9 56.4-57.0 51.0-51.4 54.2 53.7-54.72 Gly Cα 43.3 43.2-44.3 43.1 41.4-42.5 43.8-44 Pro Cα 66.32 63.31 62.3-62.82 Pro Cβ 30.6-31.12 32.11 31.6-32.12 Ser Cα 55.5 59.2 54.4-55 58.3 56.8-57.32 58.0 Ser Cβ 61.6 60.7 62.3-63.9 63.8 63.82 60.7 Table 5.2: Known chemical shifts for amino acids important in spider silk and various sec- ondary structures. All unreferenced chemical shifts are from [30]. 1 Random coil chemical shifts from [31].2 Estimated using contour plots from [32] using the random coil value and the values from Table 4.1 for the torsion angles. Material Best Fit T1 (s) T ∗1 (s) β 〈T1〉 (s) Spider Silk (200 MHz) Single 12 Spider Silk (400 MHz) Stretched 20.2± 0.8 0.77± .04 23.6± 1.3 Spider Silk (40 oC) Stretched 19.7± 0.5 0.86± 0.03 21.3± .7 MaSp1 Stretched 16.3± 0.6 0.70± 0.02 21.0± 1.0 MaSp2 Stretched 15.4± 0.4 0.71± 0.2 19.2± 0.8 Electrospun MaSp1 Stretched 21.1± .3.7 0.69± 0.13 27.0± 6.9 Table 5.3: Relaxation parameters for alanine α carbons. T ∗1 , β, and 〈T1〉 are the parameters for the stretched exponential. The 200 MHz data is from [33]. 48 Material Best Fit T1 T fast 1 (s) T slow 1 (s) % fast Spider Silk (200 MHz) Double 0.18 2 40 Spider Silk (400 MHz) Double 0.23± 0.04 1.2± 0.2 56± 10 Spider Silk (40 ◦C Double 0.29± 0.08 1.3± 0.2 43± 12 MaSp1 Double 0.40± 0.09 1.8± 0.7 70± 16 MaSp2 Double 0.26± 0.07 1.7± 0.4 53± 12 Electrospun MaSp1 Single 0.77± 0.02 Table 5.4: Relaxation parameters for alanine β carbons. The single exponential fits were included for all of the samples for comparison to the 200 MHz data [33]. is particularly useful for chemical shift assignment as there is very little overlap between structures. The chemical shift range is around 6 ppm starting at 14.6-16.0 ppm for α helices to 19.9-20.7 ppm for β sheets. The motion for methyl groups has been modeled as a fast moving rotor [34]. Because methyl group rotation is usually in the fast motion limit, longer relaxation times at room temperature correspond to faster motion. In spider silk the alanine β carbon has been well documented to have two relaxation regimes, a short T fast1 , corresponding to slow moving rigid area, and a long T slow1 , corresponding to a looser regime. The different relaxation times are shown in Table 5.4. Because alanine's α and β carbons chemical shift move in opposite directions from the random coil shifts for different conformations, using the difference in between the two peaks provides a structural metric that is both independent of the reference measurement and has much larger separations between structures which makes structural identification easier. To facilitate this, the parameter ∆CSαβala will be defined as ∆CSαβala = CS α ala − CSβala where CSαala andCS β ala are the chemical shifts of alanine α and β carbon peaks. 5.4.2 Glycine α Carbon The glycine α carbon has a very narrow range of chemical shifts of about 2.7 ppm. This starts from 41.4-42.5 ppm for the 31 helix, to 43.8-44.1 ppm for the β turn. Poly-glycine 49 Material Best Fit T1 (s) T ∗1 (s) β 〈T1〉 (s) T fast1 (s) T slow1 (s) % fast Spider Silk Single 9 (200 MHz) Spider Silk Stretched 20.8± 1.0 .66± .03 28± 2 5.5± 1.8 39± 6 37± 6 (400 MHz) Spider Silk Double 23.0± 0.8 .70± .03 29± 1 6.5± 1.3 42± 4 37± 4 (40 oC) MaSp1 Stretched 15.3± 2.2 .64± .10 21± 5 MaSp2 Stretched 18.2± 1.2 .70± .05 23± 2 Electrospun Stretched 15.6± 2.3 .63± .09 22± 4 MaSp1 Table 5.5: Relaxation parameters for glycine α carbons. T ∗1 , β, and 〈T1〉 are the components for the stretched exponential. The 200 MHz data is from [33]. The room temperature and 40 ◦ C measurements best fit to different functions, so both sets of parameters were included. tends not to form α helices but instead forms a structure known as the 31 helix, which is believed to be an important element of spider silk's amorphous region [5]. The different relaxation times are shown in Table 5.5. 5.4.3 Glutamine α/β/γ Carbons As there is only one third the amount of glutamine compared to alanine in MaSp1 and spider silk, and because the glutamine α carbon's chemical shift overlaps with the alanine α carbons, it is dominated in these spectra and only visible after relaxation. However, in MaSp2 there is a strong enough glutamine α carbon signal compared to the alanine α carbon's to differentiate its peak. Its chemical shift ranges from 51 ppm in β sheets to 57 ppm in α helices. The glutamine β and γ carbons occupy a rather wide range, from 25-32 ppm. The γ carbon ranges from 29-32 ppm, and the β carbon ranges from 25-30 ppm. This means that for peaks in their shared range they are effectively indistinguishable. Due to significant overlap with the alanine β, it was not possible to generate a consistent and reproducible relaxation time for the glutamine in the range of 25 ppm. In the literature the glutamine β and γ peak near 30 ppm was reported as being fit to a single exponential, however all of the experiments we conducted best fit a double exponential. The different relaxation parameters times are shown in Table 5.6. 50 Glutamine β/γ Carbons Material Best Fit T1 (s) T fast 1 T slow 1 (%) % fast Spider Silk (200 MHz) Single 4 Spider Silk (400 MHz) Double 10 1.7± .6 26± 3 50± 4 Spider Silk (40 ◦C Double 11 0.89± .3 21.0± 3.7 44± 7 MaSp1 Double 16 0.79± 0.38 18.2± 1.2 18± 4 MaSp2 Double 10 1.7± 0.2 23.1± 2.3 56± 4 Electrospun MaSp1 Double 13 3.4± 1.1 36± 12 41± 12 Table 5.6: Relaxation parameters for glutamine β/γ carbons. The 200 MHz results are from [33]. The single exponential fits were included for all of the samples for comparison to the 200 MHz data. 51 Chapter 6 Spider Silk NMR Results and Analysis This chapter focuses on analyzing the relaxation charactersitics of spider silk. The first section discusses the alanine residue, followed by glycine, and ending with glutamine. 6.1 Alanine The alanine α carbon was observed to have a chemical shift of 49.2 and a peak width of 2.8 ppm. This is consistent with the results observed in the literature [30, 33]. Much of the alanine α peak overlapped with the slower relaxing glutamine α carbon peak. This meant that using the entire peak would not be an accurate reflection of the alanine α carbon relaxation. To compensate for this, the integration began at 0.5 ppm downfield from the peak center. Contrary to the results reported in the literature, the best fit observed for spider silk's alanine α carbon was not to a single exponential as reported by Simmons et al. [33], but to a stretched exponential, as seen in Figure 6.1. While this is different to the literature, it should not come as a surprise as this implies that there is a distribution of correlation times within the crystals. These values were found to be T1 = 20.2 ± 0.8 s and β = 0.77± 0.07. This gives a mean relaxation time of < T1 >= 23.6± 0.7 s. Making use of our measurements and the previous measurements at lower field [33], we can characterize the molecular motion and the order parameter of the alanines. Using the mean T1, as representative of a mean single correlation time, we can put the model independent spectral density from Equation (2.97) into Equation (2.89). Because the β sheets are large 52  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) Spider Silk Alanine C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 6.1: The relaxation curve of the alanine α carbons in spider silk. crystalline blocks in a solid, we can make the assumptions for ultra slow bulk motion and use the simplified spectral density from Equation (2.100). This leaves us with a relatively simple equation for T1. Noting that the correlation time is independent of the external magnetic field which for two different magnetic fields, B1 and B2 gives; RB2I RB1I = TB11 TB21 ≈ ( 3 1+(ω B2 I τc) 2 + 1 1+((ω B2 I −ω B2 S )τc) 2 + 6 1+((ω B2 I +ω B2 S )τc) 2 ) ( 3 1+(ω B1 I τc) 2 + 1 1+((ω B1 I −ω B1 S )τc) 2 + 6 1+((ω B1 I +ω B1 S )τc) 2 ) (6.1) Comparing this to the values produced by Simmons at 200 MHz allows us to solve for the correlation time, which was found to be 5.06× 10−10 s, which is just on the slow motion side of the correlation time, as shown in Figure 6.2. We can then use this to solve for the order parameter, which was found to be S = 0.994, showing a highly restrictive structure that one would expect in a β sheet. Uncertainties are not given for either the order parameter or correlation time because the error was unknown in the relaxation data from the low field T1. It must be made clear that there are several assumptions that have been made that could have yielded incorrect values. The first is the use of the mean T1. This by no means corresponds to the mean correlation time. While typically this would only mean a small systematic error, the proximity of the resulting correlation time to the fast motion/slow motion transition means that the mean correlation time might be quite different. The second and much larger assumption was the low field T1 from the literature that was used. As the value provided was that from a single exponential fit, it is most likely not the most accurate value to use. However, as that raw data is not available, there is little else that can be done. 53 Correlation Time (s) τ (Spider Silk) MaSp2 1/ T 1  (s -1 ) MaSp1 Figure 6.2: Plot of correlation time versus 1 T1 for the alanine α carbon with an order pa- rameter of S = 0.994 using the ultra slow tumbling approximation of the Szabo model. The inverse of the T1 for MaSp2 was included to show that it does not fall within the range al- lowed with this order parameter. The inverse T1 for MaSp1 falls just outside of the allowable range, however, its uncertainty is within the allowable values for this order parameter Given the caveats, we take the correlation time and order parameters as guides providing the order of magnitude of the indicated quantities. The high temperature results lend support to the validity of this assumption. The 40 ◦C relaxation curve fitted to a stretched exponential with a T ∗1 = 19.7±0.5 s and β = 0.86±0.03 yielding 〈T1〉 = 21.0±0.92 s. While the 40◦C, T ∗1 may be statistically indistinguishable from the room temperature value, the increase of β shows that the relaxation time distribution is tightening up. This would happen as the distribution of correlation times moves into range of the minimum T1, as the change in relaxation time with respect to the change in correlation time decreases. This substantially helps to validate the choice of model used for this assumption. This is further supported by the 〈T1〉 which has a statistically significant decrease in the high temperature case. The alanine β carbon in spider silk was found to have a chemical shift of 20.8 ppm, within both the range determined in the literature and that of β sheets. There is also a slight ledge at 15.7 ppm. The peak was integrated over the range 15-21 ppm. The best fit, shown in Figure 6.3, 54  0  1  2  3  4  5  6  7  8 In te ns ity D2 (s) Spider Silk Sp1 Alanine C-beta Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 6.3: Single, double, and stretched exponential fits to the spider silk alanine β carbon relaxation data . was observed to be a double exponential fit consisting of a fast relaxation time of T fast1 = 0.23±0.04 s which made up 56±10% and a slow component of T slow1 = 1.2± .2 s . While the ratios differ somewhat from those observed in the literature, it is possible that this is a result of variations in the cross polarization parameters and factoring in error, is not particularly different from the results reported in the literature. The T slow1 is somewhat smaller than the values observed in the literature of 2 s, however as the error was unreported, it is difficult to make any definitive statements about the possible cause of this difference. The results of the measurement at 40 oC are practically identical, T fast1 = 0.29± 0.07 s making up 43% of the signal and T slow1 = 1.3 ± 0.2 s making up 57%. The increase in relaxation times length do correspond to faster motion in the fast limit as expected. These results are generally consistent with previous studies of spider silk and suggest that alanines occupy two different kinds of environments. Alanines are believed to generally adopt the backbone torsion angles of β strands [23]. The β carbon relaxation data suggests that the T fast1 corresponds to a tightly packed crystalline environment where methyl group rotation is hindered decreasing the methyl rotation frequency while the T slow1 implies a faster methyl group rotation, which corresponds to a less tightly packed β strand structure. 6.2 Glycine α Carbon The glycine α carbon in spider silk was found to have a chemical shift of 42.8 ppm, with a width of 5 ppm. The chemical shift was consistent with the values found in the literature. 55  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) Spider Silk Glycine C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 6.4: Single, double, and stretched exponential fits to the spider silk alanine α carbon relaxation data. The range used to fit the relaxation spectra began at the half height on the upfield side for the peak, and went until just downfield of the alanine α carbon peak allowing for a two component fit. The best fit to the relaxation was found to be a stretched exponential, shown in Figure 6.4, with parameters T1 = 20.8± 0.8 s and β = 0.66± 0.03. This yielded a mean relaxation time of 〈T1〉 = 28.0 ± 1.0 s. In a 200 MHz magnet, this time was reported as T1 = 9 s [33]. Making similar approximations to those used for the alanine carbon, we found an approximate mean correlation time. Because there are two protons bonded to the glycine α carbon, a factor of two was added to the prefactor of Equation (2.89). The resulting correlation time was found to be τc = 1.19 × 10−9 s which is about a factor of two longer than the value found for the alanine α carbon. This longer correlation time when compared to that of the alanine α carbon is expected as the glycine's relaxation time has a stronger dependency on the field strength. This τc was then used to find the order parameter which was found to be S = 0.996. The plot of 1 T1 versus τc for glycine is shown in Figure 6.5. This order parameter is very close to that observed in alanine α. If the assumptions made were appropriate, this could imply that the glycines observed are dominated by the ones that are present in the β sheet as their motional restrictions are similar. While glycine is only observed to be 28% β sheets in spider silk [23], it would not be surprising if glycine occupying this crystalline regions cross more efficiently than the others weighting the crystalline glycines more strongly in the spectra. The relaxation measurement at 40 oC had an interesting result. The best fit was not the stretched exponential as expected, but instead was fit best to a double exponential function. The two relaxation times were T fast1 = 6.54 ± 1.35 s making up 38 ± 7% of the signal and 56 Correlation Time (s) (MaSp2)1T1 τ (Spider Silk) 1/ T 1  (s -1 ) Figure 6.5: Plot of correlation time versus 1 T1 for the glycine α carbon with an order parameter of S = .996 using the ultra slow tumbling approximation of the SBA model. The inverse of the T1 for MaSp2 was included to show that it falls within the range allowed with this order parameter. T slow1 = 42.21± 4.35 s. While this result appears to be a large discrepancy between the two results, they are not in fact that different. The difference between these two functions is very small and would require high signal to noise data to be able to select the correct function. Considering that the test for an additional terms is simply a probabilistic test that allows a 5% chance of error, and considering how many fits are done in the course of this thesis, it is more than likely that one fit would have an optimal fit that was not correct. It is difficult to use this to confirm the choice of model as the changes in relaxation times and the change in the distribution, β, are all within the range of error. 6.3 Glutamine There is very little published work on the 13C relaxation of glutamine α carbons in spider silk. This is because in spider silk it is very difficult to measure the decay of amplitude of the glutamine α carbon as it is nestled into the alanine α carbon peak. The work by Simmons et al. [33] discounts its relevance in measuring the alanine α carbon relaxation 57  10 20 30 40 50 60 In te ns ity D2 (s) D2=0.05s D2=0.15s D2=0.5s D2=2s D2=4s D2=10s D2=15s D2=25s D2=50s Figure 6.6: Multiple spectra from the spider silk room temperature T1 relaxation experiment. While most information from this data required fitting and analysis, one result that was obvious from observation was the emergence of the ledge at 25.3 ppm into a full peak. It should also be noted that these are not all of the spectra from the T1 experiment. time as it decays faster than the alanine. While this is hardly a thorough analysis, it does provide an important insight. Like the work by Simmons, the glutamine α carbon only appears as a ledge in the spider silk cross polarization spectrum. In the present relaxation data however, this carbon also begins as a ledge, as can be seen in Figure 6.6. As the silk undergoes relaxation however, the magnitudes of the alanine peak and the peak at 54 ppm eventually become equal at a D2 of 25 seconds. This means that the relaxation of the glutamine α carbon under a large field is slower, or more simply put, the glutamine α carbon is much more field dependent than that of the alanine α carbon and therefore has a longer correlation time. This is expected as very little of the glutamine can be in β sheets, as most of the crystalline region consists of alanine and glycine. A backbone carbon in a non crystalline structure has much more freedom of motion, which should result in slower and larger motions. However, for reasons that will be discussed in Section 7.2.3, the observations of Simmons may have missed a component of relaxation in this chemical shift range that happened to have the same T1 as the alanine α carbon in a 200 MHz field. However, as will also be shown, this extra relaxation that was missed is also in the slow limit, so the result of glutamine in the slow motion regime stands, if not by sheer luck. The glutamine β and γ carbon peak in spider silk was found to range from 28-3 0 ppm. Due to the fact that all of the glutamine γ conformations lie in this range, it was impossible to deduce anything about the structure from this. There was also a very slight ledge at 25 ppm that extended downfield from the alanine β carbon that was well beyond the range of chemical shifts allowed. This most likely corresponds to a glutamine residue in the α-helix 58  0  5  10  15  20  25  30  35  40 In te ns ity D2 (s) Spider Silk Glutamine C-beta/gamma Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 6.7: Single, double, and stretched exponential fits to the spider silk glutamine β/γ carbon relaxation data. conformation which has a chemical shift of 25.6 ppm, although the 31-helix cannot be ruled out as it would appear near 26.5 ppm. The peak range of 28-33 ppm was used for the integrating over for the glutamine β/γ peak. The best fit was observed to be a double exponential, shown in Figure 6.7 consisting of a fast relaxation time of T fast1 = 1.7± 0.2 s which made up 50± 4% and a slow component of T slow1 = 26 ± 3 s. To use as a point of comparison with the single component relaxation in the literature, the one component fit yielded T1 = 9.8± 1.5 s. In the 200 MHz spectrometer that was used in the literature, the single component T1 = 4 s While we have strong reason to suspect that there is more than one structure from two very different components of the relaxation times, the increase in T1 under a larger field for the one component shows that there at least the slow component is well past the slow side of the fast/slow transition on the correlation time versus inverse relaxation time curve. We know at least the slow component has had to be in the slow regime because if it were just the fast component, the relaxation time would not increase as much (the one component is larger in both fields than the fast component). This strong field dependence could explain why the peak near 25 ppm has not been identified in the literature. The only other T1 relaxation experiment was conducted in a 200 MHz field, which would have a relaxation time at least 2.5 times faster, depending on if the fast component was in the fast regime or not. At this speed of relaxation, it is quite possible to mistake this component for relaxing at the speed of the alanine β carbon. The spectra from the relaxation experiment at 40 oC gave relaxation times of T fast1 = 0.89± 0.30 s which made up 44 ± 7% and a slow component of T slow1 = 20.9 ± 3.7 s. While the 59 error does slightly overlap with the room temperature values, this reduction in the relaxation times of both components when heated and the fact that the single component T1 was field dependent is consistent with both components having correlation times in the slow motion regime. 60 Chapter 7 Recombinant Mammalian Silk The primary goal of this work was the analysis of the MaSp1 and MaSp2 proteins produced by Nexia. The first section details the analysis of MaSp1 powder, the second section provides the analysis of MaSp2 powder, and the third section provides the analysis of the electrospun MaSp1. 7.1 MaSp1 We now turn from native spider silk to recombinant MaSp1 in powder form, the interest here is that this is the primary protein in spider silk. 7.1.1 Alanine The alanine α carbon was found to have a chemical shift of 49.6 ppm with a peak width of 3 ppm. The peak width was found by fitting the spectrum to a Gaussian the same range as the one used for spider silk. This chemical shift is within the expected range for dragline silk. The relaxation spectra were integrated from 47 to 50.5 ppm. The statistically best fit was found to be a stretched exponential, shown in Figure 7.1 with a relaxation time of T ∗1 = 16.3 ± 0.8 s and β = 0.70 ± 0.02 yielding 〈T1〉 = 21 ± 1.0 s. It is also interesting 61  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) SpI Alanine C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.1: Single, double, and stretched exponential fits to the MaSp1 alanine α carbon relaxation data. that the measured relaxation time is close to that found in the silk. This suggests both a similar mean correlation time and order parameter. The smaller β means that there is a larger distribution of vibrational modes or they are shifted away from the fast/slow motion transition point. It is interesting to note that the chemical shift from the cross polarization spectrum, along with the strikingly similar scale of relaxation time to that of natural silk suggest a large amount of β sheets. The alanine β carbon in MaSp1 was found to have a chemical shift of 21.1 ppm. This peak corresponds to β sheets. The value of the peak separation was measured to be ∆CSαβala = 28.5 ppm, which is in the range of β sheets and far from any other structure. The β carbon also appears to have a barely visible ledge between 15-16 ppm. This ledge corresponds to α helices but as a similar ledge can be seen in the spider silk data above so is not a distinguishing characteristic. The peak was integrated over a range of 15-21 ppm. The best fit was found to be a double exponential as shown in Figure 7.2, with T fast1 = 0.40 ± 0.09 s and a slow relaxation time of T slow1 = 1.8 ± 0.7 s with 70 ± 16% of the signal in the fast regime. These results are consistent for those found in spider silk's alanine residue and strongly suggests the presence of a significant β sheet component in MaSp1. 62  0  2  4  6  8  10  12  14  16  18  20 In te ns ity D2 (s) Sp1 Alanine C-beta Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.2: Single, double, and stretched exponential fits to the MaSp1 alanine β carbon relaxation data. 7.1.2 Glycine α Carbon The glycine α carbon in MaSp1 was found to have a chemical shift of 43.4 ppm, with a width of 4 ppm. The width was measured by fitting a Gaussian to the peak. The shift is consistent with the values reported in the literature, but does not in itself imply a strong presence of β sheets as this is also with the range of the random coil chemical shift, and the peak width does cover a significant region of the 31 helix chemical shift. The peak range for integration of the relaxation spectra was 41.5-45 ppm. The best fit to the relaxation was found to be a stretched exponential, shown in Figure 7.3 with parameters T1 = 15.3 ± 2.2 s and β = 0.64 ± 0.10. This yielded a mean relaxation time of < T1 >= 21.0 ± 5.0 s. This shortening of the relaxation time would be best explained by a smaller order parameter than the one found in spider silk, suggesting a looser structure than that of rigid β sheets. 7.1.3 Glutamine Like the spider silk, the glutamine α carbon peak does not appear in the cross polarization spectra. However in the spectrum with D2=5 s, a peak begins to emerge with a chemical shift of 54 ppm as can be seen in Figure 7.4, and by D2=40 s it appears to be on the same scale as that of the alanine α carbon. This suggests the presence of a much slower relaxing glutamine α carbon peak. 63  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) SpI Glycine C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.3: Single, double, and stretched exponential fits to the MaSp1 glycine α-C relaxation data  0 10 20 30 40 50 60 70 In te ns ity Chemical Shift (ppm) D2=.1s D2=.2s D2=.5s D2=1s D2=2s D2=5s D2=10s D2=20s D2=40s Figure 7.4: Multiple spectra from the MaSp1 T1 relaxation experiment. While most in- formation from this data required fitting and analysis, one result that was obvious from observation was the emergence of the ledge at 25.3 ppm into a full peak. 64  0  5  10  15  20  25  30  35  40 In te ns ity D2 (s) Sp1 Glutamine C-beta/gamma Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.5: Single, double, and stretched exponential fits to the MaSp1 glycine β/γ carbon relaxation data. The glutamine β and γ carbon peak in MaSp1 chemical shift was found to range from 28-32 ppm. Due to the fact that all of the glutamine γ conformations lie in this range, it was impossible to deduce anything about the structure from this. Also, as in the silk, there was a ledge at 25 ppm that extended downfield from the alanine β carbon that was well beyond the range of chemical shifts expected for alanine β carbon. The most likely structure for this is the glutamine α helix which has a chemical shift of 25.6 ppm, although the 31-helix cannot be ruled out as it would be near at 26.9 ppm The peak was integrated over a range of 27-30 ppm. The best fit was observed to be a double exponential, shown in Figure 7.5 consisting of a fast relaxation time of T fast1 = 0.79± 0.38 s which made up 18±4% and a slow component of T slow1 = 18.2±1.3 s. While these relaxation times are quite different from that in spider silk they are strikingly similar to those found in the 40◦C sample. The big difference between MaSp1 and spider silk, both heated and at room temperature, is the ratio of fast to slow relaxation for the glutamine β,γ carbons. Where spider silk has a ratio of around 1:1 for fast to slow, the glutamine has a ratio of 1:4, suggesting that the structure causing the fast relaxation is far more prominent in spider silk. 7.1.4 Discussion of MaSp1 The alanine α and β carbons exhibited both chemical shift and relaxation behavior that strongly suggests a strong presence of β sheets. Both carbons peaked in the range accepted for the presence of β sheets and no structure other than β sheets had a ∆CSαβala even close to 65 AB C D E 60 40 20 0 Chemical Shift (ppm) Figure 7.6: Spectra of lyophilized gland silk (B) and lyophilized denatured silk (D), compared to MaSp1 (A) and MaSp2 (C) and electrospun MaSp1. Lyophilized spectra from Hijirida et al. [20]. the value of 28.5 ppm found for MaSp1. In addition, the relaxation parameters for both the α and β carbons appeared to take almost identical values to those measured in spider silk. However, the glycine results tell a different story. The drop in relaxation time suggests a reduction in the order parameter, or loosening of the rigid structure that was measured in spider silk. This suggests that the mechanisms or requirements for the formation of β sheets may be different for alanine than glycine. Another interesting comparison is to 13C NMR data of lyophilized denatured and gland spider silk from Hijirida et al. [20], shown in Figure 7.6. In their work, the silk was denatured by formic acid before lyophilization, while the silk glands were extracted from spiders. They concluded that in both states, there were no β sheets present. This is particularly interesting because this suggests that perhaps at one point during production of MaSp1 a step was taken that allowed alanine β sheets to form, as opposed to their formation simply being a naturally preferred state. 66  0  10  20  30  40  50  60  70  80  90  100 In te ns ity D2 (s) Sp2 Alanine C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.7: Single, double, and stretched exponential fits to the MaSp2 alanine α carbon relaxation data. 7.2 MaSp2 As MaSp2 exists in only small abundances in spider silk, being able to analyze an isolated sample could help provide information into what role it plays in the formation of spider silk's secondary structure. 7.2.1 Alanine The MaSp2 alanine α-carbon is observed at 49.2 ppm with a peak width of 3 ppm, which falls within the range of both β-sheets and the 31 helix. This chemical shift is within the predicted range for dragline silk. The relaxation spectra were integrated from 48 to 50.5 ppm. The statistically best fit was found to be a stretched exponential, shown in Figure 7.7, with a relaxation time of T ∗1 = 15.3 ± 0.6 s and β = 0.71 ± 0.02 yielding 〈T1〉 = 19.2 ± 0.8 s. It is also interesting that the measured relaxation time is close to that found in the silk. This suggests both a similar mean correlation time and order parameter. The smaller β means that there is a larger distribution of vibrational modes or they are shifted away from the fast/slow motion transition point. The alanine β carbon in MaSp2 was found to have a chemical shift of 20.8 ppm and a ledge at from 16.5-15.5 ppm. The peak corresponds to β sheets, while the ledge covers a range of 67  0  1  2  3  4  5  6  7  8  9  10 In te ns ity D2 (s) Sp2 Alanine C-beta Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.8: Single, double, and stretched exponential fits to the MaSp2 alanine β carbon relaxation data. conformations that include random coil, 31 helices, and α helices. The value of the (major) peak separation was measured to be ∆CSαβala = 28.4 ppm, which is in the range of β sheets and far from any other structures. The β carbon peak was integrated over a range of 15-21 ppm The best fit was found to be a double exponential, as shown in Figure 7.8, consisting of a fast relaxation time of T fast1 = 0.26 ± 0.07 s that made up 53 ± 12% of the signal, and a slow relaxation time of T slow1 = 1.7± .04 s. These parameters are within the expected values of the accepted model for the two component nature of spider silk's crystalline region. 7.2.2 Glycine α Carbon The glycine α carbon in MaSp2 was found to have a chemical shift of 42.9 ppm with a width of 6 ppm. The chemical shift is slightly below the values presented in the literature for spider silk. The relaxation spectra were integrated over the glycine peak with a range from 41-44 ppm. The best fit to the relaxation data was found to be a stretched exponential, as shown in Figure 7.9, with parameters T ∗1 = 18 ± 1 s and β = 0.70 ± 0.05. This yielded a mean relaxation time of 〈T1〉 = 23 ± 2 s. Both the β distribution and the mean relaxation time are within the range of uncertainty for that of MaSp1. 68  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) Sp2 Glycine C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.9: Single, double, and stretched exponential fits to the MaSp2 glycine α carbon relaxation data. 7.2.3 Glutamine and Serine α Carbons In MaSp2 a peak is observed at 54 ppm that is broad but well defined. Identifying the residues in this peak is problematic as there is significant overlap between the serine α carbon peak, which has its β sheet chemical shift at 54.4-55.0 ppm and glutamine α carbon where the 31 helix structure at 54 ppm. As serine has a much larger abundance in MaSp2, it cannot be discounted. This means that the 54 ppm peak corresponds to both glutamine α carbons in 31 helices and the serine α in β sheets. The relaxation data from this peak resulted in a two component fit and is shown in Figure ??. The two components of the fit were T fast1 = 12 ± 2 s and T slow1 = 65 ± 16 s with the fast component making up 65± 5% of the signal. While the slow T1 may seem surprisingly long, particularly with it not being observed in the 200 MHz magnet [33], it is possible that it's relaxation speed was so close to that of the alanine α carbon from the literature that it was not accounted for. It is most likely that the glutamine α represents at least the slow relaxation, as the slow relaxation regime is seen in MaSp1 as it contains very little serine, as shown in Table 4.3. It is also likely that the T fast1 is also in or near the slow motion limit. The reason for this is that for it to be ignored, it would have to have to relax at least three or four times quicker than the spider silk for it to be reasonably neglected from the fit. Because the 200 MHz T1 was 12 seconds for the alanine, expecting it to have been 2 or 3.5 seconds would be a reasonable guess. The maximum field dependence that the relaxation time could have would be a factor of four in the slow motion limit. 69  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) Sp2 Glutamine C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.10: The relaxation curve of the glutamine α carbons (and possibly serine α carbons) in MaSp2. 7.2.4 Proline α and Serine β Carbons This peak at 60.8 ppm sits over the chemical shift range for the proline α and the serine β carbons. There is no peak in MaSp1 or the electrospun MaSp1 fibers at this point as neither residue has substantial abundances in these samples. The proline would have to be in an upfield configuration as the intensity drops off substantially in the higher chemical shifts that the proline α carbon can have adopt. The closest chemical shift to this is the 31 helix at 62.3 ppm, which is quite far from the peak center. The serine β carbon peak chemical shift seems to contradict the results from the serine α peak. The two most likely candidate peaks for the structural assignment are the α helices or β turns. However, these structures for the serine α carbon are in local minima. Because the two sites, proline α and serine β carbons, appear with similar abundances, and the peak is relatively featureless, it is difficult to conclude what conformation the two amino acids might adopt. Though we can say with some certainty that the proline will not adopt the α helix, which has a chemical shift of 66.3 ppm. The peak was integrated over the range of 59-63 ppm. The best fit to the relaxation curve was a stretched exponential, shown in Figure 7.11, with relaxation components T ∗1 = 16.93± 0.6 s and β = 0.60± 0.02 yielding a relaxation time of 〈T1〉 = 25.3± 1.0 s. This result suggests that either there is only one peak in this region and that one of the choices made in the chemical shift analysis above is either not present or did not cross polarize well, or that the T ′1s of the two different carbons are similar enough that they can not be distinguished. 70  0  10  20  30  40  50  60  70  80  90  100 In te ns ity D2 (s) Sp2 Pro C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.11: The relaxation curve of the proline α carbons in MaSp2. 7.2.5 Glutamine β/γ The glutamine β and γ carbon peak in MaSp1 was found to range from 29-32 ppm. Due to the fact that all of the glutamine γ conformations lie in this range, it was impossible to deduce anything about the structure from this. The ledge observed at 25 ppm in the other spectra is a well defined peak in MaSp2. This is understandable as MaSp2 was the only sample to have a well defined glutamine α peak. The most likely structure for this is an α helix which has a chemical shift of 25.6 ppm, although the 31-helix should not be be ruled out as it it would be near 26.8 ppm. The peak was integrated over a range from 28-32 ppm. The best fit was found to be a stretched exponential, shown in Figure 7.12, with parameters of T ∗1 = 1.7 ± 0.2 s, which made up 44±4% of the signal, and a slow component of T slow1 = 23±2 s. The significance of these values is that they are closer to spider silk than MaSp1, which is unexpected as MaSp1 is the dominant protein in silk. As the glutamine is primarily in the amorphous regions of spider silk, this could be interpreted as MaSp2 playing a vital role in that region as well as the development of the crystalline region as the accepted model postulates. That said, the chemical shift for this peak in spider silk is closer in line with MaSp1 than MaSp2. 7.2.6 MaSp2 Results MaSp2 has two defining characteristics. The first is that its alanine and glycine behave almost exactly like MaSp1. The relaxation parameters between the two proteins are indis- 71  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) Sp2 Glutamine C-beta/gamma Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.12: Single, double, and stretched exponential fits to the MaSp2 glutamine β/γ carbon relaxation data. tinguishable and the chemical shift results show a strong presence of alanine of β sheets. Like the MaSp1, the drop in relaxation time for glycine suggests a reduction in the order parameter, or loosening of the rigid structure that was measured in spider silk. The similar- ities in the primary structure of these two proteins suggest that the exact primary structure of the protein plays a less significant role in the formation of the secondary structure and resulting mechanical properties than the spinning procedure itself. It is possible that the differences between the two lie in the amorphous region, which are more difficult to probe using these two one dimensional NMR techniques. The second characteristic is the two peaks visible in the glutamine range. One would be tempted to assign the difference in line-shape compared to MaSp1 to the different compo- sitions of the two proteins. However when MaSp2 is compared to lyophilized gland silk, which although primarily Sp1, also has a similar line-shape for the region from 25-40 ppm, as seen in Figure 7.6. This suggests that some of the differences in the line-shape between the MaSp1 and MaSp2 are not a result of their different compositions but possibly a result of different processing conditions. 7.3 Electrospun MaSp1 Analyzing the structure of the electrospun MaSp1 is particularly important, as it could help to explain its poor mechanical properties and resolve the uncertainty surrounding the FTIR results. 72  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) Electrospun Sp1 Alanine C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.13: Single, double, and stretched exponential fits to the electrospun MaSp1 alanine α carbon relaxation data. 7.3.1 Alanine The chemical shift for the alanine α carbon of electrospun MaSp1 was found to be 52.3 ppm, far outside of the expected values for β sheets. The most likely candidate for the electrospun MaSp1's alanine α carbon is the α helix, which ranges from 52.3-52.8 ppm. No other major structure for alanine α carbons extends into this region. This is divergent from the results of Gandhi, who observed a strong β sheet component in the electrospun silk. The relaxation spectra were integrated across the peak. Due to the downfield shift of the peak, there was no way to avoid some contamination from the glutamine α peak. The best fit to the data was the stretched exponential, as shown in Figure 7.3.1, with parameters T ∗1 = 21±4 s and β = 0.7±0.1 yielding a mean relaxation time of 〈T1〉 = 27±7 s. While the large uncertainty makes any detailed analysis of this value difficult, this peak does appear to decay slower than those of spider silk and the MaSp1 and MaSp2 powder spectra shown in Figures 6.1, 7.1, and 7.7. While this could be caused by a larger, more restrictive, order parameter, this is more likely the result of a much slower correlation time that would result from the slower motion that would result from a less oriented, more amorphous structure. The alanine β carbon in electrospun MaSp1 was found to have a chemical shift of 16.1 ppm. This peak was extremely broad, only dropping slightly by 24 ppm. This is of particular interest because that α helices appear to be a dominant structure, as they are the only conformation that has a chemical shift below 16.5 ppm. The peak separation was found to be ∆CSαβala = 35.5 − 36.5 ppm, which is the range of being either α helices of β turns, but 73  0  2  4  6  8  10  12  14  16  18  20 In te ns ity D2 (s) Electrospun Sp1 Alanine C-beta Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.14: Single, double, and stretched exponential fits to the electrospun MaSp1 alanine β carbon relaxation data. far from the established value for β sheets. There is also likely a large contribution from β turns and random coils as the peak (before the plateau) does extend into their chemical shift ranges as in figure 5.2. The remarkably smaller chemical shift adds more weight to the claim that the electrospun MaSp1 alanines have a dominant α helix component, as was also observed in the α carbon. This is a departure from the structures of both silk and the powdered MaSp1. It is also inconsistent with the results of the FT-IR experiments where it was shown that the electrospun MaSp1 had a strong β sheet component, making up 42% of the structure. It is however consistent to the results from both lyophilized denatured and lyophilized gland spider silk that are shown in Figure 7.6 [20]. The peak was integrated over a range of 15-21 ppm. The best fit for this was a single exponential, shown in Figure 7.14, and is indistinguishable from the fits generated by the stretched and double exponentials. The relaxation time was measured to be T1 = 0.77 s. It is interesting that this is between the two values from spider silk, MaSp1, and MaSp2. This is another departure from both the powdered proteins and spider silk, all of which fit to double exponentials. This suggests that the electrospun MaSp1 does not contain two distinguishable states observed in the literature. Of course this is not so surprising, as these two states supposedly exist as two forms of β strands, which do not appear to be a dominant component of the electrospun MaSp1. 74  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) Electrospun Sp1 Glycine C-alpha Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.15: Single, double, and stretched exponential fits to the electrospun MaSp1 glycine α carbon relaxation data. 7.3.2 Glycine The glycine α carbon in electrospun MaSp1 was found to have a chemical shift of 42.4 ppm with a peak width of 9.7 ppm. The chemical shift is substantially below the values reported in the literature as well as compared to the other samples discussed above and corresponds to the 31 helix. However, as the peak is incredibly broad, this translates into little specific information about the types of structure, other than that there are lots of them. The peak was integrated over a range of 40-44 ppm. The result was a stretched exponential, as shown in Figure 7.15, with parameters of T ∗1 = 15.6± 2.3 s and β = 0.63± 0.09, yielding a mean relaxation time of 〈T1〉 = 21.9± 5 s. Like both the MaSp1 and MaSp2 powders, this falls below both the room temperature and hot relaxation time for spider silk. 7.3.3 Glutamine β/γ Carbons The glutamine β and γ carbon peak in Electrospun MaSp1 chemical shift was found to range from 27-29 ppm. Due to the fact that all of the glutamine γ conformations lie in this range, it was impossible to deduce anything about the structure from this. There is a peak observed at 24 ppm, which is outside of the range for both the glutamine and alanine β carbons. What carbon this peak represents is a mystery. The glycine β/γ peak was integrated over the range from 27-32 ppm. The best fit was 75  0  5  10  15  20  25  30  35  40  45  50 In te ns ity D2 (s) Electrospun Sp1 Glutamine C-beta/gamma Relaxation Data Single exponential fit Stretched exponential fit Double exponential fit Figure 7.16: Single, double, and stretched exponential fits to the electrospun MaSp1 glu- tamine β/γ carbon relaxation data. observed to be a double exponential, shown in Figure 7.16 consisting of a fast relaxation time of T fast1 = 3.4± 1.1 s which made up 58± 12% of the signal and a slow component of T slow1 = 36±12 s. Due to the large uncertainty in this fit it is difficult to make any structural characterizations from the results. 7.3.4 Electrospun MaSp1 Conclusions The most defining characteristic of the electrospun MaSp1 was the broadness of its peaks. This suggests a denatured structure that occupies a wide variety of torsion angles. While much of the relaxation data was unilluminating as the (rather large) uncertainty was greater than the discrepancies with both the dragline silk and the proteins powders, the single component fit for the alanine β carbon did reveal that the two component nature of the β sheets observed in both dragline silk was not present in the electrospun fibers. This in combination with the large increase in the value of ∆CSαβala strongly suggests that there are either no or very few β sheets present within the electrospun MaSp1. While this does not appear to be consistent with Gandhi's interpretation of the earlier FTIR measurements, it is consistent with the re-analyzed data from Gandhi's FTIR experiments on electrospun MaSp1 from Table 4.6 and Figure 4.6 which showed both a local minima for the presence of parallel β sheets and a large peak for the aggregated strands that are characteristic of denatured proteins. This denatured structure does explain the poor me- chanical properties of the electrospun silk done by Gandhi. Almost every model of spider 76 silk's mechanical properties depends at least partially on the crystalline regions that form [21, 15, 5]. Without this rigid backbone, it is not surprising that its strength and modulus drop dramatically. This is also confirmed by the fact that while the strength and modulus of the electrospun fibers dropped by several orders of magnitude from that of natural silk, as given in Table 4.4, the extendability was only reduced marginally. These results do not help resolve whether or not electrospinning is a practical method for making artificial silk fibers. While the process did yield useful fibers, the line-shape of the electrospun MaSp1 is very similar to the denatured lyophilized spider silk found by Hijirida et al. [20], as can be seen in Figure 7.6. This is rather significant as it suggests that the structural inadequacies of the fibers and the resulting poor mechanical properties may be a result of the denaturing via formic acid as opposed to the electrospinning process itself. It is possible that post spinning treatments could be used to allow for crystallization. One such technique of plasticization was done by Hijirida et al. [20] on their denatured lyophilized silk protein and showed a significant increase in β sheet crystals. This is particularly promising due to the similarities in CP-MAS line-shape between the electrospun silk and their sample. This does not however necessarily vindicate electrospinning as a choice technique for this process. The extreme motions during the process are very different to that of the relatively slow secretion through spider's silk glands [21]. How this abuse would affect the proteins while in a denatured state remains unresolved, and it is possible that proteins chains could be torn during this process, weakening the final product regardless of crystal formation. 77 Chapter 8 Concluding Remarks 13C CP-MAS spectra and relaxation times were measured for spider silk proteins in silk, powder, and electrospun fiber forms. For spider silk, this showed that the optimal relaxation fit for the backbone carbons was to a stretched exponential, implying a distribution of relaxation times, and by implication correlation times. These results were used to determine the order of the correlation time of the thermal motion of the protein backbone, showing it to be close to the fast/slow transition point. Interestingly, the powdered samples of MaSp1 and MaSp2 were shown to be more similar to each other than not, and had motion of the alanine backbones comparable to that of spider silk. The relaxation time measured for their glycine backbones were significantly faster than that of the spider silk, suggesting the glycines to be in a less rigid structure than that of the silk. The similarities to the alanine of silk, and differences between the glycine suggest that the spider's spinning process to silk is more crucial for the orientation and ordering of the poly glycine than it is to the crystallization of the polyalanine motifs. The electrospun MaSp1 was found to have very little crystallization and appeared to have a structure consistent with that of denatured proteins. This lack of crystallinity does explain the poor mechanical properties of electrospun spider silk. This result stands in contradiction to previous FTIR measurements of similarly prepared fibers, although revisiting the FTIR data raises many questions about that data's interpretation. There are multiple directions that future research for this can go in. The first is a continuation of the study of spider silk's correlation time. As the data used for the low field relaxation time was not fitted to a stretched exponential, relaxation measurements in a spectrometer 78 with a different field would make the results more accurate. This could also be done by measurements at different temperatures, although the exact fit may be difficult without identifying the order parameter via different multi field strength experiments. While this would be an intellectually interesting exercise, its usefulness is debatable as it might not provide much usable information to the understanding of spider silk. A second avenue to explore is the differences between MaSp1 and MaSp2. NMR experiments of spider silk by Holland et al. [30] used a 2-dimensional Carbon-Carbon correlation spectrum to better map the secondary structures in spider silk. The advantage of this experiment is that it shows correlations between carbons within a residue allowing structures to be more easily identified despite the broad peaks produced by spider silk. It also allows overlapping regions to be isolated and separated. This technique would show a better picture of any structural differences between the MaSp1 and MaSp2 powders. It would be particularly interesting to use this technique for MaSp2 as it would help to separate the overlapping regions of the glutamine, proline α carbons and the serine α and β carbons. This could prove particularly useful in understanding the role played by MaSp2 in spider silk and possibly help resolve the unresolved questions regarding the peaks at 54 and 60 ppm. A final avenue to explore is continuing experiments on electrospun spider silk proteins. While the initial results were not very promising, electrospinning is the simplest method for produc- ing nanofibers. This is important as the mechanical properties of silks appear to be diameter dependent, and techniques that appear to replicate secondary structures have difficulty pro- ducing fibers of a small enough diameter [35]. It is possible that with the correct post treatment technique, such as that used on the denatured lyophilized silk by Hijirida et al. [20], that the electrospun silk could take on the correct secondary structure. Other possible post treatment techniques could be tried, such as methanol which showed promising results crystallizing electrospun Bombyx mori, as done by Gandhi [10]. A more ambitious goal could be to find a method to electrospin from an aqueous protein solution instead of using formic acid. The results of the NMR experiments showed that the electrospun fiber are consistent with that of the denaturing caused by formic acid. 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