COPYRIGHT AND USE OF THIS THESIS This thesis must be used in accordance with the provisions of the Copyright Act 1968. Reproduction of material protected by copyright may be an infringement of copyright and copyright owners may be entitled to take legal action against persons who infringe their copyright. Section 51 (2) of the Copyright Act permits an authorized officer of a university library or archives to provide a copy (by communication or otherwise) of an unpublished thesis kept in the library or archives, to a person who satisfies the authorized officer that he or she requires the reproduction for the purposes of research or study. The Copyright Act grants the creator of a work a number of moral rights, specifically the right of attribution, the right against false attribution and the right of integrity. You may infringe the author’s moral rights if you: - fail to acknowledge the author of this thesis if you quote sections from the work - attribute this thesis to another author - subject this thesis to derogatory treatment which may prejudice the author’s reputation For further information contact the University’s Director of Copyright Services sydney.edu.au/copyright Advanced NMR Spectral Characteristics Used in Biochemical Studies of Anisotropic Media and Cells New Ways of Analysing Quadrupolar-Split Resonances, Dynamically Hyperpolarised Spectra, and Those Obtained With Shift Reagents Max Puckeridge, BSc(Hons) A thesis submitted for the degree of Doctor of Philosophy January 2014 School of Molecular Bioscience University of Sydney NSW 2006 Australia i Acknowledgements I wish to thank my supervisor, Professor Philip Kuchel, for the large role he played in my development as a scientist and a person. He showed an incredible commitment to me despite travelling to Singapore and becoming the head of a research institute. I am very grateful for the skills, and attention to detail, that I developed while working with him. I would like to thank Professor Arthur Conigrave, my associate supervisor, for his guidance and allowing me to participate in his group meetings while Philip was overseas. Also, I would thank Bob Chapman who was always reliable for advice and help on the NMR spectrometer. I am thankful to the other Kuchel students for mentoring me during my first year, particularly Tsz Wai Yau, who trained me in DIC microscopy and RBC preparation. I would also thank Guilhem Pag`esfor running the DNP NMR experiments in Paper II, and the many technicians in the Biochemistry building who ran glucose assays for Paper V. Last I would thank all my family. I am grateful to my sister Carla, for her support, and my parents, who allowed me to do my best and get a good education. And of course, my soul mate and partner Jana, who always keenly discussed my work and even listened to my constant ‘math talk’. ii Abstract The theme of this thesis was to quantify possible sources of adenosine triphosphate (ATP) hydrolysis in the human red blood cell (RBC). Understanding the consumption of ATP in RBCs provides insight into its energy demands, and those of other cell types and the body as a whole. The main sources of ATP hydrolysis investigated included: (i) the Na+,K+-ATPase (NKA); and (ii) cell membrane flickering (CMF) of RBCs. In addition to these studies, we developed mathematical models of RBC systems and the experimental techniques used. Many of these models described spectral characteristics of NMR spectra, including: (i) chemical shift differences induced by shift reagents (SRs); (ii) dynamic nuclear polarisation (DNP) NMR; and (iii) z-spectra of quadrupolar nuclei contained in stretched hydrogels. In each of these cases, experimental data were acquired, and methods were then developed to estimate model parameter values. Chapter 3 describes the NMR experiments that examined the chemical shift differences induced on 23Na+ by the SR, thulium 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrakis (methylenephosphonate), as functions of Na+ and other competing ions. We developed a mathematical model that successfully matched the experimental dependencies, and esti- mated various model parameters. In Chapter 4, we mathematically described the decay of magnetisation of hyperpolarised nuclei (achieved using DNP) as observed using 13C NMR spectroscopy. It was found that the longitudinal relaxation time constant, T1, estimated using a regularly timed pulse sequence was artefactually reduced. We proposed a irregu- larly timed pulse sequence, which enabled correct estimates of the longitudinal relaxation rate constant, T1, and α, the NMR pulse angle. This approach was applied to exper- imental sequences obtained on hyperpolarised 13C-urea, and parameter estimates were consistent with those independently obtained by an ‘inversion-recovery’ pulse sequence. Chapter 5 describes the application of Bayesian analysis and Markov chain Monte Carlo (MCMC) methods to estimate the myriad relaxation rate constants that describe the shape and features of the z-spectra of quadrupolar nuclei contained in stretched gels. This approach proved successful in obtaining model fits and parameter estimates to ex- perimental z-spectra of 23Na+ and 7Li+ in stretched hydrogels. iii Chapter 6 examines the stoichiometric relationship between the rate at which Na+ ions are transported across the RBC membrane by the NKA to its indirect consumption rate of glucose. We performed experimental NMR time courses on suspensions of RBCs, and determined that this stoichiometric ratio was close to that theoretically predicted. It was determined that the NKA was very efficient at consuming ATP and glucose, and not an explanation for “missing” ATP turnover in the RBC. Last, for Chapter 7 I explored the origin of CMF in human RBCs; this was done in two ways: (i) CMF was mathematically modelled as a constrained random walk (CRW); and (ii) experimental DIC recordings of RBC CMF were acquired in the presence of various effectors, and analysed using the CRW model. We found that the model had the frequency characteristics and stochastic behaviour seen with CMF. It was observed that effectors of the cytoskeleton and mem- brane flexibility could significantly affect the amplitude of CMF. Furthermore, we found that previous studies that claimed a dependence of CMF on ATP were misleading, as they ignored that the cytoskeleton was alkylated under the same experimental conditions used. Overall, this work ruled out a number of potential sources of ATP hydrolysis in the RBC, and provided several model frameworks that describe metabolic systems in the human RBC, and various NMR spectral characteristics. iv List of abbreviations ADP Adenosine diphosphate AMP Adenosine monophosphate ATP Adenosine triphosphate AR Autoregressive BPG Bisphosphoglycerate BSA Bovine serum albumin CMF Cell membrane flickering CRW Constrained random walk cs Capillary-sphere DIC Differential interference contrast DNP Dynamic nuclear polarisation DOTP 1,4,7,10-Tetraazacyclododecane-1,4,7,10-tetrakis (methylenephosphonate) FID Free induction decay GAPDH Glyceraldehyde-3-phosphate dehydrogenase GrnP(h) Dihydroxyacetone-phosphate hydrate HEPES 4-(2-Hydroxyethyl)-1-piperazineethanesulfonic acid HP Hyperpolarised Ht Haematocrit MCMC Markov chain Monte Carlo MRI Magnetic resonance imaging NEM n-Ethylmaleimide NKA Na+,K+-ATPase NMR Nuclear magnetic resonance OA Okadaic acid PBS Phosphate buffered saline PDAc Phorbol 12,13-diacetate Pi Inorganic phosphate PKC Protein kinase C v PPP Tripolyphosphate RBC Red blood cell RF Radiofrequency Rib5P Ribose 5-phosphate RMSD Root mean square displacement Ru5P Ribulose 5-phosphate RW Random walk SR Shift reagent vi Contents 1 Introduction 1 1.1 Motivation . .1 1.2 Aims . .2 2 Theory of Methods 4 2.1 NMR spectroscopy . .4 2.1.1 RBC preparation for NMR spectroscopy . .7 2.1.2 Shift reagents . .8 2.1.3 Hyperpolarised NMR . .9 2.1.4 z-Spectra . 12 2.2 Microscopy . 15 2.2.1 Phase contrast microscopy . 15 2.2.2 DIC microscopy . 16 2.2.3 RBC morphology . 16 2.3 Deduction and logic . 20 2.3.1 Probability theory . 20 2.3.2 Practical Bayesian analysis . 22 2.3.3 MCMC sampling . 27 3 Shift Reagents 30 3.1 Introduction . 30 vii 3.2 Paper I: Quantitative model of NMR chemical shifts of 23Na+ induced by TmDOTP: applications in studies of Na+ transport in human erythrocytes 32 Supporting material . 43 4 Hyperpolarised NMR Spectroscopy 52 4.1 Introduction . 52 4.2 Paper II: Simultaneous estimation of T1 and the flip angle in hyperpolarized NMR experiments using acquisition at non-regular time intervals . 54 5 z -Spectra 61 5.1 Introduction . 61 5.1.1 Quantum mechanical description . 62 5.1.2 Approach to parameter estimation . 64 5.2 Paper III: Relaxation times of spin states of all ranks and orders of quadrupo- lar nuclei estimated from NMR z-spectra: Markov chain Monte Carlo anal- ysis applied to 7Li+ and 23Na+ stretched hydrogels . 70 5.3 Paper IV: 7Li+ NMR quadrupolar splitting in stretched hydrogels: devel- opments in relaxation time estimation from z-spectra . 80 5.4 133Cs+ z-spectra . 86 6 Na+,K+-ATPase & Glycolysis Coupling 88 6.1 Introduction . 88 6.2 Paper V: Stoichiometric relationship between Na+ ions transported and glucose consumed in human erythrocytes: Bayesian analysis of 23Na and 13C NMR time course data . 90 Supporting material . 100 7 Cell Membrane Flickering 105 7.1 Introduction . 105 7.2 Paper VI: Membrane flickering of the human erythrocyte: described by a constrained random walk . 108 viii Supporting Material . 131 7.3 Paper VII: Membrane flickering of the human erythrocyte: Physical and chemical effectors . 136 Supporting Material . 154 8 Overview 162 8.1 Introduction . 162 8.2 Summary of finding . 162 8.3 Future directions . 164 8.3.1 HP studies of RBCs . 164 8.3.2 z-spectra . 164 8.3.3 ATP consumption in the RBC . 165 Bibliography 173 ix Chapter 1 Introduction 1.1 Motivation The human erythrocyte or red blood cell (RBC) is a relatively simple cell despite its impor- tant function of oxygen distribution to a wide range of tissues.