Solid State NMR Investigation of Protein-Based Biomaterials Resilin: An Extremely Efficient Elastomeric Protein by Andrew L. C. Reddin B.Sc., Dalhousie University, 2008 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) April, 2012 © Andrew L. C. Reddin 2012 Abstract Solid state nuclear magnetic resonance experiments were performed in order to investigate the microscopic properties of three resilin/resilin-like proteins: An16, rec1-resilin, and nat- ural resilin in dragonfly tendons. Three different types of experiments were performed: measurements of chemical shifts in 13C spectra, measurements of residual quadrupole cou- plings in deuterated water absorbed in the samples, and measurements of proton residual dipole couplings based on the buildup of multiple quantum coherences. The results suggest that the molecular chains in the materials tested are primarily randomly coiled and lacking in regular structure, and are able to easily change between many transient conformations. These conformations can vary significantly in terms of their structural characteristics, re- sulting in a broad distribution of localized dynamics. When stretched, An16 showed a slightly increased tendency to adopt β-sheet secondary structure. The natural resilin also exhibited slightly more rigid structure than the other materials, which may be related to greater efficiency in the natural crosslinking process. ii Table of Contents Abstract ......................................... ii Table of Contents .................................... iii List of Tables ...................................... vi List of Figures ...................................... vii Acknowledgements ...................................x 1 Introduction .....................................1 2 NMR Background .................................3 2.1 Larmor Precession................................3 2.1.1 Classical Picture.............................3 2.1.2 Quantum Mechanical Picture......................4 2.2 Bulk Magnetization...............................6 2.2.1 Thermal Equilibrium Magnetization..................7 2.3 Density Matrix Formalism...........................8 2.3.1 Thermal Equilibrium Density Matrix.................9 2.3.2 Time Dependence of the Density Matrix............... 10 2.4 The Rotating Frame............................... 10 2.4.1 Zeeman Truncation........................... 11 2.5 Radio-Frequency Pulses............................. 12 2.5.1 Pulse Propagators and Rotation.................... 13 2.6 Relaxation.................................... 14 2.6.1 The Nuclear Overhauser Effect..................... 15 2.7 NMR Spectroscopy............................... 18 2.7.1 Fourier Transform Spectroscopy.................... 19 2.7.2 2D spectroscopy............................. 21 2.8 NMR interactions................................ 23 2.8.1 Chemical Shielding........................... 23 iii 2.8.2 Dipolar Interaction........................... 25 2.8.3 Quadrupolar Interaction........................ 27 2.8.4 Residual Couplings........................... 31 2.9 Average Hamiltonian Theory.......................... 34 2.9.1 The Toggling Frame........................... 35 2.10 Multiple Quantum Coherence......................... 36 2.10.1 Excitation of Multiple Quantum Coherence.............. 38 2.10.2 MQ Coherence in Extended Spin Systems.............. 39 2.10.3 Detection of Multiple Quantum Coherence.............. 39 3 Materials Background ............................... 42 3.1 Proteins...................................... 42 3.1.1 Secondary Structure........................... 44 3.1.2 Higher Order Structure......................... 47 3.2 Elastomers.................................... 47 3.3 Resilin...................................... 50 3.3.1 Natural Occurrence and Function................... 51 3.3.2 Mechanical Properties.......................... 52 3.3.3 Molecular and Structural Properties.................. 54 3.3.4 Amino Acid Composition and Sequence................ 57 3.4 Recombinant Resilin-Like Proteins....................... 59 3.4.1 Production and Sequence........................ 59 3.4.2 Stability and Purification........................ 60 3.4.3 Crosslinking............................... 61 3.4.4 Secondary Structure........................... 62 3.4.5 Mechanical Properties.......................... 64 3.4.6 Applications of Resilin-like Polypeptides............... 65 4 Experimental Methods .............................. 68 4.1 Materials Used.................................. 68 4.2 NMR Setup................................... 69 4.3 Stretching Setup................................. 70 4.4 Carbon-13 Spectroscopy............................. 70 4.4.1 Pulse Sequence.............................. 71 4.5 Quadrupole Coupling Measurements...................... 73 4.5.1 Pulse Sequence.............................. 74 4.5.2 Trial Materials.............................. 75 4.6 Multiple-Quantum Experiments........................ 76 iv 4.6.1 Spectrometer Tuning.......................... 77 4.6.2 Pulse Sequence.............................. 79 4.6.3 Buildup Curves............................. 81 4.6.4 Pre-selection Techniques........................ 83 4.6.5 Tikhonov Regularization........................ 86 4.6.6 Analytical Distribution Functions................... 87 4.6.7 PDMS Trial Experiments........................ 87 5 Results & Discussion ................................ 91 5.1 Carbon-13 Chemical Shifts........................... 91 5.2 Residual Quadrupole Couplings........................ 96 5.3 Residual Dipole Couplings........................... 99 5.3.1 Pre-selection............................... 99 5.3.2 An16................................... 105 5.3.3 Rec1-resilin................................ 109 5.3.4 Dragonfly Tendons........................... 113 5.3.5 Discussion................................ 117 6 Conclusion ...................................... 126 Bibliography ....................................... 129 v List of Tables 3.1 The twenty-one standard eukaryotic amino acids, including their structure and the polarity and pH of their side-chains................... 43 3.2 Mechanical properties of various elastic proteins................ 54 3.3 The (previously reported) mechanical properties of natural dragonfly resilin and recombinant resilin-like proteins: rec1-resilin, An16, Dros16, Cf-resB, and Hi-resB..................................... 64 4.1 Summary of the coherence orders (and their phases) generated in the two types of MQ experiment (reference and MQ-filtered).............. 81 4.2 Analytical distributions functions P (D) used for least-squares fitting of MQ buildup curves using numerical integration................... 88 4.3 Parameters obtained from various types of fits to the experimental PDMS buildup curve.................................... 89 5.1 Parameters for the α/β-carbon chemical shift differences for the different residues....................................... 94 5.2 The effect of the different pre-selection techniques on the total intensity of the different samples................................ 103 5.3 Parameters obtained for An16 with a DQ pre-selection time of 2.5 ms.... 106 5.4 Parameters obtained for An16 with a DQ pre-selection time of 5.0 ms.... 109 5.5 Parameters obtained for rec1-resilin with a DQ pre-selection time of 2.5 ms. 109 5.6 Parameters obtained for rec1-resilin with a DQ pre-selection time of 5.0 ms. 112 5.7 Parameters obtained for the tendons with a DQ pre-selection time of 2.5 ms. 114 5.8 Parameters obtained for the tendons with a DQ pre-selection time of 5.0 ms. 116 5.9 The mean (D¯), mean deviation (∆D), and the plateau level (C) of the dis- tribution functions obtained for the different samples and pre-selection times. 120 vi List of Figures 2.1 A diagram of the energy levels and transitions for a system of spin-1/2 nuclei. 16 2.2 An illustration of a simple pulse sequence, with one ninety-degree pulse fol- lowed by acquisition of the free induction decay (FID)............. 19 2.3 Absorptive and dispersive line-shapes corresponding to the real and imagi- nary parts of a single Lorentzian......................... 21 2.4 Illustration of a typical pulse sequence used for a two-dimensional experiment. 22 2.5 Illustration of the chemical shift powder spectrum for several values of η.. 25 2.6 The dipolar powder pattern, also known as a Pake pattern.......... 27 2.7 Illustration of the quadrupolar powder spectrum for several values of ηQ... 31 2.8 Illustration of a pulse sequence used to produce and detect MQ coherence.. 40 3.1 An illustration of the formation of a peptide bond to link together two polypeptides (or amino acids) into one larger polypeptide........... 44 3.2 Molecular representations of α-helix and β-sheet secondary structures.... 46 3.3 An illustration of the difference in entropy between relaxed and extended states for a model polymer on a square lattice................. 48 3.4 Structural representation of a di-tyrosine crosslink between two polypeptides and some reactions used to produce di-tyrosine crosslinks from tyrosine residues. 55 4.1 A simplified block diagram of the spectrometer setup used in the current experiments.................................... 69 4.2 A photograph of the stretching apparatus used to control the length of the samples during testing............................... 70 4.3 The pulse sequence used to acquire 13C spectra for chemical shift