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Broadline 1H and 2H nuclear Magnetic resonance studies of binary lipid mixtures containing docosahexaenoic… Lloyd-Smith, James 1999

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B R O A D L I N E X H A N D 2 H N U C L E A R M A G N E T I C R E S O N A N C E S T U D I E S O F B I N A R Y L I P I D M I X T U R E S C O N T A I N I N G D O C O S A H E X A E N O I C A C I D . James Lloyd-Smith B. Sc. Hons. (Physics & Chemistry) Queen's University, 1996 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S D E P A R T M E N T O F P H Y S I C S & A S T R O N O M Y We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A August 1999 © James Lloyd-Smith, 1999 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics & Astronomy The University of British Columbia 1956 Main Mall Vancouver, Canada Date: Abstract Containing six double bonds, docosahexaenoic acid (DHA) is the most highly un-saturated acyl chain commonly found in biological membranes. It is present in large proportions in retinal and synaptic membranes and there is substantial evidence that specific D H A concentrations are required for proper function of some membrane pro-teins. A prevalent hypothesis attributes this functional influence to the supposed wedge shape of polyunsaturated lipid molecules, suggesting that lipids with D H A chains influ-ence conformational changes of membrane proteins by exerting pressure laterally through the centre of the bilayer. This model was tested using broadline 1 H - and 2 H - N M R techniques to study a series of binary lipid mixtures. The membrane systems were mixtures of monoun-saturated l-palmitoyl-d3i-2-oleoyl-phosphatidylcholine (POPC-d3i) and polyunsaturated l-palmitoyl-do-2-docosahexaenoyl-phosphatidylcholine (PDPC-d 0) in varying proportions (from Omol% PDPC to 100mol% PDPC), and were designed to be representative of membranes found in the brain. The deuterated P O P C acted as a reporter molecule in 2 H - N M R experiments, giving a clear picture of the effects of increasing DHA content on the surrounding lipid matrix. The 1 H - N M R signal included contributions from both lipid species, and yielded information regarding general properties of the membrane. Spectro-scopic measurements were made and analyzed in terms of orientational order parameters of the lipid acyl chains, and relaxation experiments yielded further information on mem-brane dynamics at a range of timescales. All experiments were conducted at 10° C, 25° C, and 37° C. ii The order parameter measurements showed remarkably little change across the full range of membrane compositions. As PDPC content increased, the residual second mo-ment (which is proportional to a mean-squared orientational order parameter) of the proton spectrum increased slightly, while that of the deuterium line showed a small de-crease. We infer that the average chain length and order of P D P C molecules is similar to that of P O P C - d 3 i , and possibly that species-enriched microdomains may have formed which isolated P O P C from the effects of increasing polyunsaturation. The 2 H - N M R or-der parameter profiles demonstrated clearly that the addition of P D P C influenced the conformational freedom of POPC-d 3 i 's perdeuterated chain. A slight decrease in orien-tational order was observed in the lower half of this chain, indicating greater mobility in that region. This is the first direct measurement of the effect of DHA-bearing lipids on the the chain order of other, less unsaturated lipids in.the membrane, and is not consistent with the prediction of the "wedge model" that lateral pressure increases in the centre of the bilayer. To explain this observation, it is suggested that the D H A chains spend slightly more time doubled back towards the lipid-water interface, vacating space deep in the bilayer which is occupied by other acyl chains. T\z values for both 1 H - and 2 H - N M R were found to rise significantly as P D P C was added to the membrane. Since T l 2 also increased with temperature, this is deduced to result from a decrease in the correlation times of very fast motions. A likely example, which is consistent with the above model for DHA's motions, would be speeding up of the trans-gauche isomerizations of the acyl chains. Finally, T | e values for POPC-d 3 1 ' s perdeuterated chain were found to decrease markedly as PDPC was added, dropping by almost a factor of two between the 0% and 75% P D P C samples. T 2 9 e relaxation processes are determined to arise from thermally-activated collective motions of the bilayer, and the primary mechanism is proposed to be membrane surface undulations. If the twofold change in T%e resulted entirely from increased amplitude of these fluctuations, then the iii membrane curvature energy KC has been reduced by almost 50% by the addition of 75 mol% P D P C to the P O P C - d 3 i membrane; the real effect is expected to be somewhat smaller, since other processes doubtless contributed to the observed change. The relation of the order parameter measurements to the proposed decrease in cur-vature energy is considered, and the implications of these results for D H A ' s role in mem-brane function are discussed. Whi le significant effects can be postulated for increased flexibility or altered chain packing, no explanation has emerged for the extreme specificity wi th which nature chooses D H A for certain important systems. iv Table of Contents Abstract ii List of Tables ix List of Figures x Abbreviations xii Acknowledgement xiv 1 Introduction 1 1.1 Biological Membranes 1 1.1.1 Lipids 1 1.2 Biological Motivation to Study DHA 3 1.2.1 Membrane Lipid Composition and Polyunsaturation 3 1.2.2 Evidence for a Functional Role of DHA 6 1.2.3 Possible Roles for DHA at the Molecular Level 8 1.3 Physical Properties of Polyunsaturated Lipids 10 1.3.1 Early Work - Molecular Shape and Spontaneous Curvature . . . . 11 1.3.2 Later Work - Molecular Order and Lateral Organization 12 1.3.3 The Wedge Model and the Lateral Pressure Profile 14 1.4 Motivation and Summary of Experiments . 15 1.5 Overview of Thesis 17 v 2 N M R Theory 18 2.1 Broad-line NMR Spectroscopy of Lipid Membranes 18 2.1.1 Ranges of Correlation Times 18 2.1.2 Moments of NMR Spectra 19 2.2 Relaxation 23 2.2.1 Effects of Temperature on Ti and T 2 25 2.2.2 Orientation Dependence of T 2 28 3 Experimental Methods 30 3.1 Sample Preparation 30 3.2 NMR Techniques 32 3.2.1 Preparatory NMR Experiments 32 3.2.2 X H - N M R Protocol 32 3.2.3 2 H - N M R Protocol 33 3.2.4 Temperature Control for NMR Experiments 34 3.3 Analysis 35 3.3.1 Proton Moments 35 3.3.2 Deuterium Moments 39 3.3.3 Order Parameter Profiles and Average Chain Length 39 3.3.4 Relaxation Analysis 41 4 Results and Discussion 46 4.1 Preliminary Comments 46 4.2 Moment Studies and Order Parameters 47 4.2.1 Proton Second Moment 47 4.2.2 Deuterium Second Moment 49 4.2.3 Deuterium Order Parameter Profiles 50 vi 4.2.4 Average Chain Length 52 4.2.5 Discussion of Moment and Order Parameter Results 52 4.3 Relaxation Studies 55 4.3.1 Proton Average Tlz 55 4.3.2 Deuterium Average T \ 2 57 4.3.3 Deuterium Average Tf 60 4.4 Synthesis of Moment and Relaxation Results 67 4.4.1 Fast Motions 67 4.4.2 Slow Motions 68 4.4.3 Relation Between Fast and Slow Motions 70 4.5 Suggestions for Further Work 70 4.6 Relation to Biological Motivation for Study 72 5 Conclusion 75 Bibliography 78 Appendix A Theory: Information on Flu id Membranes from N M R Spectra 92 A . l NMR Background and Goals 92 A.2 Membrane Fluidity and Correlation Times 92 A.3 Time and Distance Scales Associated with NMR Spectra in Membranes . 94 A.4 2 H - N M R of Acyl Chains on Lipid Molecules in Fluid Membranes 95 A.5 Orientational Order of Acyl Chains and Hydrophobic Thickness of Fluid Membranes 99 A. 6 Dipolar Broadened X H - and 1 3 C - NMR in Membranes 101 B Preparatory N M R Experiments 103 B. l ^ - N M R - Buffer Contribution and Water Suppression 103 vii B.2 2 H - N M R - Spectrometer Validation 105 C Supplemental Results 109 v i i i List of Tables 3.1 Lipid composition of NMR samples 31 4.1 Fit parameters for T2e orientation-dependence 66 C . l Fit parameters for M2R,H vs. mol% PDPC 109 C.2 Fit parameters for M2R,D vs. mol% PDPC 109 C.3 Fit parameters for (L) vs. mol% PDPC 109 C . 4 Fit parameters for proton Tlz vs. mol% PDPC 110 C.5 Fit parameters for deuterium Tiz vs. mol% PDPC 110 C.6 Fit parameters for temperature-dependence of the deuterium T2e rate . . 110 ix List of Figures 1.1 Schematic diagram of biological membrane 2 1.2 Molecular structure of phospholipids 4 1.3 Schematic diagram of a retinal rod photoreceptor 5 1.4 Proposed "wedge" shape for polyunsaturated lipids 13 2.1 Summary of important timescales for NMR experiments 20 2.2 Spectral densities and the Tx minimum 26 3.1 Analysis of the proton FID 37 3.2 Determination of fit-range for moment expansion of FID 38 3.3 Deuterium spectra for P O P C - d 3 i / P D P C mixtures 40 3.4 Representative T2e spectrum, with Pearson's R values from T2e fits . . . 44 4.1 Proton residual second moments, M2R,H 47 4.2 Deuterium residual second moments, M2R,D 49 4.3 Smoothed order parameter profiles, S(n) 51 4.4 Mean length (L) of POPC's 16:0-d3i chain 53 4.5 Proton average T\z 55 4.6 Deuterium average Tlz for POPC's 16:0-d31 chain 58 4.7 Regional variation of deuterium average TXz 59 4.8 Average T f for POPC's 16:0-d3i chain 60 4.9 Regional variation of T2e 62 4.10 Temperature-dependence of T2e rate 63 4.11 Orientation-dependence of T2e 65 x A . l Simulated broadline : H - and 2 H - N M R spectra 96 A.2 Typical 2 H - N M R spectra and smoothed order parameter profiles 98 A. 3 Schematic illustration of hydrophobic matching 100 B. l Proton FIDs collected using (90° ) x pulse vs. full water suppression . . . . 106 B. 2 Validation of C X P for 2 H spectroscopy using lipid standard 108 C. l Order parameter profiles, S(n), at 10° C I l l C.2 Order parameter profiles, S(n), at 37° C 112 xi A b b r e v i a t i o n s Ka Membrane Area Compressibility Modulus. KC Membrane Curvature Energy. C P M G Carr -Purcel l -Meiboom-Gil l . C X P Bruker Spectrometer Model Number. D H A Docosahexaenoic A c i d . D P P C Di-Palmitoyl-Phosphatidylcholine. E F A Essential Fatty A c i d . F I D Free Induction Decay. F R A P Fluorescence Recovery After Photobleaching. L T D Long Term Depression. L T P Long Term Potentiation. M A S - N O E S Y Magic Angle Spinning-Nuclear Overhauser Effect Spectroscopy. M i l Metarhodopsin-II. M I Metarhodopsin-I. M L V Mul t i -Lamel lar Vesicle. N M D A N-Methyl-D-Aspartate . x i i N M R Nuclear Magnetic Resonance. P C Phosphatidylcholine. P D P C l-Palmitoyl-2-Docosahexaenoyl-Phosphatidylcholine. P E Phosphatidylethanolamine. P K C Protein Kinase C. P O P C l-Palmitoyl-2-Arachadonoyl-Phosphatidylcholine. P O P C l-Palmitoyl-2-01eoyl-Phosphatidylcholine. P S Phosphatidylserine. P U F A Polyunsaturated Fatty Acid. R O S Rod Outer Segment. S N R Signal-to-Noise Ratio. sn-1, sn-2 Binding sites for acyl chains on glycerol backbone. sn-3 Binding site for headgroup on glycerol backbone. xiii A c k n o w l e d g e m e n t I have much to be grateful for as this project winds up, many friends both old and new to thank. They have given freely of laughter and friendship, knowledge and new ideas, and they have made my time at U B C enriching and joyful. I would like to thank Dr. Myer Bloom, my supervisor, for the many lessons of science and of life which he has taught by his example. It has been a privilege to learn about the philosophies and the culture of research from such a master of the trade. Equally deep thanks are due to Dr. Frank Linseisen, whose broad knowledge and great generosity -with time and with the hard-won fruits of experience - have supported me through the setbacks and triumphs of the past few years. I am also grateful to Dr. Jenifer Thewalt for her advice throughout the project and her formal participation at the end, as well as for the wonderful social influence she has exerted on our lab. I thank everyone in Room 100 for the happy hours, days, and years; such a convivial and stimulating workplace will be hard to replace. I thank my friends in Vancouver for enhancing my world with soccer, red wine and other fine things (and for their on-going efforts with swimming and olives), and for nourishing my body and soul. I thank Yulia, who from far away has helped me through good times and bad by knowing me as no one else does. Finally I thank my family, for their unwavering faith in me and for their trust and full support through the tough decisions of recent times. I would also like to acknowledge financial support from the Natural Science and Engineering Research Council of Canada. xiv Chapter 1 Introduction 1.1 Biological Membranes The lipid bilayer is a fundamental element of eukaryote biology, serving to enclose and compartmentalize the contents of the cell. As depicted in Figure 1.1, biological mem-branes are a heterogeneous mixture of lipids, proteins and carbohydrates, held together by non-covalent forces. The bilayer structure is a continuous double layer of amphiphilic lipid molecules, with "integral membrane proteins" embedded through it and "membrane-associated proteins" (including elements of the cytoskeleton) and carbohydrates (includ-ing the glycocalyx) associated with its surface. The thickness of the bilayer is typically 40-50 A . Biological membranes are highly dynamic, fluid structures, characterized by a broad range of molecular motions, rapid lateral diffusion of protein and lipid constituents, and the absence of shear forces between the monolayers. This fluidity is thought to be essential to various functions of the membrane, allowing conformational changes of membrane proteins and selective permeation of water-soluble molecules. 1.1.1 Lipids Lipid molecules typically constitute roughly 50% of eukaryotic membranes, by weight. They are divided into three main classes - phospholipids, sterols (particularly cholesterol) and glycolipids. Phospholipids are the most abundant element, and comprise the matrix 1 Chapter 1. Introduction 2 cytoskeleton integral membrane protein bilayer glycocalyx Figure 1.1: Schematic diagram of a biological membrane, showing the phospholipid bi-layer "matrix", as well as integral membrane proteins, associated carbohydrates such as the glycocalyx, and connections to the cytoskeleton. Figure borrowed from [1]. of the bilayer. The structure of a phospholipid molecule is shown schematically in Figure 1.2. A hydrophilic headgroup is connected to two hydrophobic acyl chains by the glycerol back-bone; the resulting amphiphilic character of the molecule provides the driving force for assembly into bilayers (or other phases) in aqueous environments, due to the so-called "hydrophobic effect". As shown, the acyl chains are labelled sn-1 and sn-2 - these are actually the names of their binding sites on the glycerol backbone, and the headgroup occupies the sn-3 site. Different species of phospholipid are defined by their headgroup and acyl chain com-position. Acyl chains are fatty acid molecules, and are defined by their chain length, degree of unsaturation, and position of the first double bond. (These three parameters are summarized by a common notation, e.g. the 18:ln-9 chain has 18 carbon atoms and 1 double bond, with the first double bond beginning on the ninth carbon from the methyl end1. Acyl chains with no double bonds are termed "saturated", those with one double 1This notation is extended in several ways throughout this thesis. "Perdeuterated" chains, on which the hydrogen atoms have been replaced by deuterons, are denoted like 16:0-d3i (for a 16:0 chain with Chapter 1. Introduction 3 bond are "mono-unsaturated", etc. "Polyunsaturated" acyl chains (i.e. those wi th three or more double bonds) are the major focus of this thesis - particularly docosahexaenoic acid ( D H A , or 22:6n-3), which with 6 double bonds in its 22-carbon length is the most highly unsaturated chain commonly used by nature . 1.2 Biological Motivation to Study D H A (Section 1.2 has been modified from a section of an earlier paper [1], writ ten by JL-S . ) 1.2.1 Membrane Lip id Composition and Polyunsaturation The conventional view of l ip id bilayers in the cell has been that they serve simply as physical and electrical barriers (both to the external environment and between internal compartments), and as inert substrates upon which membrane proteins carry out their functions. Whi le these roles are clearly very important, there has been a growing appre-ciation in recent years that lipids have more subtle and wide-ranging functions (e.g. [2]). These may be due to properties of the bilayer alone, such as permeability to water or ions, or to interactions wi th the proteins associated wi th the membrane, such as matching of hydrophobic thickness as mentioned earlier. For different biological systems, these prop-erties are determined (and presumably optimized, as discussed in [3]) by characteristic l ip id compositions, encompassing variation in phospholipid head groups and acyl chains as well as in proportions of other lipids. The human brain has made a striking choice in favour of polyunsaturated lipids (i.e. phospholipids wi th polyunsaturated acyl chains), and particularly of lipids containing all 31 protons replaced). A lso , the chain notat ion will be compounded to describe the composit ion of phosphol ip id molecules - e.g. 16:0/18:1-PC indicates l-palmitoyl-2-oleoyl-phosphatidylcholine, a l ipid with a phosphat idylchol ine ( PC ) headgroup, a palmitoyl chain (16:0) at the sn-1 site, and an oleoyl chain (18:1) at sn-2. Chapter 1. Introduction 4 sn-1 Figure 1.2: A space-filling diagram of a phospholipid molecule is shown on the left, depicting the hydrophilic headgroup (top) and two hydrophobic acyl chains (bottom) connected by the glycerol backbone. The acyl chains used in this study are shown, representing three important classes: the polyunsaturated docosahexaenoyl chain, or D H A (22:6), is on the left; the mono-unsaturated oleoyl chain (18:1) is on the right; in the middle is a saturated palmitoyl chain (16:0). Each of these chains can bind to the glycerol backbone (shown, top right) at the sn-1 or sn-2 site, as described in the text. The three most common phospholipid headgroups are shown in the bottom right box -they are phosphatidylcholine (PC), which is used in the experiments described in this thesis, phosphatidylethanolamine (PE), and phosphatidylserine (PS). Figure borrowed from [1]. Chapter 1. Introduction 5 D H A - so much that it is often called "cervonic acid". While DHA levels in most mem-branes range from l-6mol%, values of about 15mol%, and as high as 25-35 mol% for certain head groups, are reported in brain grey matter and synaptic membranes [4, 5]. More remarkable still are the outer segment disk membranes of the rod photoreceptor cells of the retina, with DHA comprising roughly 50mol% of the total fatty acid comple-ment [6]. These exquisitely specialized neurons (see Figure 1.3), which convert photons into electrical signals, thus have among the most highly unsaturated membranes of all vertebrate systems. disks (containing rhodopsin and DHA) Figure 1.3: Schematic representation of a retinal rod cell (taken from Alberts et al. [7]). The stacked membranous disks of the rod outer segment (ROS) contain 50mol% DHA and are densely packed with rhodopsin molecules. Maintaining polyunsaturated membranes, however, presents two serious challenges to mammalian cells. First, mammals lack the enzymes required to synthesize DHA (22:6n-3) or arachadonic acid (20:4n-t5) from scratch, and therefore must obtain the associated essential fatty acid (EFA) precursors (18:3n-3 and 18:2n-c5, respectively) from their diet, and convert them by a series of elongation and desaturation reactions [8]. Not only does this render the supply of polyunsaturated fatty acids (PUFAs) dependent on the supply of dietary precursors (and hence on environmental factors), but the conversion process is indirect and time-consuming. In fact, in very fast-growing animals (such as cattle), these enzymatic reactions are unable to keep up with bodily growth, resulting in decreased DHA levels and increased content of metabolic intermediates such as 22:5n-3 [9]. Second, polyunsaturated lipids are extremely vulnerable to oxidation, and large Chapter 1. Introduction 6 quantities of anti-oxidant agents (such as vitamin E) must be present to protect them [10]. D H A is the most highly unsaturated of all fatty acids commonly used by nature and is particularly unstable, degrading almost ten times faster than 18:3n-5 [11]. In short, polyunsaturated lipids are very difficult for the human body to produce and to maintain, and their prevalence in such vital systems as the brain and the eye poses a fascinating evolutionary puzzle. Nor can this be explained as a "fluke" occurrence -Nature's enigmatic choice of high DHA levels for neural membranes is conserved across an extremely broad range of species (including mammals, fish, reptiles and even the photosynthetic "eye-spots" of unicellular dinoflagellates), in stark contrast to the wide inter-species variability in lipid make-up of other tissues [12]. What advantage does this lipid bring which would have caused evolution to select it despite the substantial problems involved in doing so? What function could it possibly have, which could not be fulfilled by some more convenient alternative? 1.2.2 Evidence for a Functional Role of D H A A strong argument can be made that DHA plays a functional role in the visual system, and evidence is mounting that it is important for higher brain function as well. Due to the direct link between proper nutrition and adequate supply of PUFAs, any such cor-relations between lipid polyunsaturation and neural function have very significant social implications. A great effort is underway by many groups to elucidate this relationship, and a parallel line of inquiry is examining issues related to dietary supplementation. An indirect argument for the importance of PUFAs arises from the remarkable lengths to which neural cells will go to maintain their membrane polyunsaturation. The extraor-dinarily high DHA content in the rod outer segment (ROS) disks is retained tenaciously during dietary deficiencies of its EFA precursor (18:3n-5), and radiographic studies have revealed an elaborate recycling mechanism which minimizes its loss [13]. Membranes of Chapter 1. Introduction 7 the brain similarly resist loss of DHA, but under conditions of extreme E F A deficiency substantial decreases have been observed. Such changes are often accompanied by in-creases in concentration of 22:5n-c5, the closest structural match to DHA outside the n-3 family [14, 15]. Dietary EFA depletion during pregnancy and infancy, while the brain and nervous system are undergoing rapid development, has been shown to lead to decreased D H A lev-els and to impaired visual function in rats [16], rhesus monkeys [17] and human premature infants [18]. The latter studies have led to pre-formed DHA being declared provisionally essential for human infants, presumably due to the heavy needs of the developing ner-vous system; very high levels of DHA are also found in human placental blood and breast milk, and faced with dietary deficiency the mother's body will sacrifice its own needs to ensure that the baby receives an adequate supply of PUFAs [12]. Similar studies have concluded that n-3 deficiency leads to reduced learning ability and psychomotor develop-ment in animals and human infants [16, 19]. One relatively recent, very lucid review of the field emphasizes the need for caution in drawing conclusions linking EFA deficiency to intellectual or cognitive deficits [20], but sufficient evidence has arisen in subsequent years to firmly establish that learning is affected (at least in rats) [15, 21, 22, 23]. Such ef-fects of n-3 deficiency have even been associated with morphological changes in synapses; intriguingly, these changes are observed only in animals which have been challenged with learning tests [15, 21]. A different source of evidence for the link between PUFAs and neural function comes from a number of congenital diseases in which abnormal membrane composition is associ-ated with visual or mental impairment. For example, retinitis pigmentosa, an eye disease leading to night blindness and visual field constriction, is correlated with low D H A levels in the retina [18]. Zellweger syndrome, a disorder of the peroxisomes (cellular centres of lipid metabolism, involved in synthesis of DHA), is characterized by extremely low levels Chapter 1. Introduction 8 of D H A [24]. Infants suffering from this disease are born with severe psychomotor retar-dation, become blind and deaf shortly after birth, and usually die within their first year. Preliminary results indicate that DHA supplementation can lead to clear improvements in the normal development and clinical outcome of afflicted patients [25, 26]. Finally, a recent study of the brains of individuals with Alzheimer's disease has identified signif-icantly decreased levels of DHA in the phosphatidylethanolamine (PE) phospholipids; such changes were not observed in the brains of normally aging patients [27]. These observations have motivated many experiments into how polyunsaturation af-fects the physical properties of membranes, and particularly into the role of D H A in the retina. The photoreceptor has been the favoured experimental paradigm since the visual system is much more tractable (less complex, more accessible to experiment, and much more easily quantified) than the brain and its higher functions. Furthermore, the studies on vision have been greatly aided by the enormous strides taken by the biochemistry community during the 1980s, which have led to a near-quantitative understanding of the molecular basis of photoreceptor activity [7, 28]. This has allowed experiments to be devised which focus on the specific molecular processes where DHA may exert its influence. 1.2.3 Possible Roles for D H A at the Molecular Level Phototransduction, the process of translating a visual stimulus into an electrical signal, takes place in the outer segments of rod and cone photoreceptor cells in the retina. Most experimentation has dealt with the highly sensitive, monochromatic rod cells, whose outer segments contain stacks of membranous disks, as shown in Figure 1.3. These ROS disk membranes, the site of high DHA content in the rods, in turn are densely packed with the integral membrane protein rhodopsin. Rhodopsin initiates the light response by absorbing a photon and undergoing a series of rapid conformational changes. Chapter 1. Introduction 9 After passing through a number of unstable intermediate states wi thin microseconds, rhodopsin is transformed into metarhodopsin-I (MI). The next reaction is an acid-base equilibrium, in which M I can be protonated to become metarhodopsin-II ( M i l ) . M i l is the enzymatically active form of rhodopsin, and catalyzes the G-protein transducin to trigger a cascade of biochemical reactions which results in the closure of ion channels in the rod plasma membrane, and subsequent hyperpolarization of the cell. Significant formation of M i l is clearly critical to the transmission of the visual signal, and modulation of the M I / M I I equilibrium (which of course takes place embedded in the disk membrane) seems a plausible way for membrane composition to exert its functional influence. Indeed, M i l formation has been shown to be diminished considerably in model membranes wi th lower-than-physiological levels of D H A [6]; these experiments and others which address possible mechanisms for this effect wi l l be discussed in Section 1.3. Though the retina is an extension of the brain and thus photoreceptors are in fact highly specialized central neurons, it is unclear whether such specific experiments have any relevance to the high D H A content observed in the synapses and grey matter of the brain. It is a distinct possibility, however, that D H A ' s putative interactions wi th rhodopsin could be generalized to the large family of G-protein linked receptors (of which rhodopsin is a member), al l of which share very similar structure particularly in their transmembrane domains [7]. This could certainly extend D H A ' s role throughout the nervous system, since G-proteins are involved in many signal transduction pathways in the brain, and quite possibly beyond into other systems of the body. Recent studies have also revealed a host of other membrane proteins upon which D H A exerts specific functional influences. N a + - K + - A T P a s e , an ion pump crit ical to maintaining the ionic concentration gradients which subserve al l of neuronal signalling, suffers reductions in activity of up to 4 5 % in the absence of physiological D H A levels [4 ] . Several voltage-gated ion channels have been shown to be blocked by free D H A in solution Chapter 1. Introduction 10 (i.e. the fatty acid form; physiologically, DHA can be freed from the membrane by the actions of several common enzymes) [29, 30], and activation of acetylcholine pathways has been demonstrated to selectively increase uptake of DHA by the membrane, suggesting "a primary role for DHA in phospholipid mediated signal transduction" at cholinergic synapses [31]. Even more intriguing, DHA levels in the membrane affect activity of protein kinase C (PKC) [32], and free DHA increases the channel-open probability for the NMDA-type glutamate receptor [33]. These molecules (PKC and N M D A receptors) are thought to be critical factors underlying the phenomena of long term potentiation (LTP) and long term depression (LTD), which are leading topics of investigation into the molecular basis of learning and memory. Indeed, a very recent study has demonstrated a direct relationship between DHA levels in solution and the suppression of L T D [34]; together with the above results, this could be interpreted as the first concrete indication of a molecular site of action for DHA's effects on cognitive function. Taken together, the above results (most of which date only from the last few years) suggest a role for DHA in brain function which is significant and wide-ranging. It seems reasonable to expect this rapid growth of knowledge to continue, resulting in a much fuller appreciation of the influences of this extraordinary lipid on the brain. 1.3 Physical Properties of Polyunsaturated Lipids The desire to understand the role of DHA in membrane function has drawn researchers from many fields, and the pace of investigation (and progress) has increased greatly in re-cent years. Much of this effort has focused on the "non-specific" physical and mechanical properties (as opposed to "specific" chemical interactions, some of which are described above) imparted by DHA to lipid membranes. A summary of relevant results in this field is presented here; for further details, there are two recent, comprehensive reviews of the Chapter 1. Introduction 11 subject [1, 35]. 1.3.1 Ear ly Work - Molecular Shape and Spontaneous Curvature The work of Brown on DHA's interaction with rhodopsin [6] highlights several key points. Using optical spectroscopy to measure the success of rhodopsin's crucial MI-MII transi-tion as a function of membrane composition, he confirmed the importance of polyunsatu-rated lipids for M i l formation. Testing other lipid species, he found that those with bulky acyl chains and small headgroups could also produce the favourable effect. From these observations, Brown concludes (i) that a bulk property of the membrane must underlie the effect, rather than a DHA-specific chemical interaction, and (ii) that this property is "negative spontaneous curvature", the tendency of a lipid monolayer to curve in a concave manner at the lipid-water interface. A model of the interaction with rhodopsin is sug-gested, in which this curvature stabilizes a purported increase in hydrophobic thickness as MI changes to M i l 2 . The role of DHA-bearing lipids in rhodopsin function is thus proposed to arise from their molecular "shape", which is related to the range of conformations assumed by the acyl chains. At the time of Brown's studies, preliminary work had indicated that polyunsaturated chains might be unexpectedly flexible. Applegate & Glomset performed the first computer-modelling of static DHA chain conformations [37, 38, 39]. In addition to defining certain zero-energy states, their work indicated that the C-C single bonds in D H A were remarkably free to rotate - the energy barriers to bond rotation were much lower than those of a saturated chain. Early NMR work by Baenziger et al. complemented 2 A recent theoretical study has explored the possibil ity of such coupl ing between protein conforma-t ional changes and resultant membrane deformations [36]. Contr ibut ions due to hydrophobic mismatch, "splay-deformation" of the membrane protein (e.g. changing from cyl indrical to conical , and thus affect-ing the orientat ion of neighbouring l ipid molecules), and surface tension are model led explicitly, and the former two mechanisms are predicted to be capable of exerting significant influences on conformational equi l ibr ia (and hence on function). Chapter 1. Introduction 12 this result, using site-specific deuteration on a di-unsaturated lipid (16:0/18:2-PC) to reveal surprisingly low orientational order for the carbon between the two double bonds [40, 41]. These results challenged the intuitive view that DHA's many double bonds would render the chain rigid. 1.3.2 Later Work - Molecular Order and Lateral Organization The first definitive work on the influence of polyunsaturation on membrane orientational order was conducted by Holte et al. [42], in the Gawrisch laboratory. They used deuterium NMR to study a series of one-component membranes, consisting of PC phospholipids with a perdeuterated stearoyl chain at the sn-1 site, and a series of progressively more unsaturated chains at sn-2 (i.e. 18:0-d3s/X-PC, where X is 18:ln-9, 18:2n-t5, 18:3n-3, 20:4n-f5, 20:5n-3, or 22:6n-5 (DHA)). From smoothed order parameter profiles, which give a measure of local orientational order for each carbon on a perdeuterated lipid chain, they found that polyunsaturation causes decreased order in the lower half of the saturated chain (i.e. the end nearer to the middle of the bilayer). The largest changes were seen between the lipids with 1, 2 and 3 double bonds - little difference was found in going from 3 to 6 unsaturations. This localized disorder is consistent with the 18:0-d35 chain becoming more "wedge-shaped" with increasing sn-2 unsaturation. In subsequent discussions, though, the en-tire polyunsaturated lipid molecule is depicted as a wedge, and the authors speculate about its possible interactions with membrane proteins (see Figure 1.4) [42, 43]. This is strongly reminiscent of Brown's hypothesis of negative spontaneous curvature, caused by acyl chains bulkier than their headgroups - indeed Holte et al. refer to the "curvature stress" experienced by such membranes when confined to the lamellar state. It must be emphasized, however, that Holte's measurements were sensitive only to the order of the deuterated 18:0 chain, and that great caution must be exercised in extending them to Chapter 1. Introduction 13 the molecule as a whole. Figure 1.4: Lipids with polyunsaturated chains are shown to occupy wedge-shaped vol-umes in the bilayer in this figure taken from the literature [43]. Relative to neatly-packing saturated chains (above), lipid molecules with small headgroups and polyunsaturated chains (below) are proposed to accommodate certain protein transitions because of their wedge-like shape. The Gawrisch group has continued to make substantial contributions. Combining deu-terium NMR and X-ray diffraction techniques, they determined that lipids bearing D H A chains have much greater lateral compressibilities than saturates or monounsaturates; the same study revealed significantly higher cross-sectional areas for the polyunsaturated membranes [44]. The compressibility was proposed to facilitate conformational changes involving lateral expansion of transmembrane proteins, while the greater area is again consistent with the wedge-shaped hypothesis. Another recent study, which combined 1 H - (MAS-NOESY) and 2 H - N M R techniques, showed that cholesterol interacts preferentially with saturated chains in mixed-chain lipids [45]. Polyunsaturation (as well as headgroup composition) was suggested to af-fect lateral organization of lipid molecules, perhaps leading to the formation of transient "microdomains" in the presence of cholesterol. This conclusion is foreshadowed in the Chapter 1. Introduction 14 work of Mitchel l & Li tman , who used fluorescence depolarization methods to examine the effects of "free volume" (ensemble-averaged voids in l ip id packing) on the M I - M I I equi-l ibr ium (reviewed in [46, 35]). They proposed that polyunsaturated lipids form dynamic lateral clusters which exclude cholesterol and hence mitigate its inhibitory effect on M i l formation - further experiments have indicated that d i - D H A - P C is especially effective at buffering cholesterol's influence in this way [47]. Smaby et al. report results consistent wi th this model, and hypothesize that the czs-unsaturated "kinks" of the polyunsatu-rated chains interfere wi th favourable van der Waals interactions between the chains and the smooth ring structure of cholesterol [48]. 1.3.3 T h e Wedge Mode l and the Lateral Pressure Profile Proposed explanations for the role of D H A in membrane function are cast in terms of decreased acyl chain order and disrupted l ip id packing. (Even hypotheses like domain formation have their bases in these experimentally accessible parameters.) Encouraged by Brown's findings and the order parameter profiles of Holte et al., a model arose in which polyunsaturated l ip id molecules occupy wedge-shaped volumes which cause the monolayers to want to curve (in a concave manner) about their headgroups. When confined to a lamellar bilayer (due to the hydrophobic effect which dominates l ipid-water interactions), such lipids would lead to packing irregularities near the lipid-water interface and crowding in the hydrophobic interior of the membrane. This "curvature stress" could influence protein conformational changes, essentially by exerting pressure laterally through the l ip id bilayer. A fascinating theoretical study examining this "lateral pressure profile" as a function of l ip id composition has just been published by Cantor [49]. Using mean-field statistical thermodynamics 3 , the author finds that highly unsaturated chains such as D H A shift 3 T h e configurat ional entropy of the acy l chains is calculated using a mean-field approx ima t ion of Chapter 1. Introduction 15 lateral pressure away from the bilayer interior - exactly contrary to what the wedge model would predict. The model shows an increase in pressure near the lipid-water interface, which is offset by decreased crowding in the interior such that the membrane thickness (also calculated) is minimally affected. (Note that the calculations impose a constant density condition on the hydrophobic region, such that free volume cannot exist. In the worst case, this could seriously skew the results by eliminating a key contribution to the real physical effect.) Cantor concludes that the functional role of polyunsaturated lipids in membranes is to redistribute lateral pressures - thus influencing membrane protein conformation, as argued in an earlier work [50] - while maintaining constant thickness to facilitate hydrophobic matching. These results, which appear only as this report is being written, provide a welcome new perspective on the DHA question. 1.4 Motivation and Summary of Experiments The basis for DHA's observed influences on membrane function is not yet understood. As described above, a prevalent hypothesis suggests that polyunsaturated lipids occupy wedge-shaped spaces in the membrane, affecting protein conformation via lateral pres-sure through the bilayer. Such a shape has never been directly demonstrated, however. 2 H - N M R measurements on mixed-chain lipids (e.g. 18:0-d3s/22:6-PC) have indicated that the saturated chain occupies a wedge-shaped cloud of conformations, but the re-lation of this result to the shape of the DHA chain, or that of the entire lipid molecule, is ambiguous. Furthermore the majority of experiments have been conducted in single-component model bilayers, very dissimilar to the complex mixtures of lipid (and protein) species excluded volume which accounts for bond orientational correlations. T h e bilayer free energy is est imated, and the negative of its derivative with area determines the lateral pressure; the pressure profile is derived f rom values of this derivative at different layers in the cubic lattice used for the calculations. Chapter 1. Introduction 16 invariably found in physiological membranes. It is conceivable that exceptional proper-ties of polyunsaturated lipids might be expressed through their interaction wi th other membrane constituents; clearly the single-species experiments would not be sensitive to such effects. This study addresses the above issues by examining the effects of increasing acyl chain polyunsaturation in binary l ip id mixtures. The phospholipid species used were monoun-saturated l-palmitoyl-d 3 1-2-oleoyl-phosphatidylcholine ( P O P C - d 3 i , or 16 :0 -d 3 1 / 18 : l -PC) and polyunsaturated l-palmitoyl-d 0-2-docosahexaenoyl-phosphatidylcholine ( P D P C - d 0 or 16:0/22:6-PC), in proportions ranging from 0 to 100mol% P D P C . These molecules, shown in Figure 1.2, were chosen to crudely approximate the l ip id composition of neu-ral membranes [51], where D H A exerts its functional role 4 . Varying the concentrations allows for the possibility of anomalous behaviour arising from particular molar ratios of the l ip id species. The P O P C - d 3 i / P D P C mixtures were studied using broadline : H - and 2 H - N M R tech-niques. Since only P O P C has a deuterated portion, all 2 H - N M R results report directly and exclusively on P O P C ' s 16:0-d 3i chain. The deuterium signal thus provides an unam-biguous report of the effect of increasing P D P C concentration (i.e. of greater polyunsat-uration) on other membrane components, and wi l l directly test for the lateral pressure predicted by the wedge model. Meanwhile, X H - N M R lends an independent and comple-mentary assessment of conditions in the rest of the membrane. In addition to standard spectroscopic measurements, which yield information on ori-entational order and fast motions of the l ip id molecules, relaxation measurements were performed to learn more about l ip id dynamics. T\ experiments provide further insight 4 Phosphat idy l cho l ine ( PC ) headgroups were selected for consistency with earlier work in the field. Po lyunsaturated chains are often associated with phosphat idylethanolamine ( PE ) headgroups in physi -ological membranes, and it would be of great interest to conduct a parallel series of experiments using P E l ipids. Chapter 1. Introduction 17 into very fast molecular motions, while T 2 can describe slower, collective modes of the membrane. Since in-depth relaxation studies have not yet been reported for polyunsat-urated membranes, these experiments are a foray into relatively uncharted territory. All measurements were conducted at 10° C, 25° C, and 37° C. This thesis addresses the following questions: 1. What mechanical effects do polyunsaturated lipids (and particularly those bearing D H A chains) have on other bilayer components? 2. Does a bilayer with acyl chain composition closer to that found in neural membranes have special properties? Is there a concentration-dependent "magic mixture" effect? 3. Can new insights be gained into the role of DHA in membranes by probing unex-plored timescales (and hence distance scales)? 1.5 Overview of Thesis The thesis is organized largely in a conventional manner. In Chapter 2, the NMR theory relevant to the experiments and their interpretation is summarized. A significant part of this summary (included as Appendix A) was borrowed from the proceedings of the 1998 Fermi School of Physics [1]. Chapter 3 outlines the details of experimental techniques and analysis. The results are presented in Chapter 4, with accompanying discussion; the chapter concludes with suggested extensions of the study, and the relevance of the findings to the biological question is assessed. Chapter 5 is a brief concluding statement. Appendix A is the background theory described above. Certain preliminary NMR experiments are described in Appendix B. Appendix C includes tabulated numerical results, as well as several figures not presented in Chapter 4. Chapter 2 N M R Theory 2.1 Broad-line N M R Spectroscopy of L ip id Membranes The reader is referred to Appendix A for a general overview of broadline NMR spec-troscopy of lipid membranes. Written by Professor Myer Bloom, it is an excerpt from a paper entitled "Insights from NMR on the functional role of polyunsaturated lipids in the brain", from the proceedings of the 1998 Fermi School of Physics [1]. Throughout the text results will be cited freely from this summary, with comments added as required. The following two sections extend discussions from the appendix on topics of particular relevance to this study. 2.1.1 Ranges of Correlation Times In Section A.2, the complex spectrum of correlation times associated with various mo-tions in a fluid bilayer is discussed, and examples are given of motions at a few ranges of T c . Section A.3 goes on to classify these motions as "slow" or "fast", depending on their relation to the spectroscopic time scale r s , where TS « 1/Au. The definition of Au will vary with circumstance, but a working definition is Au = ( M 2 ) - ^ , where M 2 is the second moment (or residual second moment) appropriate for the question being consid-ered. Within this classification, "fast" motions give rise to narrower spectral features by motional averaging, while "slow" motions do not appreciably affect the lineshape. It is useful to introduce a further discrimination between ranges of correlation times, 18 Chapter 2. NMR Theory 19 relevant to Ti and T2 relaxation processes. Motions for which U0TC 3> 1 (including the "slow" and a subset of the "fast" motions defined above) will be denoted "adiabatic", using the word in the sense described by Abragam [52]. The remaining "non-adiabatic" motions, for which UJ0TC <C 1, will be labelled "very fast". Timescales of interest will thus be divided into three regimes: slow adiabatic, fast adiabatic, and very fast non-adiabatic, as shown in Figure 2.1. The NMR parameters affected by motions in the three ranges are also shown, as well as representative motions present in fluid bilayers. 2.1.2 Moments of NMR Spectra The study of spectral moments is of considerable importance in broadline NMR. At their simplest, moments provide a quantitative measure of the "shape" of an NMR absorption line, which proves useful for study of complex or featureless spectra (like the deuterium and proton spectra derived from lipid samples; see Figures 3.3 and A. l ) . In certain instances spectral moments can be related rigorously to theory, which allows their value to be related to real physical parameters. The nth moment of a lineshape function f(u) can be defined as + o o / \u - u0\n f(u)duj Mn = = ^ (2.1) J f(u)du — o o where uQ is the Larmor frequency. The second moment, when n = 2, gives the mean-squared frequency splitting ((Ao;)2) and is of particular interest in NMR studies. While the true value of the second moment (M 2) never changes, the presence of fast motions with correlation times rc <§; ( M 2 ) ~ 5 will cause narrowing of the absorption line as described above. The experiment ally-measured second moment is then less than M 2 , and is termed the residual second moment M 2 r . Since it is related to fast molecular motions, the reduction in M 2 can be interpreted Chapter 2. NMR Theory 20 Slow adiabatic — • ~+ Fast adiabatic • — Very fast, non-adiabatic T C ( S ) 10"4 IO"5 10-6 io-7 10-8 l 0-9 10-10 H 1 1 — — I 1 1 h NMR parameters affected: M M2rorS •+ T l •+ T 2 Motions in fluid bilayer: Surface undulations M Compressional modes Lipid rotations I 1 Headgroup "nodding" trans-gauche isomerizations Figure 2.1: Summary of important timescales in NMR experiments, showing the three regimes of motion as defined in the text. Note that the precise boundaries will be determined by the field strength (influencing l/u>0 and thus the limit of "adiabatic" times) and the spectroscopic timescale (r S ) assumed here to be roughly 10 _ 5s, which defines the boundary of the motional narrowing regime as discussed in Section A.3). Beneath the bar showing r c values, selected NMR parameters are shown along with the range of timescales to which they are sensitive. At the bottom, representative motions present in fluid bilayers are shown, along with estimated ranges of their correlation times [1, 53, 54]. Chapter 2. NMR Theory 21 in terms of "order parameters". These unitless parameters, denoted S, describe the orientational order of a molecular system. Ideally they take on a value from 0 to 1, where S = 0 indicates total isotropic disorder and 5 = 1 indicates absolute orientational order. T h e Proton Second Moment and Pseudo-Order Parameter The well-known Van Vleck formula gives the dipolar second moment for a rigid lattice of identical nuclei (with spin / and gyromagnetic ratio 7) [52], 4 B  NAB where RAB is the distance between dipolar coupled spins A and B and 6AB is the angle between ~R*AB and the external magnetic field, I^0. In systems of protons, the dipolar interaction dominates and Equation 2.2 applies in principle. For lipid molecules in fluid membranes, this value is reduced by several factors, in-cluding lateral diffusion of the lipids, rapid rotation of the molecules about the bilayer normal, and a random "powder" distribution of orientations of the normal. The resulting relation between M 2 and M 2 r is discussed in depth by Bloom et al. [55, 56], who obtain M2R = M2 (\SAB\2) 4 E E M?>BSAB (2.3) where M2A'B is the contribution of spins A and B to the second moment, and SAB — (P2(cosQAB)/TAB) 1 S the proton dipolar pseudo-order parameter, as mentioned in Section A.6. The prefix "pseudo-" is used because \SAB\ depends on the length of the vector joining the interacting spins as well as its orientation. If the ground-state geometry of the molecule is known, M2 can be calculated from Equation 2.2. Experimental measurement of M2R then allows determination of (\SAB\ 2^ -If M2 is not known, changes in M2R can still provide a relative measure of order. In either Chapter 2. NMR Theory 22 case, caution must be exercised in interpreting the results due to the possible influence of the inter-proton distance on \SAB\. The Moment Expansion of the Free Induction Decay In broadline 1 H - N M R experiments, the beginning of the FID is usually lost during the recovery time of the receiver (unlike 2 H-NMR, it is not simple to refocus the proton signal). In order to Fourier transform the data this lost signal must be extrapolated, making it difficult to reliably determine M 2 r in the frequency domain. Under certain circumstances (the FID is properly phased and collected on-resonance), it is possible to obtain the residual M 2 (and other moments) directly from the real part of the FID, F(t), by means of the "moment expansion". By Taylor expanding F(t) and applying the definitions of the Fourier transform and of spectral moments, one obtains: m = T,yjrM2n^. (2.4) By truncating this expression and performing a polynomial fit in t2, the residual values of M 2 n can be obtained experimentally (as discussed in Section 3.3.1). The Deuterium Second Moment The order parameter \SCD\ derived from 2 H - N M R measurements is discussed at length in Appendix A. Its interpretation is less complex than in the dipolar case, for two reasons: (i) it is a pure orientational order parameter, depending only on the orientation of the C-D bond in space, and (ii) the discrete nature of the quadrupolar splitting allows direct measurement of \SCD\ from an oriented (or de-Paked) spectrum. Since \SCD\ is the factor by which the quadrupolar splitting is reduced by motion (see Section A.4), the residual second moment is proportional to its mean-squared value. For Chapter 2. NMR Theory 23 a powder pattern of perdeuterated lipids in the fluid membrane, one obtains [57]: where e2qQ/h is the quadrupolar coupling constant for a methylene C-D group. (Note that this expression neglects the much smaller contribution from dipolar interactions.) The deuterium M2r is a useful index of molecular order in its own right, or in comparison with the proton M 2 r in partially deuterated systems. 2.2 Relaxation "Spin-lattice" (Ti) and "spin-spin" (T2) relaxation studies are very important tools for investigating the dynamic properties of spin systems. NMR relaxation in membranes has been studied in considerable depth [58, 59, 60, 61, 62, 63, 64], and has contributed greatly to our understanding of the wide spectrum of motions present in this complex system. Experiments described in this thesis deal exclusively with T i z , the relaxation time of the Zeeman polarization, and T 2 e , the transverse relaxation time of a spin 1 system as measured by a two-pulse quadrupolar echo sequence. (Experimental details are described in Sections 3.2.2 and 3.2.3.) Comments below pertain to these parameters only, though many of the principles extend to other relaxation times. For ease of reading the notations Ti and T 2 will be used throughout, except in a few statements where greater precision is required. Ti relaxation describes the return of an excited system to thermal equilibrium, as the spins re-align with the external magnetic field. T 2 relaxation is concerned with the loss of phase coherence of the transverse components of the nuclear magnetization. The general theory of spin relaxation [52] describes how these processes arise from fluctuations in NMR interactions. The fluctuations are due to various motions present in the system, (2.5) Chapter 2. NMR Theory 24 and are characterized by their correlation times, r c . Describing the motions in terms of their "reduced spectral densities", J(OJ), the following expressions (valid for fluctuations with r c <C TA) are obtained: ^ = d [ai j(u>0) + a 2 j(2u0)} (2.6) J- I ^ = C 2 [boj(0) + h J(OJ0) + b2j(2u0)} (2.7) where C\ and C 2 are coupling constants for the interaction in question and a^, b{ are proportional to the mean-squared amplitude of the fluctuations at the appropriate fre-quencies. u>0 is the Larmor frequency for the particular nucleus and field strength. It is evident from Equation 2.6 that 7\ processes are sensitive to fluctuations at OJ = u>0 and OJ = 2OJ0; this is because T\ relaxation involves exchange of one or two quanta of Zeeman energy between the spin system and the lattice1. Spin-spin relaxation requires no such exchange, so the T 2 rate receives contributions from a zero-frequency spectral density j(0) as well as J(OJ0) and J(2OJ0). This additional term in 1/T 2 has profound consequences: not only is T 2 < Ti always satisfied, but also T 2 <C Ti in the presence of slower "adiabatic" motions. The difference in sensitivity of T\ and T 2 to motions with different r c greatly expands the power of relaxation techniques to study dynamics. Systematic variation of parameters like field strength (and hence OJ0) and temperature or pressure (and hence r c) allows the "spec-trum" of correlation times to be studied through a great range of amplitudes. Studies of this nature have been the source of much of our current knowledge regarding molecular motions in membranes. ' T h e surroundings o f the spins are collectively called "the latt ice" , and are assumed to be an infinite heat bath. Chapter 2. NMR Theory 25 2.2.1 Effects of Temperature on Tx and T 2 Raising the temperature of the sample can affect the spin system in several ways. The first, of particular interest for T x relaxation, is that correlation times can shorten as molecular motions become more rapid [52, 65]. The second, important for T 2 processes dominated by adiabatic motions, is that thermally-activated modes can increase in am-plitude [63, 66]. Obviously a third class of effect would be observed if the system were to undergo a phase transition, but this is outside the current discussion. To understand the effects of these changes on relaxation times, it is useful to give functional form to the equations shown above. In the case of truly random fluctuations, r c will be the time constant of an exponentially decaying correlation function. The spectral density (related by a Fourier transform) will then take on a Lorentzian lineshape, j(u) = 1 + 7 j ? 2 T 2 • It is important to note that the area under the spectral density curve is fixed for all r c , and that the amplitude of is roughly constant for UJ < l / r c , beyond which it drops rapidly towards zero (see Figure 2.2a). Decreasing r c (as when temperature is raised) thus causes the spectral density to become broader and flatter. The value of j(u) at a specific u (say UJ0) will rise and then fall as the shoulder of the lineshape (at u ~ l / r c ) passes through that frequency. Correspondingly, as motions accelerate and r c decreases, we see from Equation 2.6 that the value of 1/Ti will first increase (while l / r c < ui0) then decrease (when l / r c > ui0). The plot of Ti versus l / r c thus features two roughly linear portions and a minimum at rc ~ l/to0, as shown in Figure 2.2b. While these effects apply equally to the j(ui0) and j(2co0) terms of the 1/T 2 expression, in the presence of adiabatic motions these terms are swamped out by j(0). In membrane NMR, relaxation in the T 2 e experiment is caused primarily by "thermally driven fluctu-ations in the quadrupolar splittings" [67]. These fluctuations, the causes of which are Chapter 2. NMR Theory 26 Figure 2.2: (a) The reduced spectral density, J{UJ), corresponding to different values of r c . As described in the text, |jf(a;) | is roughly constant for u> < l / r c , then rapidly approaches zero; since it is normalized, this causes the maximum value of \j(to)\ to vary greatly as a function of r c . (b) The plot of T\z as a function of l / r c (or equivalently of temperature) goes through a minimum near l / r c ~ ui0. Chapter 2. NMR Theory 27 discussed in the following section, have mean-squared amplitudes (b0 in Equation 2.7) proportional to ksT, such that raising the temperature leads to increases in the T 2 rate. A direct linear relationship is not assured due to possible temperature-dependence of material properties which also influence the amplitudes. Of course, temperature can also affect the correlation times of these adiabatic modes and motions. If ((SOJ)2) represents the contribution to the second moment from the fluctuating interaction responsible for relaxation, then TS = {(SOJ)2)-1^2 is the relevant spectroscopic timescale. (A reasonable estimate of TS in fluid bilayers with perdeuterated chains is 10 _ 5s [61].) For fast adiabatic motions (i.e. 1/OJ0 « T C « TS) which give rise to uncorrelated fluctuations, Equation 2.7 yields the classic result: In the limit of slow motions (i.e. r c 3> r s), the dependence of T 2 9 e on r c is inverted [60]: As for T i , the variation of T 2 e with r c thus has a minimum in the neighbourhood of TS. Note however that this theory describes only a single contribution to transverse relaxation. In a system as complex as a perdeuterated membrane there will be many contributing processes, perhaps with a spectrum of rc's corresponding to each. If this r c spectrum is shifted significantly by temperature, then it may be expected that changes in T 2 e due to motions on either side of the minimum will partially cancel out. It is also possible that the rc's will not shift, however, since for certain important mechanisms the range of r c is limited by physical constraints which do not vary significantly with temperature (e.g. surface undulations, discussed below). The temperature-dependence of T 2 e in membranes is thus difficult to predict a priori - the observed behaviour will be a complex superposition of effects, many of which are (2.8) (2.9) Chapter 2. NMR Theory 28 not yet fully understood. Increases in the fluctuation amplitudes, however, will invariably make the relaxation processes more effective. If correlation time effects are assumed to balance out or to be negligible, then raising the temperature can be expected to decrease T f . 2.2.2 Orientation Dependence of T2 The following is a brief summary of the dependence of deuterium T2 relaxation rates on 9, the angle between the membrane surface normal and the external magnetic field. For details the reader is referred to the "phenomenological theory" by Bloom [68, 69]. From Section A.4 we learn that the quadrupolar splitting for a deuteron on an acyl chain is given by u> = UJQP2(COS9)SCD- Since UQ is a constant, the adiabatic fluctuations which dominate T2 relaxation in membranes can arise from motions which modulate either 9 or SCD- We assume these parameters to be independent, and define the motions by effective correlation times Te and r a , respectively2. Changes in 6 could arise from undulations of the membrane surface, while variation in SCD corresponds via Equation A.3 to fluctuations in membrane thickness, or equivalently (assuming the bilayer to be an incompressible fluid) in membrane surface area a. The mean-squared fluctuations {(S9)2) and ((5a)2) can be related to measurable ma-terial properties of membranes by thermodynamic considerations. Under appropriate conditions, the "curvature energy" KC [66] and the "isothermal area compressibility" 1/Ka [67] govern the two types of fluctuations, as follows: 2 Approaches to determinat ion of these correlation times, a difficult problem not addressed here, are discussed in the literature [66, 63]. (2.10) (2.H) Chapter 2. NMR Theory 29 where A M and A m are the maximum and minimum wavelengths for membrane undula-tions. (Note that these limits on A, which are based on geometrical considerations and are not expected to vary with temperature, define the range of correlation times TQ of undulational modes [66].) Another mechanism for fluctuations in 6 could be diffusion of molecules on the curved surface of the vesicle, but this is discussed elsewhere and judged not to be a dominant effect in T 2 e of membranes [63]. Assuming that the relevant correlation times satisfy Tj <C {(SUJ)2)~1^2, Equation 2.8 is used to assess the contributions of these fluctuations to T 2 relaxation. The T 2 rate due to adiabatic motions is: where the coefficients B and C are determined from Equations 2.10 and 2.11, the expres-sion for the quadrupolar splitting, and estimates or models of the effective T j . When a con-stant term is added for the nearly isotropic contribution of fast motions, an orientation-dependence of the following form is expected: This model may be tested by plotting experimentally-determined values of T 2 as a func-tion of frequency for a Pake doublet spectrum, which represents a map of doublets for different local bilayer orientations 6. = B sin2 9 cos i20 + C[P 2(cos0)] 2 (2.12) (2.13) Chapter 3 Experimental Methods 3.1 Sample Preparation The perdeuterated lipid, l-palmitoyl-2-oleoyl-phosphatidylcholine with deuterons substi-tuted at all sites on the palmitoyl chain (POPC-d 3 i, or 16:0-d3i/18:l-PC), was purchased from Avanti Polar Lipids (Alabaster, AL). Protonated P O P C - d 0 was obtained from Northern Lipids (Vancouver, BC). l-palmitoyl-2-docosahexaenoyl-phosphatidylcholine (PDPC, or 16:0/22:6-PC) was purchased from Sigma (St. Louis, MO), as were the D 2 0 (<0.04 atom% 1 H) and phosphate buffer mixture ( K H 2 P 0 4 / K 2 H P 0 4 with added NaCl). Deuterium-depleted Ff 20 (<0.05 atom% 2 H) was supplied by Isotec (Miamisburg, OH). Five samples were prepared, with molar concentrations of P D P C of 0%, 25%, 50%, 75% and 100%, as shown in Table 3.1. To attain constant signal-to-noise in the 2 H - N M R measurements, 40 mg of POPC-d 3 i were used in each sample and P D P C amounts were adjusted accordingly (except in the 75% PDPC sample, for reasons of expense). While the total amount of lipid thus varies between samples, in all cases the concentration is well within the dilute limit. (Phospholipids are fully hydrated for water concentrations greater than ~ 40 wt% [70].) Throughout this thesis, samples will be referred to by their molar percentage of P D P C (e.g. "25% PDPC" refers to the sample which is 25% P D P C and 75% POPC-d 3 i ; "0% PDPC" refers to the sample which is pure POPC-d 3 1 ) . For each lipid species, a stock solution was prepared in methylene chloride (CH 2Cl2) and stored under argon at -20° C. Buffer solutions were prepared using deuterium-depleted 30 Chapter 3. Experimental Methods 31 Table 3.1: Lipid composition of NMR samples. Sample Amount P D P C Amount P O P C - d 3 i 0% P D P C 0 mg 40 mg 25% PDPC 13 mg 40 mg 50% PDPC 40 mg 40 mg 75% P D P C 60 mg 20 mg 100% PDPC 40 mg 0 mg water (or D 2 0 for some preparatory experiments), and adjusted to pH 7.4. These so-lutions contained 10 mM phosphate buffer ( K H 2 P O 4 / K 2 H P O 4 ) and 140 mM NaCl. To eliminate dissolved oxygen, buffers were degassed by bubbling argon through them for 15 minutes. For each sample, stock solutions were mixed in appropriate proportions, the solvent was evaporated, and the samples were placed under vacuum overnight. The lipids were hydrated with an excess of deuterium-depleted buffer solution (500 ph) and vortexed for five minutes to create multilamellar vesicles (MLVs). The resulting dispersions were transferred into teflon sample tubes, and sealed under argon. All manipulations were carried out under a stream of argon, and shielded from light whenever possible; NMR measurements were conducted under a constant flow of dry nitrogen cooling gas, as described in Section 3.2.4. A recent study by Drobnies et al. [71] examines the effects of lipid oxidation on membrane order, as measured using 2 H - N M R on MLVs composed of PAPC -d3 i (16:0-d3i/20:4-PC). It is shown that 10% lipid oxidation produces drastic effects on the deu-terium powder pattern, in which all sharp features of the spectrum are "blurred out", presumably by the presence of a range of slightly altered lipid species. Such blurring was not observed in any of the spectra collected in the present study, which instead were qualitatively similar to the results shown for 3% oxidation. We thus conclude tentatively that significant sample degradation has not occurred. Chapter 3. Experimental Methods 32 3.2 N M R Techniques A l l N M R measurements were carried out using a Bruker C X P spectrometer wi th het-eronuclear broadband capability, at a Larmor frequency of 200 M H z for protons and 30.7 M H z for deuterium. Proton and deuterium protocols, described in Sections 3.2.2 and 3.2.3, were implemented for each sample at temperatures of 10° C , 25° C and 37° C. 3.2.1 Preparatory N M R Experiments To minimize the risk of oxidative damage to the polyunsaturated lipids, it was desirable for al l experiments on a given sample to be completed in as short a period as possible. It was thus necessary to l imit the duration of the N M R experiments, and imperative that the experimental protocol be finalized before the first samples were prepared. (Sam-ples frozen and later rethawed for further experiments would likely undergo chemical or physical changes. Certain N M R parameters, especially T2e, are highly sensitive to such variations in sample handling and thermal history [69].) Many preliminary experiments were performed to address these challenges - experimental parameters were optimized to balance data quality wi th experiment duration, and possible systematic errors were examined and eliminated. This work is described in Appendix B . 3.2.2 ^ - N M R Protocol The * H - N M R experiments were conducted at 200 M H z . The duration of a 90° pulse was 3 ps, and the recovery time for the receiver was approximately 8 ps. 2048 complex points were collected wi th a dwell-time of 2 ps, and the receiver filter width was 2 M H z . The repetition time was 2 s. Chapter 3. Experimental Methods 33 The proton FID was collected on-resonance to determine spectral moments. A "mod-ified inversion recovery" scheme was used to reduce systematic noise from probe ring-down, in which the inverted signal following a 180° pulse was subtracted from the signal from a single 90° pulse. When both methods of water suppression were incorporated (see Appendix B), the basic pulse program was: 180* - r 0 - 90y - t - r 2 - 180* - (r 3 - 180 x) 1 6 (+) 180* - r 0 - 180* - n - 90y - t - r 2 - 180* - (r3 - 180*)16 (-) in which the signals collected during t are added and subtracted in computer memory (as indicated by (+) and (-), above) to yield the FID. The first 180° pulse is the "pre-inversion" pulse for water suppression, and r 0 = 2 s ( « T l z - ™ t e r ) was selected to minimize the water contribution as described in Appendix B. T\ = 5 ms was chosen to satisfy T2,upid <^  T\ <C Tujipid, in order to correct systematic errors without sacrificing signal-to-noise. r 2 and r 3 were selected (200 ps and 400 ^s, respectively) to obtain a sufficient number of well-formed C P M G echoes to fit accurately. 128 scans were signal-averaged, with 8-CYCLOPS phase-cycling. T i 2 data were collected using the same modified inversion recovery sequence, which for relaxation studies has the added advantage of'being insensitive to non-idealities in the 180° pulse and yielding FID amplitudes which decay exponentially. Ten values of T\ were used, logarithmically spaced between 1ms and 1000 ms. 16 scans were averaged for each value of T\, with 8-CYCLOPS phase-cycling. As is standard practice, r values were interleaved in data collection to guard against instrumental drift. 3.2.3 2 H - N M R Protocol 2 H - N M R measurements were conducted at 30.7 MHz, with a 4ps 90° pulse. The spec-trometer was tuned to doped D 2 0 at 25° C, and set on-resonance for lipids using the Chapter 3. Experimental Methods 34 chemical shift relation vuPid = VD2O — 142 Hz. The signal was detected in quadrature with phase cycling for all sequences, with 300 ms repetition time. 2048 complex points were collected with a dwell-time of 2 ps, and the receiver filter width was chosen to be 80 kHz. The deuterium lineshape and quadrupolar echo spin-spin relaxation time, T2e, were measured using the quadrupolar echo pulse sequence: 90x - T - 90y - t For lineshape measurements, r = 40 ps and 10,240 transients were averaged. Ten values of r were used to measure T2e, spaced logarithmically from 38ps to 750ps. To measure the Zeeman spin-lattice relaxation time, T\z, the quadrupolar echo se-quence was combined with modified inversion recovery: 90x - r - 90„ - t (+) 180x T\ 90x T 90y t (-) where the echoes collected during t were added and subtracted to yield a decaying ex-ponential function of T\. r was kept constant at 40ps, while T\ was varied over ten logarithmically-spaced values between 1ms and 150 ms. For both T | e and T\z measure-ments, delay values were interleaved, with 1024 scans collected for each value. 3.2.4 Temperature Control for N M R Experiments Temperature was regulated using a Bruker BV-T1000 variable temperature unit, control-ling an electric heating coil which warmed the nitrogen gas (boiled off from a dewar of liquid nitrogen) that blew constantly through the sample chamber. A copper-constantan (type T) thermocouple served as temperature sensor. Chapter 3. Experimental Methods 35 The spectrometer was tuned to each sample at 25° C, then experiments were con-ducted at 10° C, 25° C and 37° C. At each temperature change, the sample was allowed to equilibrate for 30 minutes after the establishment of the new temperature in the probe. This period was chosen after studying the moments of the deuterium spectrum for a POPC-d3i sample as a function of time following changes in temperature. The temperature control system was calibrated immediately before data collection began; incorporating all sources of uncertainty, sample temperatures were constant and accurate during NMR experiments to within ±0 .5° C. 3.3 Analysis 3.3.1 Proton Moments The proton residual second moments, M2T,H, were obtained directly from the FID, in a process summarized in Figure 3.1. The proton signal was baseline corrected and a zeroeth order phase correction (a constant phase factor) was applied. The peaks of the C P M G echoes were fitted to a line, which was extrapolated to zero time and subtracted from the whole signal to eliminate the contribution from the water and buffer (see Appendix B). For the moment expansion of Equation 2.4 to apply, it is necessary for the FID to be properly phased and on-resonance (i.e. the corresponding absorption line must be symmetric). The spectrometer was tuned to the signal from the entire sample, which is dominated by water. Subtraction of the slow-relaxing fraction has isolated the lipid signal, but still the FID was collected at the resonant frequency for the water-dominated sample. It is readily shown that an additive offset in the frequency domain corresponds to a linear phase shift in the time domain (i.e. f(u + 5u>) = f*™ F(t)e^ u , + ( 5^ t), so a first-order phase correction must also be performed (i.e. F(t) multiplied by e - t ^*) . The required frequency offset was determined to be 512 Hz, by taking the difference in Chapter 3. Experimental Methods 36 resonance frequencies between two POPC samples in H 2 0 and D 2 0 buffer solutions. After these corrections, the FID was fitted to a truncated form of the moment expan-sion: ^ ) = J ( 0 ) ( i - ^ + ^ - « ^ + . . . ) . (3.1) This is a polynomial in t2 and could be solved routinely by a standard package (Igor v3.14; WaveMetrics, Lake Oswego, OR), using a linear matrix-solving algorithm. A considerable effort was made to understand the effects of the fit parameters (such as the number of terms, the range of the FID which was fitted, and the precise placement of the origin) on the moment values obtained, in order to achieve accurate and stable solutions. A four-term fit was chosen (i.e. to order i 6), with the origin set to the centre of the 90° pulse. The fit-range was chosen to begin 17 ps after the end of the pulse, to ensure that ring-down noise would not influence the result. As the range of data included in the fit was increased, M 2 r ) # was found to vary widely at first, then to settle to a relatively stable value (see Figure 3.2). Balancing this stability against the increasing influence of higher-order terms at higher t, an end-point of 57 ps after the end of the pulse was selected for the final analysis. A representative fit is shown in Figure 3.1. The uncertainties for the derived M2R,H values were generated by the fitting algorithm, and correspond to the diagonal elements of the covariance matrix for the fit. It should be noted that these errors do not contain information regarding the goodness-of-fit of the moment expansion to the FID, but instead are derived directly from the standard error values provided for the data. (For the parameters described above, the expansion always fitted the data adequately, such that x2 <v where v is the number of degrees of freedom [72].) A second estimate of the uncertainty was obtained by analyzing three separate runs of the same sample (0% PDPC), and produced results of similar magnitude. Chapter 3. Experimental Methods 37 a b 1/ I- , 1 1 100 200 300 400 Time (fis) / 1 1 1 1 1 500us "i * o o o o o o -^e-e-&-e-ci^ a^~ 1 1 1 1 120 130 140 150 Time ((is) l 160us Figure 3.1: Analysis of the proton FID. (a) shows the FID as collected using the pulse sequence described in the text. The lipid signal is the small, fast-decaying component at the far left. The linear fit to the C P M G echo peaks is shown as a dotted line; the boundaries of this fit are marked by the arrows, (b) shows an expanded view of the lipid signal, after the slow-decaying signal is removed and the phase corrected. The solid curve shows the moment expansion fit-line corresponding to Equation 3.1; the arrows show the range fitted. (Note that the 90° pulse began at t — 100/xs on the time-scale shown.) (c) shows a further blow-up of the fit obtained using the moment expansion -again the fit-range limits are shown by the arrows. The fit-line matches the FID data well throughout the range fitted. Chapter 3. Experimental Methods 38 4.5x10° H * 4.0 O A T3 a o o <U 3.5 -] 3.0 2.5 A M 2 r / / from fit o Relative error on M 2r,# r - 0.6 o A d>o° A Selected value o f f, A ! oOo o o o 140 i 1 1 r 150 160 170 180 End of fit range, tf ((is) 190 0 5 ^ h 0-4 I' 0.3 8 o 3 0.2 ^ 0.1 0.0 a: Figure 3.2: The calculated value of M2R\H a n d the statistical uncertainty derived from the fitting process are shown as a function of the end-point of the fit-range, tf. (The results shown are for a four-term expansion (i.e. to order t6) wi th the fit-range beginning at 120 ps. A s in Figure 3.1, the excitation pulse began at t = 100 ps, and is 3 ps long.) M2R,H varies wildly as the range is increased, then settles to a relatively constant value for tf > 150 ps. The relative error of the M2R,H value (scale shown on right axis) decreases almost monotonically, but as noted in the text it does not account for possible misfitting of the experimental data, tf = 160/^s was selected as the end-point for analysis which yielded the results presented in Section 4.2.1. Chapter 3. Experimental Methods 39 3.3.2 Deuterium Moments Because the quadrupolar echo refocuses the signal well after the excitation pulses, no information is lost due to the receiver dead-time, and the time signal can be Fourier transformed to produce a complete spectrum. Before transforming, the signal was base-line corrected and phase-shifted so that the real channel had maximum amplitude. The peak of the echo was then symmetrized using a cubic spline fit [72], to avoid possible artifacts in the spectrum [58]. The out-of-phase channel was then zeroed, for a \/2 gain in signal-to-noise (SNR), and the real signal was left-shifted to the peak of the echo and zero-filled. The signals were then Fourier transformed, yielding the powder spectra shown in Fig-ure 3.3. The residual second moments were obtained directly by integration, as described by Equation 2.1. 3.3.3 Order Parameter Profiles and Average Chain Length The deuterium powder pattern spectra were de-Paked to give spectra equivalent to those of oriented samples, as described in Section A.4. The resulting spectra are shown in Figure 3.3. The smoothed order parameter profile, showing the approximate value of \SCD\ f ° r each carbon position on the deuterated chain, was obtained using the method of Lafleur et al. [73]. Seelig's method of determining the membrane thickness d from the average order parameter (S) is described in Section A.5. (5) was calculated from the S(n) results, above (with \SCD\ values for CI and C16 derived from linear extrapolation of the neighbouring four and two points, respectively) [73], and the mean length of the perdeuterated chain was calculated using Equation A.3. Chapter 3. Experimental Methods 4 0 0 10 20 30 0 10 20 30 kHz kHz Figure 3.3: Deuterium spectra for the series of P O P C - d 3 i / P D P C binary mixtures, col-lected at 25° C (and halved for display purposes). Powder patterns are shown on the left side; on the right are the de-Paked spectra used to obtain smoothed order parameter profiles. Chapter 3. Experimental Methods 41 3.3.4 Relaxation Analysis Proton T i z For T\z analysis, the FIDs were baseline- and phase-corrected, and the water signal was subtracted as described in Section 3.3.1. The amplitude of the FID (actually the mean value of 4 points, beginning 6 ps after the maximum to avoid dead-time artifacts) was recorded for each delay time T\. The logarithm of these amplitudes was plotted versus T\, yielding a linear relationship for the shorter delay times. A linear fit was applied to the short-Ti points, and a T\z value was obtained from its slope. Since the largest T\ value used in the fit (50 ms) is small relative to T\z, this result can be shown rigorously to be the weighted average of all proton T\z contributions in the sample (except the slow-relaxing water and buffer protons, of course, whose signal was removed earlier). Deuterium Tu To obtain the average T\z times from the deuterium experiments, the amplitude of the (baseline- and phase-corrected) quadrupolar echoes was measured for each delay time. Mean T\z values were obtained from linear fitting of the short-r data, as described above. The variation of the relaxation times with chain position was a desirable complement to the order parameter profiles, but the data were too noisy to generate a full "oriented spectrum" of relaxation times by de-Paking the raw data and calculating T\z point-by-point (or peak-by-peak). Instead, a coarser measure was obtained by taking Gaussian-weighted averages over three regions of the de-Paked spectra (shown in Figure 4.7), corresponding roughly to the plateau region (C2-C9), the middle of the chain (C10-C12), and the "tail" of the chain (C13-C15, not including the methyl protons). Mean T\z values were calculated for each region, as above. Chapter 3. Experimental Methods 42 Note that uncertainties for these regional T l z ' s were calculated from the spread of values obtained for three determinations of the 0% P D P C sample, but do not account for certain errors inherent in the analysis. Since the three regions were defined using landmark features of the spectra, relative changes in \SCD\ m & y have caused the peaks corresponding to certain carbon positions on the chain to move into or out of their ranges. This could systematically skew the relaxation results, particularly for the tail region where greater changes in peak position were observed in the S(n) analysis. Powder-pattern "T\z spectra" were produced for these results as well, using the tech-niques described below for T2e, but no noteworthy results were obtained. Deuterium T2e and Orientation-Dependence The deuterium T2e mean values and regional variation were determined exactly as for deuterium T\z, above. In order to study the complex orientation-dependence of T2e, a "T2e spectrum" was also generated for each experiment [74]. To do this, the quadrupolar echo for each delay time was processed and Fourier transformed, yielding a series of powder spectra. For each frequency point in the spectra, the amplitudes for all values of T were collected and a short-r linear fit was performed. (Since the fitting procedure involves a logarithm, amplitudes which were negative due to random noise could not be processed. In these instances, which occurred only in the far shoulder and baseline of the spectra, the T2e value was set to zero.) By plotting the calculated T2e values as a function of frequency, a T2e powder spectrum could be generated. As described in Section 2.2.2, the orientation-dependence of deuterium T2e in lipid vesicles is predicted by this equation: Previous work on T2qe spectrum fitting [68] was restricted to a specifically deuterated (3.2) Chapter 3. Experimental Methods 43 sample (i.e. deuterated at only one site, so the spectrum was a single Pake doublet), signal-averaged sufficiently that the entire T 2 9 e spectrum was well-defined. Equation 3.2 was expressed in terms of orthogonal functions (Legendre polynomials) and the fitting coefficients were determined using the values at discrete points in the spectrum. The problem could be solved analytically, and quantitative results obtained. The current study differs in several respects. The superposition of Pake doublets arising from the perdeuterated chain, combined with poor signal-to-noise due to the rigid constraints on experiment duration, prevent the application of such rigorous meth-ods. Indeed, the T2e spectra calculated from the data collected as described above were judged to be too complex and too noisy for meaningful results to be obtained from fitting them. Instead, to learn about T2e mechanisms in P O P C / P D P C mixtures in general, a higher SNR measurement (10,240 scans per r value rather than 1024) was made for a representative sample (25% PDPC at 25° C). The resulting T2e spectrum is shown in Figure 3.4. Even with the higher SNR, the T2qe values become quite erratic towards the edges of the spectrum. The Pearson's R coefficient (representing the strength of linear correlation of the fits from which the individual T2e values were obtained [72]) was thus used to discriminate between data which were reliable and those which were too heavily influenced by noise. R was plotted across the spectrum - also shown in Figure 3.4 - and found to drop off rapidly in the outer region. A threshold of R = 0.8 was selected arbitrarily to define the "trustworthy" region of the T2e spectrum. The complexity of the spectrum, due to the superposition of Pake doublets from different sites on the chain, was a source of further difficulty. Since the problem of fitting the series of individual peaks was intractable, it was decided to focus solely on the large outer peaks corresponding to the plateau region of the chain (in which the contributions of roughly half the carbon sites are summed). The total range over which the T2e spectrum Chapter 3. Experimental Methods 44 kHz Figure 3.4: The "T 2 9 e spectrum" for a representative sample (25% PDPC, at 25° C), showing values of T$e for each frequency across the powder pattern. To determine the range of reliable data, the Pearson's R coefficients for the linear fit (performed to calculate a mean T2e value) are plotted as a function of frequency. The R values drop off sharply beyond ~ 22 kHz, defining the outer bound of the region to be fitted; the inner limit is defined by the edge of the large peak corresponding to the plateau carbons. Chapter 3. Experimental Methods 45 was fitted is thus as shown in Figure 3.4. "Fitting" was carried out entirely by eye, and consisted of characterizing the effects of the three coefficients on the fit function, then honing in on the best solution for the region defined above. It must be emphasized that the terms in Equation 3.2 are not orthogonal, so this problem is fundamentally ill-posed. Because of this and the approximations made above, there is no pretense that quantitative conclusions can be drawn from these results. A satisfactory solution was obtained, however, and by varying the values of the coefficients the confidence limits could be estimated in an informal way. Chapter 4 Results and Discussion 4.1 Preliminary Comments As described in Section 3.1, the samples were binary mixtures of mono-unsaturated P O P C - d 3 i and polyunsaturated PDPC. Samples will be referred to by their molar per-centage of P D P C (e.g. "0% PDPC" refers to the 100% POPC-d 3 i sample, etc.). Obviously, the composition of the samples must be borne in mind when interpreting the NMR results. The 1 H - N M R measurements include contributions from both POPC-d 3 i and PDPC, and indeed from headgroup and glycerol protons as well as from the acyl chains of both species. Changes in ^ - N M R parameters observed upon increasing PDPC concentration may be due to its effect on the other lipid - and thus, presumably, on the membrane environment generally - or simply to an increasing proportion of PDPC's own distinctive contribution. In contrast, all 2 H - N M R results come directly from the deuterium-labelled 16:0 chain of P O P C - d 3 1 . Therefore, any effects on 2 H - N M R measurements as P D P C concentration is raised are direct indications of the polyunsaturated lipid's effect on other components of the membrane. Unless otherwise noted in the Analysis section, the uncertainties shown here were determined from the variation in results from several identical experiments (using the same sample or different samples with the same composition). They are thus functional measures of the experimental error, encompassing uncertainties from sample preparation 46 Chapter 4. Results and Discussion 47 and oxidation as well as those inherent in the techniques of analysis. Numerical results of curve-fitting are not shown below except when relevant to the discussion. They are included in Appendix C. 4.2 Moment Studies and Order Parameters 4.2.1 Proton Second Moment The proton residual second moments, M2r<H, are shown as a function of P D P C content in Figure 4.1. Considering the vast range of sample compositions, the values are remarkably constant. While a slight upward trend is apparent, only for the 25° C data did the slope of the least-squares fit line differ statistically from zero. 3.0x10° - f 2.5 -4 1-5 -4 1.0-1 —~© „ J < t < *- J ^ r ^ r ^ T T - J "] -- • - 10° C -m- 25° C - * - 37° C 25 50 75 100 mol% P D P C Figure 4.1: Residual proton second moments, M2R,H, of binary mixtures of P D P C (16:0/22:6-PC) and POPC-d 3 i (16:0-d3i/18:l-PC), as a function of mol% P D P C and temperature. M2ryH values were determined directly from the proton FID using the mo-ment expansion, as described in Section 3.3.1. Results of the least-squares linear fits to these data are included in Appendix C. Chapter 4. Results and Discussion 48 While this surprising lack of variation could be the net result of larger, offsetting changes, it seems that the two individual lipid species (POPC-d 3 1 and PDPC) simply have very similar M 2 r , / / values. Examination of the 0% PDPC and 100% P D P C data reveals that their M2TIH values differ by no more than 18% for any of the temperatures measured (cf the ~ 500% change in M2R.:H between gel and fluid phases of DPPC-do [57]). Since the relationship at intermediate compositions is linear, it is impossible to distinguish whether the observed trend results from interactions between the two species, or simply from an increased weighting of PDPC's slightly greater intrinsic M2R,H-As described in Section 2.1.2, M2T>H is proportional to the mean-squared dipolar pseudo-order parameter. It is thus a function of the range of angles sampled (at a suitable speed) by all proton-proton vectors, and of the time-averaged distance between protons. (Note that in fluid membranes, intermolecular interactions are averaged to zero due to rapid lateral diffusion of lipid molecules. Since dipolar interactions fall off like 1/R6, each proton on the acyl chains "feels" the fields of only the four nearest C H 2 groups and roughly 50% of M2R,H arises from interactions between "geminal" protons bound to the same carbon atom [56, 57]. Since the distance between geminal protons is fixed - with apologies to infrared spectroscopists - this contribution will vary only with orientation.) The reduction of M2 to M2R arises from fast motions for which r c rs, where TS = (M2)~^. For intramolecular proton-proton dipolar interactions in typical phospholipids the proton M 2 ~ 2 x 10 1 0 s - 2 [57], so this condition requires r c <t; 10~5 s. Referring to Figure 2.1, we see that relevant motions would include trans-gauche isomerizations and rotational diffusion about the bilayer normal, as well as nodding motions of the phospholipid headgroup and the smallest-wavelength undulations. To the extent that it is significant, the small increase observed in M2T,H indicates a net decrease in fast re-orientations or time-averaged inter-proton distances. Whether these changes occurred in the acyl chains or the lipid headgroups, and even whether they Chapter 4. Results and Discussion 49 result from interactions between the species or are simply properties of PDPC, cannot be stated from this evidence. 4.2.2 Deuterium Second Moment Deuterium residual second moments (M2 r,£>) were calculated directly from the powder patterns, as described in Section 3.3.2, and are summarized in Figure 4.2. As with the proton moments, there is no strong change in Mirp as the proportion of P D P C increases. Least-squares linear fitting yielded only one slope which was significantly different from zero - that for 10° C, which shows a slight decline with increasing DHA content. 4.0x1 ( f 3.5 2.5 -4 2.0 -4 1 1 — ~ — , 10° C > 25° C —A— 37 ° C 25 50 mol% PDPC 75 Figure 4.2: Residual second moment values, M2R,D, of the deuterium spectrum arising from the 16:0-d3i chain of POPC-d 3 i . Fitting results are tabulated in Appendix C. As discussed in Sections 2.1.2 and A.4, the residual second moment is proportional to (SQD), where SCD = (^(cos^)} is the orientational order parameter. Since M2R,D is relatively constant, we see that adding PDPC to the membrane has little net effect on the orientational order of the other lipid species (or, more specifically, on that of its Chapter 4. Results and Discussion 50 perdeuterated chain). Moving from a membrane which is composed entirely of POPC -d3 i to one which is 75 mol% PDPC, the M2R,D of the deuterated chain changes by only ~ 5%. Again the effect is surprisingly small - this can be interpreted several ways. It could be that the two lipid species have such similar properties that addition of P D P C does not disturb POPC's state. This would seem to agree with the observation that the 0% P D P C and 100% P D P C samples had very similar values of M2R,H- Another possibility is that the lipids are separating into species-enriched domains, so the perdeuterated 16:0 chains are largely isolated from the increasing proportion of P D P C in the membrane. While this is reminiscent of the dynamic clustering proposed by other investigators [46, 47], these domain models have been developed to explain DHA's lack of interaction with cholesterol and have not been extended to sterol-free membranes. Further insight into these questions is gained by consideration of the variation in \SCD\ as a function of position on the acyl chain. 4.2.3 Deuterium Order Parameter Profiles Smoothed order parameter profiles, obtained from de-Paked spectra using the method of Lafleur et al. [73], are shown in Figure 4.3. As PDPC is added, a progressive decrease in orientational order is observed in the lower half of POPC's perdeuterated 16:0 chain (i.e. in the half of the chain closer to the centre of the bilayer, from C9 to C15). This indicates that the 16:0-d3i chain is experiencing greater conformational freedom, corresponding to a slightly expanded "cloud of conformations" in this region. A concomitant, very slight increase in order is discernible in the plateau region of the profiles, though it barely exceeds the uncertainty of the measurement. A general caveat must be stated with respect to the sensitivity of order parameter profile measurements to lipid oxidation. The recent study by Drobnies et al. [71] shows Chapter 4. Results and Discussion 51 Carbon number, n Figure 4.3: Smoothed order parameter profiles S(n) for the series of lipid mixtures, cal-culated from the de-Paked 2 H spectra by the method of Lafleur et al. [73]. Representative error bars, derived from the variation in four separate measurements, are shown for the 25% P D P C profile. For clarity, only the results at T = 25° C are shown; the profiles for 10° C and 37° C, which show qualitatively similar results, are included in Appendix C. Chapter 4. Results and Discussion 52 that \SCD\ varies significantly as oxidation of a polyunsaturated lipid (PAPC, or 16:0-d 3i/20:4-PC, in their study) proceeds - changes of up to about 0.03 units for 10% oxidized lipids. While such an effect is certainly large enough to account for (or to overwhelm) the trends reported here, there is good reason to believe that oxidation has not progressed this far in any of the samples used (see Section 3.1). Furthermore, oxidation was shown to decrease S(n) at all carbon sites on the chain, whereas Figure 4.3 distinctly shows regional variations as a function of PDPC content, and even slight increases in the plateau region. It should be noted, though, that in the Drobnies study the perdeuterated chain is on the same lipid molecule (at sn-1) as the polyunsaturated chain (at sn-2); the extension of these results to our two-species system is not obvious. 4.2.4 Average Chain Length Figure 4.4 shows the average length, (L), of the perdeuterated acyl chain as a function of P D P C content. The chain length decreases (almost imperceptibly) as P D P C is added - the 75% P D P C membrane is ~ 1% thinner than the 0% PDPC sample. In terms of the S(n) profiles, the decreased order in the central region of the bilayer has "won out" over the slight rise in the plateau, leading to the slight thinning effect. In practical terms, however, this trend is so subtle that (L) can be considered constant for all samples studied. 4.2.5 Discussion of Moment and Order Parameter Results The surprisingly small variation in the proton and deuterium M 2 r results indicates that the lipid species are "well-matched" and do not perturb one another in the membrane, or perhaps that they separate into species-enriched microdomains. The order parameter profiles are more telling - there is a clear effect of increasing P D P C content on POPC's Chapter 4. Results and Discussion 53 14.0 -4 13.8 -4 g> 13.6 -I I 13.4 - | S 13.2-1 13.0 10° C 25° C —*— 37° C 0 n r 25 50 mol% PDPC Figure 4.4: Average length (L) of the perdeuterated 16:0 chain of P 0 P C - d 3 i , determined as described in Section 3.3.3. Fitting results are tabulated in Appendix C. saturated chain, which allows us to address the question of DHA's effect on other con-stituents of the membrane. The S(n) results argue compellingly against the "wedge" model for polyunsaturation (described in Section 1.3). If it were true that lipids bearing DHA chains are wedge-shaped and exert lateral pressures through the middle region of the bilayer, then adding more P D P C should squeeze the other lipids in the membrane, reducing the conforma-tional freedom of the lower half of their chains. Instead we saw that the perdeuterated chain on POPC -d3 i gained conformational freedom as the proportion of polyunsaturated lipid increased. (Indeed we see that a perdeuterated chain on one lipid molecule responds to polyunsaturation on another much as the sn-1 chain responded to polyunsaturation at sn-2 in the earlier study [42].) Rather than forming wedge-shaped molecules which crowd the centre of the bilayer, it seems the DHA chain actually allows more space in this Chapter 4. Results and Discussion 54 region, so that all neighbouring chains (on the same or different molecules) have greater conformational freedom. Inspired by several sources [37, 71, 75], we propose that the D H A chain is spending more time doubled back toward the lipid-water interface than do less unsaturated chains. This would account for the S(n) results, since space is vacated (in a time-averaged sense) in the middle of the bilayer for the perdeuterated chains to occupy. Furthermore, it is consistent with the slight increase in S(n) observed in the plateau region, as these sites are slightly crowded by the doubled-back DHA chains. This model is being actively investigated by Gawrisch as a follow-up to the earlier S(n) study, and as a possible explanation for DHA's known repulsion for cholesterol [75]. A similar "snorkelling" mechanism, in which polar oxidized sites on the chain tend to migrate to the lipid-water surface, was invoked to explain the effects of lipid oxidation on order profiles [71]. A related argument could be applied (though less convincingly) based on the slightly polarizable nature of DHA's many double bonds. Finally, in Applegate Sz Glomset's early work on computational modelling of DHA's ground state, a "hairpin" configuration was found to be the lowest-energy state but has been largely ignored due to presumed difficulties in packing [37]. The snorkelling model would also help explain why replacing the 18-carbon oleic acid of P O P C with the 22-carbon DHA chain of PDPC leads to slight thinning of the membrane, since the longer chain would spend more time doubled up. Even the curious increase in M2r,Hi discussed in Section 4.2.1, can be explained: the hairpin conformation leads to smaller intramolecular inter-proton distances, increasing dipolar coupling and hence M2r,H as well. Chapter 4. Results and Discussion 55 4.3 R e l a x a t i o n S t u d i e s 4.3.1 P r o t o n A v e r a g e T l z Average proton T\z values were obtained by fitting the early points in the relaxation curve to a single exponential. The results are plotted in Figure 4.5, and exhibit a clear (20-25%) rise in T l z as P D P C content is increased from 0 mol% to 75 mol%. J I I I L 500 -4 c ID B 400 300 -4 Figure 4.5: Mean value of T l z for all l ip id protons, determined from a single-exponential fit to short delay time data (T\ <C T l z ) collected wi th a modified inversion recovery pulse sequence (as described in Section 3.2.2). F i t t ing results are tabulated in Appendix C . To understand these results, we must first determine the range of correlation times of the important T l z relaxation processes. A s shown in Figure 2.2, the fact that T l z times increase wi th temperature indicates that the predominant mechanisms are motions for which OJ0TC <C 1, and these "very fast" motions (such as trans-gauche isomerizations) get even faster as the temperature is raised. This conclusion cannot automatically be extended, however, to explain the observed Chapter 4. Results and Discussion 56 increase in T\z with P D P C content at each temperature. While speeding up the very fast motions is definitely a viable explanation, it is also conceivable that T\z rates decrease due to a slowing down of certain motions (such that they become adiabatic and cease to contribute to j(u>0)), or that certain contributing modes are extinguished by increasing P D P C content. To weigh these alternatives we appeal to the surprisingly small changes measured in M2R,H as P D P C was added. The very fast, non-adiabatic motions that underlie T l z relaxation certainly satisfy the criterion r c <C rs for contributing to motional averaging; indeed rapid chain motions and rotational diffusion are commonly assumed to be the primary causes of line narrowing in lipid NMR. If these modes were extinguished in any appreciable number - or slowed such that r c > TS - the loss of motional narrowing would cause a significant increase in M2R,H, which was not observed. This does not rule out the possibility of motions being slowed from the very fast regime (r c <§; l/a>0) to the fast adiabatic regime [rs < T c < l / ^ o ) i but the likelihood of large classes of motions being slowed by 3 to 4 orders of magnitude seems small. Furthermore, the temperature dependence asserts that non-adiabatic motions are dominant over the full range of sample compositions. The greater values of T i z could also be due to decreases in the mean-squared fluctu-ation amplitudes of the relevant fluctuations (the constants ai and a2 in Equation 2.6). However, the relationship between T l z and lipid order is 1/Ti z oc (1 — S2) (for small S) [63]. If we generously approximate (S) « 0.2, then 1 — (S2) « 0.96 and the observed 20% rise in T l z requires a 120% increase in (S) (or a five-fold increase in {S2))\ It is clear from the M2T,H results of Figure 4.1 that this is not the case. A final alternative could involve spin exchange between the lipid and the surrounding water (since the experiments were carried out in H 2 0 buffer solutions). Bilayers composed of polyunsaturated lipids have been proposed to be highly permeable to water [76, 77], Chapter 4. Results and Discussion 57 which might be expected to influence T l z if spin exchange is an important mechanism. This possibility was investigated by measuring average T\z for POPC-do in D 2 0 and H 2 0 buffer solutions. The results do not differ greatly, indicating that exchange processes do not contribute significantly to T i 2 of these systems. We thus conclude that the observed rise in average T\z with increasing polyunsat-uration results from decreasing correlation times for a class of very fast, non-adiabatic motions. We are once again unable, however, to distinguish whether this is due to PDPC's influence on P O P C or simply from an increasing proportion of PDPC's contribution. (As with the M2r,H results, it is evident from the 100% PDPC sample that the mixture of lipids is not required to observe the effect.) Likewise, the average T\z values entail con-tributions from all protons, so that chain, headgroup or backbone motions could underlie the changes. 4.3.2 Deuterium Average T\z Deuterium average Tiz values also increase as DHA-bearing lipid is added to the mem-brane, as shown in Figure 4.6. All the arguments of the proton case still apply, so again we interpret this as a decrease in correlation times for the very fast motions which domi-nate Tiz processes. The change is now localized, however, to the perdeuterated palmitoyl chain of P O P C - d 3 i , indicating (i) that chain motions - likely trans-gauche isomerizations - underlie the effect, and (ii) that the effect can arise in P O P C - d 3 1 solely as a result of PDPC's influence. Combining these findings, we see that adding P D P C to the membrane somehow speeds the motions of POPC's saturated chain. Attempting to further localize the effect, average T i z values were determined for ranges of the de-Paked spectra, as described in Section 3.3.4. The results are shown in Figure 4.7. The 0% P D P C results agree generally with those obtained in detailed studies of T i z as a function of chain position in oriented samples of POPC-d 3 i [62], lending confidence Chapter 4. Results and Discussion 58 Figure 4.6: Average values of T\z for the perdeuterated 16:0 chain of P O P C - d 3 i , as determined from a single-exponential fit to short-r data. Fitting results are tabulated in Appendix C . Chapter 4. Results and Discussion 59 in the analysis technique. As PDPC is added, clear increases in T\Z are visible in the plateau and middle regions of the chain. The results for the lower chain are more erratic, but as discussed in Section 3.3.4 there is reason to doubt their reliability even beyond the uncertainties shown. It is thus difficult to discern any further detail regarding the changes in the 16:0-d3i chain's motion - another study with better SNR would be required to learn more. 0 25 50 75 0 25 50 75 0 25 50 75 m o l % P D P C m o l % P D P C m o l % P D P C 10° C - » - 2 5 0 C - T k - 3 7 0 O Figure 4.7: Average values of TLZ for different regions of the perdeuterated 16:0 chain of P O P C - d 3 i . Gaussian-weighted integrals of the de-Paked spectrum isolated the signal from different parts of the chain (assuming a monotonic decrease in \SCD\ with carbon number); a single-exponential fit yielded average T\Z for each series. From left.to right, the plots correspond to the "tail" region of the chain (roughly C13-15), the middle of the chain (C10-12), and the plateau region (C2-9). Chapter 4. Results and Discussion 60 4.3.3 Deuterium Average T2e Addition of P D P C to the membrane had marked effects on the average T2e of POPC's deuterated palmitoyl chain. As shown in Figure 4.8, T2e decreases almost twofold going from 0% to 75% P D P C - the most striking change observed in any parameter in this study. 800 -\ 600 -\ 400 -4 200 -4 -•— 10° C —•— 2 5 ° C 3 7 ° C T 0 i r 25 50 m o l % P D P C 75 Figure 4.8: Average values of T2e for the perdeuterated 16:0 chain of P O P C - d 3 i , as calculated from a single-exponential fit to the peak amplitudes of the quadrupolar echoes for a range of delay times. A decrease of nearly 50% is observed in moving from 0%PDPC to 75% PDPC, the most striking effect observed in this study. T2e is much less than the deuterium Tu, indicating that adiabatic motions are present and dominate transverse relaxation. This is expected from the complex nature of the membrane environment (as recognized by Davis [58]), and prior studies have concluded that T2e relaxation in fluid membranes is due largely to thermally-activated adiabatic modes [63, 67]. This is consistent with the observed temperature dependence, as the decrease in T2e as temperature rises could be due to increased efficacy of the thermal Chapter 4. Results and Discussion 61 mechanisms. Alternatively, though, this decrease could be explained in terms of shrinking correlation times, since for very slow motions T2e oc r c (see Section 2.2.1). Since an understanding of the nature of the T2e mechanisms is essential to intepreting this dramatic result, we will consider all available evidence to discriminate between these models. To begin, in Figure 4.9 we see the "regional" variation of average T%e results. It is clear that the decreasing trend applies roughly equally to all regions of the perdeuterated chain, indicating that the T2 processes may be dominated by "collective motions" of the membrane which affect each molecule as a whole, rather than by localized conformational changes. In addition, Figure 4.10 shows that the plot of T2 rate versus temperature is almost perfectly linear, as predicted for thermally-activated mechanisms by Equations 2.10 and 2.11. Furthermore, as noted in Section 2.2.2, the correlation times for certain adiabatic modes are not expected to vary greatly with temperature. (For membrane surface undu-lations, for instance, r c is thought to be determined largely by geometric considerations such as the thickness of the membrane and the separation between neighbouring bilayers in multi-lamellar vesicle (MLV) systems [67].) Finally, any shift of the r c spectrum in the vicinity of r c « ((<5u;)2)-3 will at least partially cancel itself out due to contributions from either side of the "T2e minimum" (described in Section 2.2.1), making it difficult to obtain the large net effect which has been observed. It is thus unlikely that changes in correlation times underlie the significant dependence of T2e on either temperature or P D P C content. Orientation Dependence of Deuterium T2e All evidence is thus consistent with thermally-activated collective modes making the dom-inant contribution to T2e relaxation. If this is the case, then the orientation-dependence of T2e should be described by Equation 2.13, and should yield further details regarding Chapter 4. Results and Discussion 62 0 25 50 75 0 25 50 75 0 25 50 75 m o l % P D P C m o l % P D P C m o l % P D P C -0- 10° C -m- 25° C -*- 37° C Figure 4.9: Regional dependence of mean T^ 6 values for the perdeuterated 16:0-d3i chain. As described in the caption for Figure 4.7, from left to right the plots correspond to the "tail" region of the chain (roughly C13-15), the middle of the chain (C10-12), and the plateau region (C2-9). The decrease in T2e is seen clearly for all parts of the chain, indicating that the mechanism responsible for T2e relaxation is probably a "collective motion" which affects each molecule as a whole. Chapter 4. Results and Discussion 63 3500 -f! 3000 2500 2000 1500 -|i 1000 - v -J ! ' . jr • 0 % 2 5 % A 5 0 % • 7 5 % P D P C 1 1 1 1 1 I 280 285 290 295 300 305 310 Temperature (K) Figure 4.10: Dependence of the mean T2e rate on temperature, for the perdeuterated chain of P O P C - d 3 1 in binary mixtures with PDPC. The linear relation with temperature agrees with the predictions of Equations 2.10 and 2.11 for thermally-activated relaxation mechanisms. Results from least-squares linear fitting are included in Appendix C. Chapter 4. Results and Discussion 64 the important mechanisms as described in Section 2.2.2. In principle this could allow us to quantitatively compare membrane parameters (such as the curvature energy or area compressibility) as a function of PDPC content, but this was not possible for the reasons outlined in Section 3.3.4. Instead, to investigate general properties of T2e processes in P O P C - d 3 i / P D P C binary mixtures, a representative measurement was taken with higher SNR for one sample from the series (25% PDPC at 25° C). Even for this case only qual-itative conclusions can be drawn, but these are of great value in interpreting the T2e trends described above. Figure 4.11 shows the representative uT2e spectrum". The characteristic signature of the sin 2 9 cos2 9 term in 1/T2e is immediately evident, as the T2e values peak sharply at the shoulders (9 = 90°) and edges (9 = 0°) of the spectrum. This behaviour has been reported in all previous studies of angular dependence of T2e in MLVs. Attempts to fit the spectrum were limited to the ranges indicated on the figure (as discussed in Section 3.3.4) and were strictly qualitative in nature. The "best-fit" line, generated from the three-termed 1/T 2 expression of Equation 2.13, is shown in Figure 4.11. To assess the tolerance of the fit parameters, the coefficients were varied by 10% (yielding acceptable solutions) and 50% (giving poor fits), as also shown1. The order-of-magnitude of the best-fit parameters is thus judged to be known with confidence, and their numerical values are probably estimated to within 20-30%. The values of the parameters are shown in Table 4.3.3. The results presented in Figures 4.9 and 4.10 indicated that the dominant T2e mech-anisms in this study were likely to be thermally-activated adiabatic modes; the fact that the ^-dependence of T2e is described by Equation 2.13 confirms this result. Information 1As discussed i n Sect ion 3.3.4, the f i t t ing terms were not or thogonal , so var ia t ions i n the coefficients cou ld pa r t i a l l y compensate each other. T o obta in the worst-case estimate o f uncer ta inty in the "best-fit" results, the signs of the 10% and 50% variat ions shown i n Table 4.3.3 were adjusted so tha t the changes wou ld offset. Chapter 4. Results and Discussion 65 -20 -10 0 10 20 30 k H z Exper imenta l T 2 spectrum Best solut ion, in range fitted 1 0 % change in fit coeff ic ients 5 0 % change in fit coeff ic ients Figure 4.11: Representative T2e spectrum, displaying orientation-dependence of T2e re-laxation mechanisms. The spectrum is dominated by the contributions from the plateau region, and displays characteristic sin2 9 cos2 9 dependence, featuring peaks at 9 = 90° (near ± 1 3 kHz) and 9 = 0° (near ± 2 6 k H z ) . The central peaks are due to the methyl group, and are ignored. The spectrum has been fitted to Equation 2.13, with coefficients as shown in Table 4.3.3. The best-fit line is shown, as well as the lines generated by de-liberate variation of the fit parameters, intended to assess the uncertainty on the best-fit values. The spectrum shown is derived from high-SNR measurements of a 25% P D P C sample at 25° C, as described in Section 3.3.4, and is intended to be representative of P O P C - d 3 i / P D P C binary mixtures. Chapter 4. Results and Discussion 66 Table 4.1: Fit parameters for T2e orientation-dependence, from modelling the T2e spec-trum using Equation 2.13. The 10% and 50% changes impose variations on the best-fit results, in order to assess the tolerance of the coefficients. As described in the text, the signs of these changes were chosen such that they offset and give the worst-case estimate of uncertainty. All coefficients are in units of s - 1 . A B C Best-fit 1800 21000 1000 10% changes 1600 2000 23000 19000 900 1100 50% changes 900 2700 31500 10500 500 1500 regarding the nature of these modes can be derived from the relative magnitudes of the fit coefficients, in particular the sin2 9cos2 9 and [P2(cos#)]2 terms (i.e. the B and C co-efficients). For comparison purposes B must be divided by 4 (since the maximum value obtainable by sin2 9cos2 9 is one-fourth that of [P2(cos#)]2), but clearly it is the larger contribution to the best-fit solution. Further evidence that the sin2 9 cos2 9 term domi-nates the orientation-dependence of T2e comes from the interdependence of B and C in the fitting process. A two-term function with C = 0 was found to fit the data adequately; as C was increased from zero to the maximum value which allowed a reasonable fit (with A and B adjusted freely), B varied by only 20% of its best-fit value. With B — 0 no solution could be found. We thus conclude that sin2 9 cos2 9 is the critical term in the angular dependence of T 2 9 e for P O P C - d 3 i / P D P C mixtures in MLV form. As discussed in Section 2.2.2, this behaviour is predicted for T2e mechanisms arising due to fluctuations in the orientation of the membrane surface normal. Specific interpretations of this result are discussed below, in Section 4.4.2. It must be emphasized, though, that many approximations have been made in analysis of the T2e spectra, and that this should be considered to be a possible conclusion rather than a definitive one. It agrees, however, with more in-depth Chapter 4. Results and Discussion 67 studies of the ^-dependence of T2e, which have found that the sin2 9 cos2 9 term is clearly dominant in M L V samples [63, 68]. 4.4 S y n t h e s i s o f M o m e n t a n d R e l a x a t i o n R e s u l t s 4.4.1 Fas t M o t i o n s Increased values of average T\z were interpreted to mean that correlation times decreased for very fast motions as P D P C was added to the membrane. While the proton results give no indication as to the site of this change, the deuterium measurements show that it certainly does occur in the 16:0-d3i chains of the P O P C molecules. (Note that this is not an exclusive result - motions could be faster in other regions, as well.) This could be taken to indicate that greater PDPC content decreases the "viscosity" of the membrane, though the meaning of that term on the molecular scale is somewhat vague. In the interest of producing a self-consistent model, we will consider how this result matches the conclusions drawn from the moment and order parameter studies, which also provide information on fast motions in the system. (A deliberate blurring of the distinction between "fast" and "very fast" regimes has occurred here - the important point is that both sets of measurements have been interpreted largely in terms of chain-bending transitions). In Section 4.2.5 an interpretation is presented in which increasing polyunsaturation frees up space in the middle of the bilayer. Chains like DHA are proposed to spend slightly more time doubled back on themselves, explaining the observed decreases in orientational order of other chains (such as the perdeuterated 16:0 of POPC-d3i). This was shown to be consistent with the measured values of M2r for protons and deuterons; we now present a qualitative argument that such a model can account for the observed Tiz increases as well. Chapter 4. Results and Discussion 68 Acyl chain conformational changes encounter energy barriers due to rotation about the C-C bond (e.g. from trans to gauche) and from steric interactions with neighbouring chains. If, as suggested above, the central region of the bilayer becomes less crowded due to doubling back of the DHA chains, then the steric contribution to the barrier is reduced and the low-lying states become more accessible. At a given temperature, these conformations are thus sampled more freely by random motions, leading to faster loss of spatial correlation and hence smaller values of r c . While admittedly crude, this argument demonstrates that the T\z and order parameter measurements - i.e. all results pertaining to "fast" classes of motions - can be explained within the same molecular model. A more quantitative or definitive interpretation is not possible given the current results, however; further work would be required to test this hypothesis and to develop its details. 4.4.2 Slow Motions The T2e results give information on a very different timescale, indicating that spin-spin relaxation in POPC-d3i /PDPC samples is dominated by collective modes which slowly modulate the orientation of the membrane surface normal. We suggest that the motions in question are undulations of the membrane. While other mechanisms, such as diffusion on a curved surface ([61], later argued against in [63]) or "order-director fluctuations" [78], could also give rise to the observed ^-dependence of T2e, surface undulations seem the most likely choice. As described in Section 4.3.3, the linear dependence of 1/T2e with temperature matches the prediction of Equation 2.10 for undulational modes. Undulations also resolve the apparent paradox wherein 2 H Tf values are almost halved in going from 0% P D P C to 75% PDPC, while M2R^D is virtually constant: 1/T2e varies linearly with ((SO)2) (Equation 2.12), while Chapter 4. Results and Discussion 69 M2R,D is reduced by a factor (P2cos<5#)2 & (l — ^y^) • Since a rough estimate (using values from [66]) gives ((59)2) m 0.02, then a two-fold decrease in T2e due solely to membrane undulations reduces the M2r^D by only 6%. In addition, the link between acyl chain polyunsaturation and membrane undulations has been demonstrated elsewhere by independent means. In mechanical measurements of membrane area expansion as a function of applied tension, Evans & Rawicz found the curvature energy KC of di-arachidonoyl-phosphatidylcholine (20:4/20:4-PC) to be roughly half that of l-stearoyl-2-oleoyl-phosphatidylcholine (18:0/18:1-PC) [79]. That is, polyun-saturation of both chains led to a two-fold decrease in the membrane curvature energy (which from Equation 2.10 would cause the mean-squared amplitude of surface undu-lations to double). Furthermore, KC is predicted to scale linearly with the area com-pressibility modulus Ka [79, 67]. Koenig et al. measured Ka by combining X-ray and NMR techniques (see Section 1.3), and again found an almost two-fold decrease moving from mono-unsaturated SOPC-d35 (18:0-d35/18:l-PC) to polyunsaturated SDPC-d35 (18:0-d35/22:6-PC) [44]. (Note that higher values of Ka correspond to less compressible membranes, just as higher values of KC indicate less flexibility.) It thus seems reasonable to attribute the striking decrease in T2e values to the effect of increasing P D P C content on membrane surface undulations. If this were the sole cause of the observed changes, then the curvature energy KC would diminish by almost 50% in going from 0% P D P C to 75% PDPC. However, since some of the alternate mechanisms discussed earlier (but judged not to be dominant) likely did contribute to some extent, the change in KC is probably somewhat smaller. Finally, it should be acknowledged that T2e measurements on membrane systems are frequently difficult to reproduce, probably due to effects of preparation and thermal history on adiabatic processes [69]. Chapter 4. Results and Discussion 70 4.4.3 Relation Between Fast and Slow Motions Clearly it is desirable to relate the hypothesized decrease in KC to the changes in fast chain motions proposed above. However, the task of understanding meso- or macro-scopic membrane properties in molecular terms is exceedingly difficult, and comprises a field of research unto itself. Evans concludes that chain-packing irregularities and chain flexibility act to diminish membrane rigidity [67, 79], but it seems unlikely that the subtle order differences measured in this study could be the cause of such a striking increase in undulation amplitudes. It is possible that the molecular basis for the proposed large changes in K C lies in a region where our experiments are not sensitive - the lipid-water interface is an obvious candidate. It is conceivable that changes in the headgroup environment could signif-icantly influence the bending rigidity, and other investigators have proposed effects of lipid polyunsaturation on this region [76, 42, 77]. The greater cross-sectional area of polyunsaturated lipids, as reported in the literature [44] and consistent with our results, would certainly lead to increases in headgroup spacing. 4.5 Suggestions for Further Work The results discussed above suggest a host of further experiments, which would serve to confirm and expand upon the conclusions drawn in this study. A few are quite obvious and need no explanation, such as field-dependence and T I Q studies to characterize the spectral densities of fast motions, or the x^e~cpm9 experiment [61] to map the correlation times of very slow motions. A few others will be discussed in slightly greater depth. The nearly two-fold decrease in membrane curvature energy is the most striking result obtained in this study, but the analysis which led to this conclusion included many uncertainties. The most direct confirmation would be an experiment of the sort performed Chapter 4. Results and Discussion 71 by Evans k, Rawicz [79]; indeed such work could lead to an in-depth research project, exploring the complementarity of T 2 experiments and micromechanical techniques for the study of membrane mechanical properties. Working within the NMR techniques applied above, a cleaner Tf spectrum could be obtained by improving the SNR and by using a specifically-deuterated lipid in place of POPC-d 3 i . This would allow more rigorous fitting of the ^-dependence (expressing the fitting function in orthogonal components), yielding quantitative results for the fit coefficients. It would be of great interest to measure the change in the B term as a function of PDPC content in the membrane - clearly we would expect B to increase proportionally to 1/Tf if undulations are indeed the cause of the faster relaxation. Finally, a F R A P (fluorescence recovery after photobleaching) experiment could provide an independent assessment of lateral diffusion rates in the membrane, which would aid in quantifying the effective correlation time T9 for undulations [66] as well as understanding the origin of the sin2 9 cos2 9 dependence. The proposed doubling-back motions of the DHA chains could be tested by a number of NMR approaches. (Recent work by Huster et al. has demonstrated the potential of 1H MAS-NOESY cross-relaxation experiments to yield specific information on the nature of acyl chain disorder, but preliminary experiments did not find evidence for the hypothesis [75].) High resolution/magic angle spinning 1 3 C - N M R is capable of resolving the chemical shifts of the unsaturated carbons on the DHA chain [80]. A site-specific T l z study with and without paramagnetic ions present in the solution should reveal whether the tail end of the D H A chain spends more time near the lipid-water interface. Along similar lines, if the synthetic work were possible one could 1 3C-label DHA's methyl terminal as well as the headgroup on a mixed lipid such as PDPC, then selectively excite one of them and watch for transfer of the magnetization. Of course, the most direct (and informative) approach would be to specifically deuterate sites on the DHA chain for study using 2 H - N M R , but the biochemical synthesis is extremely difficult. Chapter 4. Results and Discussion 72 It would also be very interesting to apply the protocol from this study to a number of related systems, using the P O P C - d 3 i / P D P C series as a reference. Also, D H A in the free fatty acid form has been found to influence function of several integral membrane proteins (see Section 1.2.3), but it is not known whether this effect is chemical or mechanical in nature. Similarly, cholesterol's interaction with polyunsaturates (or, more precisely, its lack thereof) is a subject of much speculation, and is thought to spur formation of lipid microdomains [48, 35, 47]. Each of these components could be added to a known POPC-d 3 i / P D P C binary mixture, and changes in the parameters discussed above could be interpreted within the existing models. Another potentially valuable spin-off experiment would be to replace P D P C with another polyunsaturated lipid (perhaps 16:0/18:3-PC), to test whether any of the effects reported here could contribute to nature's strong and specific preference for DHA in certain systems. Also (as mentioned in Section 1.4), an analogous series of experiments using P E lipids could yield novel insights into the role of headgroup composition in the properties of polyunsaturated lipids. Finally, the recent study by Cantor (discussed in Section 1.3.3) presents the tantalizing possibility of comparing our experimental results to a specifically-designed theoretical model. Cantor's technique is readily amenable to predicting "lateral pressure profiles" for binary mixtures of lipids (indeed he presents results for several mixtures in his recent paper [49]), which are natural candidates for comparison with order parameter profiles. It is a promising sign that Cantor's predictions for the effects of polyunsaturation are qualitatively consistent with the S(n) results reported above. 4.6 Relation to Biological Motivation for Study The results and analysis described above shed considerable light on proposed bases for the functional role of DHA in certain membranes. The notion that polyunsaturated Chapter 4. Results and Discussion 73 lipid molecules occupy a wedge-shaped volume in the membrane, and influence protein conformations by exerting lateral pressure through the central portion of the bilayer, has been disproven. Indeed the reverse has been demonstrated to be true, as other membrane species were observed to have slightly greater conformational freedom as the proportion of polyunsaturated lipid was increased. The subtlety of the effect, however, was equally surprising, as average order parameters stayed nearly constant across a huge range of membrane compositions. This could be a result of our deliberate mimicry of the natural lipid composition, analogous to the easy integration of integral membrane proteins into native-like bilayers due to hydrophobic matching [67]. An alternate interpretation is that polyunsaturate-enriched microdomains are formed, isolating the other lipids from DHA's influence on a local scale. Such dynamic lipid clustering has been proposed to underlie polyunsaturated lipids' observed resistance to cholesterol condensation, and is the subject of on-going studies in several prominent research groups [48, 45, 47, 81]. Large-scale surface undulations are unlikely to occur in biological membranes (due to the scaffolding effect of the cytoskeleton), but local fluctuations in bilayer curvature could potentially couple to conformational changes of membrane proteins. Such fluctu-ations are linked with small density differences between membrane monolayers [79], and the associated changes in lipid packing may transiently favour certain protein transitions or states. Likewise, if the observed change in curvature energy is attributed to increased lateral compressibility of the membrane (since K C OC Ka, as discussed in Section 4.4.2), then the beneficial role of polyunsaturation may relate to accommodation of changes in protein cross-sectional area [44]. On the cellular scale, the rise in membrane flexibil-ity may facilitate vesicular fusion and budding events, of particular importance in the synaptic terminals where DHA is thought to be concentrated. The problem of nature's striking specificity for DHA remains, however. There is no Chapter 4. Results and Discussion 7 4 indication of any property imbued by D H A which could not also be achieved by a dif-ferent polyunsaturated species. The largest effect observed i n this study - the marked increase in membrane flexibility as P D P C was added - is thought to be common to al l polyunsaturated membranes. (Indeed, this belief was cited in reaching the conclusion, which could be argued to be a poor approach to finding a DHA-specific property. Never-theless, D H A is a polyunsaturate and thus must be attributed the known or hypothesized properties of that family.) To conclude on a speculative note, perhaps the specific requirement of certain mem-branes for D H A is due to a combination of mechanical and chemical roles. Various effects on membrane physical properties have been linked to D H A , but in no instance have these been markedly different for other polyunsaturates. Functional influences of D H A v ia binding interactions (particularly of the free fatty acid form) have also been reported (see Section 1.2.3); these would be expected to involve greater specificity. It is possible that mechanical properties provide broad selectivity for polyunsaturated lipids, while specific chemical interactions favour lipids bearing D H A chains in particular. Such an explanation is even consistent with Brown's lipid-substitution experiments (the most direct evidence against a chemical role for D H A ) : the stabilization of metarhodopsin-II selects for physical properties, while an as-yet-undetermined chemical role narrows the choice to D H A . Similar dual roles can certainly be imagined in the complex environment of the synaptic membrane. Whi l e this is undeniably a shot in the dark, one general lesson which emerged in the preliminary stages of this study is that nature tends to use al l available degrees of freedom. If a reasonable mechanism can be imagined but has not been observed, it seems often to be the case that we simply haven't found it yet. Both mechanical and chemical roles have been proposed for D H A - it 's not inconceivable that nature employs them both. Chapter 5 Conclusion The experiments presented here provide an intriguing picture of the effects of DHA on the molecular and mechanical properties of membranes. Interpretation of the results has generated a model which is internally consistent, but cannot be claimed to be definitive. The questions we hoped to address at the outset of this study were outlined in Section 1.4. They are reiterated below, with discussions of what we have learned: 1. What mechanical effects do polyunsaturated lipids (and particularly those bearing DHA chains) have on other components of the bilayer? This study presents the first direct evidence that polyunsaturation leads to inter-molecular effects between phospholipids, and generated two unexpected insights. First, the addition of small or large amounts of P D P C were found to have little net effect on the average orientational order of the membrane, as determined from both proton and deuterium M 2 r values. This was interpreted to mean that pure P D P C does not differ greatly from POPC in these parameters, so its introduction does not perturb the membrane greatly. Second, the order parameter profiles showed that the polyunsaturated lipid does not exert lateral pressure on its neighbours in the central region in the bilayer (i.e. the P D P C molecule does not assume a wedge shape). Instead, the D H A chains are proposed to spend a statistically greater fraction of their time doubled back toward the lipid-water interface. 75 Chapter 5. Conclusion 76 2. Does a bilayer with acyl chain composition closer to that found in neural membranes have special properties? Is there a concentration-dependent "magic mixture" effect? In almost every case, the variation of results with P D P C content was linear to within experimental uncertainty. (The exception was T2e times, for which nearly half of the observed change took place in going from 0% to 25% PDPC.) For the proton results alone, this led to ambiguity of interpretation as the results could be attributed either to a concentration-weighted increase in PDPC's contribution or to its influence on the other species. Reporting only from the perdeuterated chain of POPC, however, changes in deuterium results were unequivocally due to inter-species effects. No evidence was found for exceptional properties associated with a particular mem-brane composition, but such a "magic mixture", if it existed, could well involve different headgroups, other lipid classes such as sterols, etc. 3. Can new insights be gained into the role of DHA in membranes by probing unex-plored timescales (and hence distance scales)? Measurement of the average T2qe of POPC-d3i 's palmitoyl chain revealed a powerful effect of P D P C content on adia-batic collective modes of the systems. These are suggested to be due primarily to increases in the amplitude of membrane surface undulations, indicating a diminish-ment of up to 50% in the curvature energy, K C , of the membrane. This conclusion is in keeping with prior studies of polyunsaturated membranes, though such an effect has not been reported in a binary lipid mixture. The greater question, of course, is what special property of D H A underlies its re-markable prevalence in certain membrane systems. How can we understand its observed effects on visual and mental function? The above conclusions comment usefully on sev-eral leading hypotheses for DHA's role, and bring attention to the hitherto unconsidered Chapter 5. Conclusion 77 alternative that membrane flexibility be an important factor. It is clear, though, that much further work will be required before the secrets of this enigmatic lipid are revealed. Faced with a dearth of truly unique properties which might explain the striking speci-ficity of nature's preference for DHA, one only wonders whether we're moving in the right direction. Bibliography [1] Myer Bloom, Frank Linseisen, James Lloyd-Smith, and Michael Crawford. Insights from NMR on the functional role of polyunsaturated lipids in the brain. In: Bruno Maraviglia, editor, Magnetic Resonance and Brain Function, Fermi International School of Physics, Varenna, Italy, 1998. Italian Physical Society. [2] O.G. Mouritsen. 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Nuclear magnetic resonance line shapes in lyotropic liquid crystals and related systems. Journal of Chemical Physics, 66:3012-3020, 1977. [56] Myer Bloom, Elliott E . Burnell, Alexander L. MacKay, Christine P. Nichol, Marko I. Valic, and Gerald Weeks. Fatty acyl chain order in lecithin model mem-branes determined from proton magnetic resonance. Biochemistry, 17:5750-5762, 1978. [57] A. L. MacKay. A proton NMR moment study of the gel and liquid-crystalline phases of dipalmitoyl phosphatidylcholine. Biophysical Journal, 35:301-313, 1981. [58] James H. Davis. The description of membrane lipid conformation, order and dy-namics by 2 H - N M R . Biochimica et Biophysica Acta, 737:117-171, 1983. [59] M . F. Brown, A. A. Ribeiro, and G. D. Williams. New view of lipid bilayer dynamics from 2 H and 1 3 C - N M R relaxation time measurements. Proceedings of the National Academy of Sciences of the United States of America, 80:4325-4329, 1983. [60] K. P. Pauls, A. L. MacKay, O. Soederman, Myer Bloom, A. K. Tanjea, and R. S. Hodges. Dynamic properties of the backbone of an integral membrane polypeptide measured by 2 H-NMR. European Biophysical Journal, 12:1-11, 1985. Bibliography 86 [61] Myer Bloom and Edward Sternin. Transverse nuclear spin relaxation in phospho-lipid bilayer membranes. Biochemistry, 26:2101-2105, 1987. [62] Clare Morrison and Myer Bloom. Orientation dependence of 2 H nuclear magnetic resonance spin-lattice relaxation in phospholipid and phospholipidxholesterol sys-tems. Journal of Chemical Physics, 101:749-763, 1994. [63] Myer Bloom, Clare Morrison, Edward Sternin, and Jenifer L. Thewalt. Spin echoes and the dynamic properties of membranes. In: D. M . S. Bagguley, editor, Pulsed Magnetic Resonance: NMR, ESR and Optics, pages 274-316. Clarendon Press, Oxford, 1992. [64] A .A . Nevzorov and M.F. Brown. 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Relaxation spectra in model membranes by deuterium nuclear magnetic resonance. Journal of Magnetic Resonance, 93:279-290, 1991. [75] Daniel Huster and Klaus Gawrisch. NOESY crosspeaks between lipid headgroups and hydrocarbon chains - spin diffusion or molecular disorder? Experimental NMR Conference, Abstract 116, 1999. [76] William Ehringer, Daniel Belcher, Stephen R. Wassail, and William Stillwell. A comparison of the effects of linolenic (18:3n-3) and docosahexaenoic (22:6n-3) acids on phospholipid bilayers. Chemistry and Physics of Lipids, 54:79-88, 1990. Bibliography 88 [77] Daniel Huster, Albert J. Jin, Klaus Arnold, and Klaus Gawrisch. Water perme-ability of polyunsaturated lipid membranes measured by 1 7 0 NMR. Biophysical Journal, 73:855-864, 1997. [78] J. Stohrer, G. Groebner, D. Reimer, K. Weisz, C. Mayer, and G. Kothe. Collective lipid motions in bilayer membranes studied by transverse deuteron spin relaxation. Journal of Chemical Physics, 95:672-678, 1991. [79] E . 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North-Holland, 1988. [86] R. B. Gennis. Biomembranes. Springer-Verlag, New York, 1989. Bibliography 89 [87] Myer Bloom and J. Thewalt. Spectroscopic determination of lipid dynamics in membranes. Chemistry and Physics of Lipids, 73:27-38, 1994. [88] Myer Bloom and Jenifer L. Thewalt. Time and distance scales of membrane domain organization. Mol Membr Biol, 12(1):9-13, 1995. [89] E. Sternin, Myer Bloom, and A. L. MacKay. De-pake-ing of NMR spectra. Journal of Magnetic Resonance, 55:274-282, 1983. [90] Frank M . Linseisen, Jenifer L. Thewalt, Myer Bloom, and Thomas M . Bayerl. 2 H -NMR and DSC study of SEPC-cholesterol mixtures. Chemistry and Physics of Lipids, 65:141-149, 1993. [91] Michel Lafleur, Pieter R. Cullis, and Myer Bloom. Modulation of the orientational order parameter profile of the lipid acyl chain in the 1-alpha phase. European Biophysical Journal, 19:55-62, 1990. [92] A. Seelig and J. Seelig. The dynamic structure of fatty acyl chains in a phospholipid bilayer measured by deuterium magnetic resonance. Biochemistry, 13:4839-45, 1974. [93] H. Schindler and J. Seelig. Deuterium order parameters in relation to thermody-namic properties of a phospholipid bilayer. a statistical mechanical interpretation. Biochemistry, 14:2283-7, 1975. [94] John Hjort Ipsen, Ole G. Mouritsen, and Myer Bloom. Relationships between lipid membrane area, hydrophobic thickness, and acyl-chain orientational order. Biophysical Journal, 57:405-412, 1990. [95] M . B. Sankaram and T. E. Thompson. Deuterium magnetic resonance study of Bibliography 90 phase equilibria and membrane thickness in binary phospholipid mixed bilaryers. Biochemistry, 31:8258-8268, 1992. [96] Dalian Lu, Irene Vavasour, and Michael R. Morrow. Smoothed acyl chain ori-entational order parameter profiles in dimyristoyl-phosphatidylcholine/distearoyl-phosphatidylcholine mixtures: A 2 H - N M R study. Biophysical Journal, 68:574-583, 1995. [97] Ole G. Mouritsen and Myer Bloom. Mattress model of lipid-protein interactions in membranes. Biophysical Journal, 46:141-153, 1984. [98] Ole G. Mouritsen and Myer Bloom. Models of lipid-protein interactions in mem-branes. Annual Review of Biophysics and Biomolecular Structure, 22:145-171, 1993. [99] Myer Bloom and Ole G. Mouritsen. The evolution of membranes. In: R. Lipowsky and Erich Sackmann, editors, Handbook of Biological Physics, pages 65-95. Elsevier Science B. V. , 1995. [100] J. Ulmius, H. Wennerstrom, G. Lindblom, and G. Arvidson. Proton NMR band-shape studies of lamellar liquid crystals and gel phases containing lecithins and cholesterol. Biochim Biophys Acta, 389:197-202, 1975. [101] Jeffrey Forbes, John Bowers, X i Shan, Liam Moran, and Eric Oldfield. Some new developments in solid-state nuclear magnetic resonance spectroscopic studies of lipids and biological membranes, including the effects of cholesterol in model and natural systems. Journal of the Chemical Society, Faraday Transactions 1, 84:3821-3849, 1988. Bibliography [102] J . H . Davis, M . Auger, and R. S. Hodges. High resolution X H nuclear magnet resonance of a transmembrane peptide. Biophys J , 69:1917-32, 1995. Appendix A Theory: Information on F lu id Membranes from N M R Spectra (Appendix A has been contributed by Dr. Myer Bloom, and is an excerpt from an earlier paper [1].) A . l N M R Background and Goals We shall assume that the reader has a good background understanding of basic NMR. Many excellent introductory books [52, 82] and articles on NMR are available, including some in which broadline NMR of special importance in the study of biological membranes is emphasized [83, 84, 85]. Our intent is simply to summarize concisely in this section the nature of the information obtainable from NMR [67] on the physical properties of biological membranes. A .2 Membrane Fluidity and Correlation Times There is convincing evidence from NMR [83, 84, 85, 67] and a myriad of other physical measurements (see [86] for a large number of references) that biological membranes are invariably fluid under physiological conditions. At the macroscopic level, fluidity in this context implies that membranes do not support shear restoring forces. Model membranes consisting of a single type of lipid (e.g. saturated lipids such as DPPC and mono-unsaturated ones such as POPC) have an apparent viscosity of about 1 poise, a typical value for fairly thick oil. Their lipid 92 Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 93 molecules have been shown (using standard NMR methods) to diffuse parallel to the membrane surface with an effective diffusion constant D of about 4 x 1 0 - 1 2 r a 2 s - 1 . At the molecular level, lipids undergo several types of motion having a hierarchy of correlation times [83, 84, 85, 67, 86, 62, 66, 78]. We list below typical correlation times for various motions studied for representative model membranes. NMR has played an important role in the determination of the correlation times for the motions listed below via standard relaxation time measurements (Ti, T2, Tip, etc.). Some of these motions may be modified in biological membranes which often consist of many types of lipids, as well as up to about 50% protein (by weight). In addition, large quantities of sterols such as cholesterol [67] are found in the plasma membranes of all eukaryotic cells. Although biological membranes can be complex aggregates of lipids, sterols and proteins (see Figure 1.1), their lipid bilayer cores [67] are invariably fluid and are characterized partially by the following motions and correlation times: 1. The fatty acyl chains and polar head groups of the lipid molecules undergo rapid conformational changes, often referred to as "trans-gauche isomerization"1. Typical correlation times for conformational changes fall in the range 10 - 1 0 to 10 _ 9s. 2. The lipid molecules rotate about the local membrane surface normal n with corre-lation times in the range 10~9 to I O - 8 s. Think about a cloud of molecular confor-mations undergoing rotational diffusion about n. 3. The membrane surface exhibits highly damped undulations with a spectrum of wavelengths and associated correlation times ranging from microseconds to seconds for vesicles as large as 10 pm [67, 78]. The lower limit is set by the membrane thickness and the upper limit by the vesicle size. 1 T h e s e conformations refer to rotations about indiv idual C-C bonds. T h e y should not be confused wi th trans or cis double bonds Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 94 A.3 Time and Distance Scales Associated with N M R Spectra in Membranes The recording and interpretation of a spectrum of any type implicitly involves a spec-troscopic time scale [87, 88]. For membranes, there is an associated length scale which must be kept in mind. Suppose that the spectral lines associated with different molecular states extend over a range of angular frequencies Au> and that the rate at which the system undergoes transitions among all these states corresponds to a correlation time r c . The spread of frequencies allows us to define a spectroscopic time scale T3 « 1/Au. For long correlation times (r c 3> T S ) , the spectrum is an appropriately weighted superposition of spectral lines associated with the individual states and has a width of order Au. For short correlation times ( T c <C T S ) , the spectrum is a suitably weighted "average spectrum" of all the accessible states. This narrowing effect of the motion is called "motional averaging" or "motional narrowing" [52, 82]. Deuterium ( 2 H-)NMR of acyl chains on lipid molecules in fluid membranes is charac-terized by a coupling constant UJQ « 2TT X 125 kHz, giving r s « 10 _ 6s. The spectrum is motionally narrowed due to conformational and rotational motion of the lipid molecules since r c <C TS for these motions (see section A.2). As discussed below, the quadrupolar splitting of a given deuteron is decreased by a factor \ S C D \ called an "orientational order parameter" for that C-D bond. \ S C D \ c a n take on values in the range 0 < \ S C D \ < 0.5 for methylene groups in the fluid membrane lamellar phase. Analogous dipolar order pa-rameters, \SHH\ and \SCH\, may be defined from proton ( 1H)- and ( 1 3 C)-NMR spectra, respectively, and are associated with given H-H and C-H vectors in the molecule. NMR has provided major insights into the physical properties of fluid membranes via the mea-surement of such orientational order parameters, which are quite sensitive to interactions between lipids and molecular components of membranes (lipids, proteins and sterols). In Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 95 effect, NMR provides a quantitative measure of the anisotropy of membrane fluidity as a function of position on the acyl chain. We have tried to illustrate the extremely inhomogeneous nature of biological mem-branes in Figure 1.1. The question arises as to whether this inhomogeneity manifests itself in a complex NMR spectrum. Suppose, for example, that the difference between the quadrupolar splitting close to and far from a protein corresponds to Au; « 10 4 s _ 1 or, equivalently, TS « 10 - 4 s. Such a change in splitting of Au m 104s - 1/(27r) sa 1.6 kHz is very easy to measure. Nevertheless, superpositions of NMR spectra reflecting mem-brane inhomogeneity of the type shown in Figure 1.1 are normally not seen in biological membranes. The reason for this is that the molecules diffuse a distance corresponding to Ls « y/6Drs = ~ 500 A during the spectroscopic time scale required to distinguish different regions - farther if Atu is smaller. Effectively, NMR averages \SCD\ over a large number of lipid, protein and/or sterol interactions. So, contrary to the intuition of most spectroscopists, NMR does not really provide molecular information about membranes. It provides molecular information averaged over a large number of interacting molecules spread over mesoscopic distances [67]. A . 4 2 H - N M R of A c y l Chains on Lipid Molecules in F lu id Membranes Consider a deuteron on a methylene (CH2)fc group, k = 2, 3 . . . (N — 1), of acyl chain COO(CH 2 ) jv-2CH 3 . Its NMR spectrum in a fluid membrane, whose surface normal h makes an angle 9 with the external magnetic field, is a doublet (see Figure A. la) at angular frequencies u± symmetrically displaced from the Larmor frequency OJ0: where Pi(p) — u±=co0± u)QP2{p)SCD{k) (A.l) (Sp2 —1)/2, p = cos# and the orientational order parameter SCD (k) = Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 96 i—|—i—i—i—i—|—i—i—i—i—|—i i—|— i — i — i — i — | — i— i— i— i—|— i -50kHz 0 50 -50kHz 0 50 Frequency [kHz] Frequency [kHz] ' H - N M R I — | — i — i — i — i — | — i — i — i — i — | — i i— |—i—i—i— i—|— i— i— i— i— |—i -50kHz 0 50 -50kHz 0 50 Frequency [kHz] Frequency [kHz] Figure A . l : Simulated broadline 1 H - and 2 H - N M R spectra. The top row shows the spec-tra corresponding to samples being oriented with bilayer normal h parallel to the magnetic field: (a): Doublet for the case of 2 H-NMR; (b): Gaussian lineshape, representing the type of smooth featureless spectra associated with dipolar broadening in 1 H-NMR. The bottom row shows the results of calculating the powder spectra (random orientation) from the top row oriented spectra (c): Pake Doublet lineshape; (d): "Superlorentzian" lineshape. Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 97 (P2(pk)). The average in ScD(k) is taken over the distribution of values of pk = cosXk(t) implicit in the motional averaging discussed in sections A.2 and A.3 where Xk(t) is the in-stantaneous angle between the C-D bond direction and the symmetry axis h for motional averaging. The superposition of doublets for a uniform distribution of values of p in the range { —I < p < 1} (isotropic distribution of surface normals) corresponds to the well known Pake Doublet lineshape with splittings: \u+-w-\ =2uQ\SCD(k)\\P2(p)\ (A.2) as illustrated in Figure A.lc . It exhibits an integrable singularity at 9 = 90° or P2(p) = —0.5 corresponding to \5u\ — ojQ\Sco(k)\. Because of the singularity, it has proven to be relatively simple to De-Pake the Pake Doublet, or even a superposition of Pake Doublets [89], in a reliable manner, yielding a spectrum equivalent to that of an oriented sample. From such a complex spectrum (see Figure A.2b) one can use the method of Lafleur et al. [73] to extract the superposition of "smoothed values" of |<Sc£>|, shown in Figure A.2c. Various aspects of 2 H - N M R spectra of acyl chains in fluid phospholipid membranes (DPPC in this case) are illustrated in Figure A.2. The I S C D W I profile varies with temperature, head group (e.g. PC, PS, P E - see Figure 1.2) and cholesterol concentration (see Figure A.2d). Increasing cholesterol concentration or P E / P C ratio and decreasing temperature all lead to an increase in the \ScD(k)\ values along the entire acyl chain, leaving the shape of \ScD(k)\ basically unchanged. The reasons for these increases in \ S C D \ values can be stated in very simple physical and geometrical terms: • Cholesterol has a smooth ring structure so that lipid-cholesterol interactions favour the all- trans chain conformations. Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 98 Figure A.2: Typical 2 H - N M R spectra and smoothed order parameter profiles. Figures (a), (b) and (c) show results for chain perdeuterated DPPC (16:0-d3i/16:0-d3i-PC) at T = 50°C: (a): Superposition of Pake Doublets, produced by multi-lamellar vesicles; (b): Result of "De-Paking" the spectrum shown in (a); (c): smoothed order parameter profile, as calculated from Figure (b). (d): Smoothed order parameter profiles for a number of different mixtures of SEPC (16:0-d3i/18:l-PC) and cholesterol (cholesterol percentage given) at T = 50°C [90]. Note that the carbon number in (c) and (d) represents the ordering of the magnitudes of the quadrupolar splitting and not necessarily the chain position [73]. Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 99 • The P E head group has a smaller area than that of PC so that more crowding of lipids in the presence of P E also causes the acyl chains to stretch out. • Lower temperatures favour the lowest energy all- trans conformations. A remarkable feature of the \ScD(k)\ profiles is that, even though these three pertur-bations of orientational order involve different parts of the P O P C molecules, the shapes of the \ScD(k)\ profiles are virtually identical [91]. It is as though only a single parameter is required to specify changes of \ScD(k)\ f ° r the entire acyl chain in the case of a simple model membrane in the fluid phase. For convenience in what follows, we choose this parameter to be the chain averaged magnitude of Sco{k), i.e. S = {\SCD (k)\). A . 5 Orientational Order of A c y l Chains and Hydrophobic Thickness of F lu id Membranes Seelig and other researchers [84, 92, 93, 94] have shown that the hydrophobic bilayer thickness d is linearly related to the average order parameter as follows: d = dmax{aS + P) (A.3) This was derived by approximating the conformational states of the acyl chain by po-sitions on a diamond lattice, and identifying the hydrophobic thickness of a monolayer, d/2, as the average projection of the end-to-end vector of the acyl chain along the bilayer normal n. In eq. A.3, dmax « 2.5 Ax(iV — 1) is the maximum hydrophobic bilayer thick-ness corresponding to acyl chains in their all- trans conformation. In this fully extended conformation the C-D bonds are perpendicular to the axis of reorientation and give a value of \SCD\ — 0.5 for all chain positions. The value of Smax — 0.5 for an all-trans acyl chain rotating about its long axis leads to the following relation between a and B: a/2 + B = 1 (e.g. consistent with a = 1.0 and B = 0.5). Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 100 The use of NMR to determine membrane hydrophobic thickness via eq. A.3 should be regarded as a semi-empirical, secondary method and its application to mixtures of lipids requires further work [95, 96], both theoretical and experimental. A recent comparison with X-ray diffraction [44] has demonstrated the relative sensitivity, reliability and ease of use of the NMR method for pure lipid bilayer membranes, even for lipids consisting of one unsaturated and one saturated chain. The success of Seelig's method of determining membrane thickness has allowed NMR spectroscopists to explore mechanical properties of fluid membranes [94, 44, 74, 90]. Fur-thermore, it has generated a major advance in the quantitative description of lipid-protein interactions, namely that integral membrane proteins invariably have hydrophobic regions that are matched to the hydrophobic regions of the lipid bilayer membrane in which they are located [97, 98, 99, 2]. We believe that this hydrophobic matching comes about as a result of the optimization of the physical properties of membranes via evolution [99]. A schematic illustration of hydrophobic matching and how lipid-protein interactions couple proteins to mechanical aspects of membranes is given in Figure A.3. Figure A.3: Schematic illustration of hydrophobic matching. The dark parts of the lipids and the integral membrane proteins are hydrophilic, the lipid chains and the light regions of the proteins are hydrophobic. Figure (a) shows the case of a protein having a smaller hydrophobic thickness than the membrane, leading to local positive curvature of each lipid monolayer and possible mechanical strain; Figure (b) shows the opposite case. Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 101 A . 6 Dipolar Broadened X H - and 1 3 C - N M R in Membranes The motionally averaged dipolar interaction between a pair of spins, A and B, is governed by a dipolar pseudo-order parameter SAB = (P2 {tIAB)/'i'\B) [55, 56], where the vector joining A and B has the instantaneous length RAB and length R°AB in the all-trans conformation, such that rAs = RAB/R°AB- PAB is given by PAB = cos 8AB (in analogy with fik in section A.4) with 8AB being the polar angle between the dipole-dipole vector and the surface normal h. Because dipolar interactions only fall off with distance as P ~ 3 , many pairs of spins normally contribute to the spectrum. As a consequence, the NMR spectrum in fluid membranes is usually a broad featureless lump (see Figure A. lb and d) and the potential of 1 H - and 1 3 C - NMR for investigating basic physical properties of fluid membranes has not been explored to the same degree as 2 H-NMR. In view of the discussion in section A . 5 , however, one wonders whether measurements of dipolar second moments [52, 82] in membranes, which would provide quantitative measures of ^|<SAB|2)> might be useful in the same spirit as is the determination of S using 2 H-NMR. In common with 2 H - N M R , the dipolar-broadened spectrum scales with orientation as P2(^) (with p = cos 8 and 8 being the angle between the membrane surface normal n and the magnetic field). This scaling property has several profound consequences: 1. The spectrum fe(u>) of a sample being oriented at an angle 8 between its surface normal h and the external magnetic field, can easily be calculated from the spectrum fo(u) of a sample, oriented at 0°: 2. The powder spectrum fp(u>) can be easily calculated from the oriented spectrum (A.4) Appendix A. Theory: Information on Fluid Membranes from NMR Spectra 102 fo(w) (see Figure A . l for example spectra) as: f ' { w ) = l \PM\ d" (A-5) 3. Regardless of the detailed shape of the oriented spectrum fo(u) (with the excep-tion of spectra having sharp features, as for quadrupolar splittings in 2 H - N M R and anisotropic chemical shifts in 3 1 P - N M R and 1 3 C - N M R ) the powder spectrum, fp(u) has a "super-Lorentzian" shape /p(u>) = fsi(uj) w a + b\n.{u) [55, 100] (see Figure A.Id). The approximation fsi{u) m a + 6ln(u;) is only valid for umin -C u <C ujmax, where umin = 1/T2 and umax « yjM\. The powder spec-trum has a rapid cut-off near ui w u)max a n d a finite peak amplitude at to = 0. The "superlorentzian" fsi(u>) falls off more slowly in the wings than a Lorentzian, except for ui > u>max, but has a finite second moment because of the cut-off. 4. The isotropic, motionally averaged spectrum in small vesicles [56] is an unusual superposition of Lorentzians weighted by fo(u>), leading to subtleties in the inter-pretation of the line-width. 5. Magic angle spinning (MAS) is very effective in producing high resolution spectra for dipolar broadened spectra in membranes [101]. This has already given rise to interesting studies of peptide structure in membranes [102]. We anticipate that MAS studies will become increasingly important in the study of fluid membranes. Appendix B Preparatory NMR Experiments B . l X H-NMR - Buffer Contribution and Water Suppression Unless otherwise noted, all samples were prepared in buffers made with deuterium-depleted H 2 0 . The ^ - N M R signal thus contains a small contribution from the buffer molecules and an overwhelming contribution from the water, in addition to that of the lipid. To assess the effects of the buffer protons, free induction decays (FIDs) were mea-sured for pure deuterium-depleted water and for buffer solution, as well as for P O P C samples prepared (as above) in pure water and in buffer solution. The presence of buffer led to no observable differences in the FIDs (or the corresponding spectra); in particular, there was no fast-relaxing component (or broadened line) in the absence of lipid. This finding was verified by measuring the proton FID of a D 2 0 buffer solution, which showed only a low-amplitude, slow-relaxing component with T 2 roughly that of water (~ 0.5 s). The signal from the buffer protons is thus shown to be indistinguishable from that of the water for the purposes of our broadline experiments. The more difficult problem in the ^ - N M R experiments pertains to separating the relatively small lipid signal from the much larger signal due to the water and buffer. Since the dispersions were prepared in excess buffer solution, typically less than 20% of the protons in a sample were found on lipid molecules. Add to this that the T 2 of lipid is tens of microseconds while that of water is often hundreds of milliseconds, and extracting quantitative information from the lipid proton signal becomes a significant 103 Appendix B. Preparatory NMR Experiments 104 challenge. The unaltered FID resulting from a single 90° pulse is shown in Figure B . l . The first approach to this problem made use of the differing Ti z 's of the two proton pools (TiZ ]#2o ~ 3s; TiZiuPid « 400 ms), by adding a "pre-inversion" (180°) pulse before the excitation (90°) pulse. The pulses are spaced such that the excitation pulse coincides with the zero-crossing of the water signal, i.e. after a time ~ 2 s. As a result, only the lipid signal - which has almost fully relaxed by this time - is excited. This works very well for a single-scan experiment, cleanly eliminating the slow-relaxing component and isolating the solid-like lipid signal. However, if the water signal is not allowed to relax fully between scans, then the delay between the pre-inversion and excitation pulses must be reduced (in essence because the water signal has a "head start" towards its zero-crossing). Given the need to minimize the duration of the NMR protocols (due to concerns about sample integrity), the water could not be allowed to come to equilibrium (a ~ 15 s wait) before each scan. As a result, the pulse spacing required to fully eliminate the water signal was so short that much of the lipid signal would have been lost as well - clearly an unacceptable result. An alternative solution employed the Carr-Purcell-Meiboom-Gill (CPMG) pulse se-quence to refocus the slow-relaxing signal into a series of echoes following the FID. The echo maxima were fitted to a line (higher-order fits did not differ significantly for these data), which was extrapolated to t — 0 and subtracted from the FID. This technique isolates the lipid signal quickly and easily, but has two drawbacks. The first is that the FID is "scarred" by the C P M G pulses, and cannot be Fourier transformed to yield a meaningful spectrum; this is not a concern for our purposes, since as described in Section 2.1.2 the desired information can be derived from the proton FID. The second disadvan-tage is that since the full amplitude of the water signal is collected in this technique, only a small portion of the dynamic range of the receiver is devoted to the lipid signal. This could lead to inaccurate representation of the data and decreased signal-to-noise ratio, Appendix B. Preparatory NMR Experiments 105 due to coarser binning of the lipid signal by the analogue-to-digital converter. Motivated by the dynamic range consideration, a combination of the two approaches was used in the final proton protocol, since even a partially effective pre-inversion pulse allowed greater dynamic range for the lipid signal. The effectiveness of water suppression by the pre-inversion technique increased with inter-scan repetition time, such that gains in dynamic range were offset by increased experiment duration. A compromise was selected in which the relative contribution of lipid to the FID was doubled, but so was the data-collection time. This gain in signal-to-noise significantly exceeds the usual factor of y/t derived from signal-averaging with random noise. A sample FID obtained in this way is shown in Figure B . l . B .2 2 H - N M R - Spectrometer Validation The Bruker C X P spectrometer used for these experiments had not previously been used for 2 H - N M R measurements with this spectral width (we required ~ 100kHz), and some doubt existed regarding whether it would distort higher-frequency components of the spectra. To investigate this possibility, comparative measurements were performed on the C X P (at 30.7 MHz) and on a dedicated deuterium spectrometer (custom-built, operating at 46.7MHz; details in [71]) with established capabilities. Quadrupolar echo data were collected (with identical parameters, except for Larmor frequency) for the same DPPC-d62 sample above and below the main transition temperature, and the iirieshapes were compared. The normalized fluid phase spectra are shown in Figure B.2. The reference spectrum was found to have greater intensity towards its outer edge than that of the CXP, which can be attributed to the higher field strength of that spec-trometer. (The stronger field causes the vesicles to be more ellipsoidal in shape, aligning with their long axes parallel to the field. This results in a higher proportion of molecules Appendix B. Preparatory NMR Experiments 106 a 1 2 3 4 ms b 1 2 3 4 ms Figure B . l : Comparison of proton FIDs collected wi th and without water suppres-sion techniques. Figure (a) shows the F I D signal collected using a standard (90°)x pulse-and-collect sequence. The l ip id contribution is lost in the large water signal. F ig -ure (b) shows an F I D collected using the pulse sequence shown in Section 3.2.2, using a pre-inversion 180° pulse and C P M G train to suppress and quantify the water signal. The l ip id contribution is the small, fast-decaying component at the far left of the C P M G echo-train. Appendix B. Preparatory NMR Experiments 107 with their membrane normal oriented near 6 = 90°, so that the Pake doublet arising from each deuterated site is distorted to have greater amplitude near its peaks. When the dis-torted doublets for all sites on the perdeuterated chain are superposed, the plateau region dominates and leads to relatively higher amplitudes near the outer edge of a normalized spectrum.) This effect will lead to quantitative differences in spectral moments, order parameter profiles, and even relaxation times measured using the different instruments, but no particular field strength is inherently preferable. Rigorous comparisons can be made safely between measurements taken on a given spectrometer, as in this study. Figure B.2 also shows a slight difference in the width of the powder patterns, equiva-lent to a constant scaling factor. This was found to be corrected by a small adjustment in temperature, and prompted a new temperature calibration for the deuterium probe of the C X P before the main series of experiments was begun. Appendix B. Preparatory NMR Experiments 108 Figure B.2: Val idat ion of the spectrometer for 2 N M R work. Powder pattern spectra are shown for D P P C - d 6 2 in the fluid phase, as measured by the Bruker C X P spectrometer used for these studies and by a dedicated deuterium spectrometer (SFU) known to be reliable. The difference in peak amplitudes across the edges of the spectrum is explained in the text; the slight difference in width of the spectra was corrected by re-calibration of the C X P temperature control system. Appendix C Supplemental Results Table C . l : Fit parameters for proton residual second moments, M2R,H, as a function of P D P C content; results shown graphically in Figure 4.1. Units: s - 2 /mol% PDPC. Temperature Slope ± Uncertainty 10° C (+1.0 ± 1.2) x 105 25° C (+3.1 ± 1.4) x 105 37° C (+1.1 ± 1.6) x 105 Table C.2: Fit parameters for deuterium residual second moments, M ^ D , as a function of P D P C content; results shown graphically in Figure 4.2. Units: s _ 2 /mol% PDPC. Temperature Slope ± Uncertainty 10° C (-2.7 + 3.0) x 10e 25° C (+0.5 + 3.7) x 106 37° C (-0.1 + 5.2) x 10b Table C.3: Fit parameters for the average length of the perdeuterated chain, (L), as a function of P D P C content; results shown graphically in Figure 4.4. Units: A/mol% PDPC. . . Temperature Slope ± Uncertainty 10° C (-14.3 + 6.0) x 10~4 25° C (-7.6 + 5.8) x 10"4 37° C (-9.9 + 5.7) x 10"4 109 Appendix C. Supplemental Results 110 Table C.4: Fit parameters for the average proton Tu, as a function of P D P C content; results shown graphically in Figure 4.5. Units: ms/mol% PDPC. Temperature Slope ± Uncertainty 10° C +0.62 ± 0 . 1 2 25° C +0.95 ± 0 . 1 6 37° C +0.75 + 0.19 Table C.5: Fit parameters for the average deuterium T l z , as a function of P D P C content; results shown graphically in Figure 4.6. Temperature Slope ± Uncertainty 10° C (+3.9 ± 1.0) x 10"a 25° C (+8.3 + 1.3) x 10~2 37° C (+9.2 + 1.7) x 10~2 Table C.6: Fit parameters for the average deuterium T%e rate, as a function of tempera-ture; results shown graphically in Figure 4.10. Units: s - 1 K - 1 PDPC content Slope ± Uncertainty 0mol% +19.5 + 0.2 25 mol% +23.7 + 0.8 50mol% +24.6 + 0.2 75 mol% +25.4 + 1.3 Appendix C. Supplemental Results 111 Figure C . l : Smoothed order parameter profiles, S(n), for P O P C - d 3 i / P D P C mixtures, measured at 10° C . Note the qualitative similarity to the results from 25° C, shown in Figure 4.3 and discussed in Section 4.2.3. Appendix C. Supplemental Results 112 Figure C.2: Smoothed order parameter profiles, S(n), for P O P C - d 3 i / P D P C mixtures, measured at 37° C . Again , note the similarity to the results from 25° C, shown in Figure 4.3 and discussed in Section 4.2.3. 

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