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Integral protein and cholesterol in model membranes : a ²H NMR study Nezil, Frank Arthur 1992

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I N T E G R A L P R O T E I N A N D C H O L E S T E R O L I N M O D E L M E M B R A N E S : A N M R S T U D Y . Frank A r t h u r N e z i l B . Sc. (Physics) M c G i l l U n i v e r s i t y A THESIS 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 D O C T O R O F P H I L O S O P H Y i n 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 We accept this thesis as conforming to the required s tandard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A September 1991 (c) Frank A r t h u r N e z i l 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 The University of British Columbia Vancouver, Canada DE-6 (2/88) A b s t r a c t Deuter ium (^H) nuclear magnetic resonance ( N M R ) is used to study bilayer hydrophobic th i ck -ness and thickness expansivity i n La phase l i p i d bi layer membranes containing combinations of P O P C , cholesterol, and synthetic amphiphi l l i c polypeptides of différent hydrophobic lengths . Subsequent analysis relates N M R thickness expansiv i ty measurements to micromechanical measurements of the area expansivity, a ^ . M o d e l membrane area expansivity to date has sel-dom been considered i n typ i ca l analyses of N M R data . W e study a case, using a n d ^^P N M R , i n w h i c h considerations of (XA are central : spontaneous vesiculation i n model membranes composed of P O P C and P O P S , w i t h and wi thout cholesterol. Subsequent freeze-fracture elec-t ron microscopy confirms that membrane eruptions occur i n response to positive temperature changes and upon add i t i on of, for instance, mye l in basic protein ( M B P ) . Erupt ions are shown to occur more readi ly i n the presence of cholesterol. Est imat ions of OCA based upon N M R data i n these systems is found to be i n agreement w i t h micromechanical measurements of Q ^ . Orientation-dependent spin-spin (T2) re laxation i n some of the above systems potent ia l ly con-founds the interpretat ion of apparent thickness changes as being due to inclusion of integral polypeptides. A procedure is outl ined which allows empir i ca l correction of distorsion i n inhomo-geneously broadened N M R spectra due to orientation-dependent relaxation processes. T h i s is then appl ied to data of previous studies, thereby r u l i n g out T2 distorsion as an artifactuaJ "cause" of previously described changes i n bilayer hydrophobic thickness. The method is then used to suggest some directions for future study. Table of Contents A b s t r a c t i i List of Tables v i List of Figures ix Acknowledgement x 1 Introduct ion 1 1.1 Reader -Or ientat ion 1 1.2 M o d e l Membranes : General Considerations 2 1.2.1 Nuclear Magnet i c Resonance 12 1.2.2 M o t i v a t i o n : M e d i c a l Connections 13 1.3 S u m m a r y 21 2 EflFects of Integral Polypeptides on Bi layer Thickness 22 2.1 C h a p t e r Overview. ^ 22 2.2 Introduct ion 23 2.3 E x p e r i m e n t a l Procedures 24 2.3.1 Mater ia l s 24 2.3.2 Sample Preparat ion 25 2.3.3 Nuclear Magnet i c Resonance 25 2.4 Results 25 2.5 Discuss ion 29 'This chapter closely follows a previously published paper (Nezil and Bloom, 1992). 2.5.1 N M R T i m e and Distance Scales 29 2.5.2 Or ientat ional Order and Bi layer Thickness 29 2.5.3 U n u s u a l Features of the Results 31 2.5.4 Molec idar P a c k i n g Considerations 34 2.5.5 Membrane M o d e l For L ip id -Cho les tero l M i x t u r e s 35 2.6 Conc lud ing Remarks 38 3 Vesicle Erupt ions 40 3.1 Chapter Overview ^ 40 3.2 Introduct ion 41 3.2.1 Some Useful Theory 44 3.3 E x p e r i m e n t a l Procedures 45 3.3.1 Mater ia ls 45 3.3.2 Sample Prepara t i on 46 3.3.3 Freeze-Fracture E lec t ron Microscopy 47 3.3.4 Nuclear M a g n e t i c Resonance 47 3.3.5 Determinat ion of Isotropic Intensity 48 3.4 Results 48 3.4.1 N M R 48 3.4.2 Freeze-Fracture Microscopy 56 3.5 D I S C U S S I O N 60 3.6 C o n c l u d i n g Remarks 64 4 F u t u r e Direct ions : Relaxat ion-Spectra 66 4.1 Overview ^ 66 4.2 N u m e r i c a l Methods 67 ^This chapter closely follows, with slight modifications, a previously published paper (Nezil et ai, 1992). ^The early parts of this chapter are a slightly modified version of paxt of a previously published paper (Nezil et al, 1991). 4.3 Re laxat i on i n P e p t i d e - L i p i d Systems 70 4.3.1 E x a m p l e : Order ing Effect of P i e i n Bi layer B2 70 4.3.2 Relaxat ion-Corrected Spectra for B1/B2 ± Peptides 75 4.4 Orientat ion-Dependent Re laxat ion 77 4.4.1 Example :Headgroup-deuter iated D P P C 80 4.5 Future directions: a qual itat ive discussion 80 4.5.1 A d d i t i o n of Cholesterol to P O P C - d a i 82 4.5.2 A d d i t i o n of Peptides 85 4.6 Conc lus ion 87 5 Bib l iography 88 Appendices 105 A 2 H N M R in L i p i d Systems: Basics 105 A . l Nuclear Magnet i c Resonance 105 A . 1 . 1 Quadrupo lar H a m i l t o n i a n 105 A . 1 . 2 Order Parameters 110 A . 1 . 3 D i s t r ibut i on of Spectral Intensity: T h e Pake Doublet 113 A . 1.4 Density M a t r i x 116 A . 1.5 Pulse Sequences 117 B M o d e l M y e l i n M e m b r a n e s 125 B . l Proposed N M R studies i n M M M ' s 125 B . 1.1 2 H - N M R Exper iments 127 B . 2 M B P : Isolation and Separation into Charge Isomers 129 B.2.1 Isolation of Bas i c Prote ins from B r a i n W h i t e M a t t e r . 130 B.2.2 Fract ionat ion of M B P Into Charge Isomers 131 B . 3 A l k a l i n e G e l Electrophoresis 137 List of Tables 2.1 Bi layer Hydrophob i c Thickness 30 4.1 Re laxat ion of F i r s t M o m e n t 72 A . l C o m m u t a t i o n relations for orthogonal spin-1 basis operators 118 List of Figures 1.1 Phospholipid-cholesterol B i layer 3 1.2 POPC- .Cho les te ro l Phase D i a g r a m 7 1.3 M y e l i n Compos i t i on 15 1.4 M B P - i n d u c e d Isotropic L i n e 18 1.5 M B P and P O P C Headgroup Quadrupolar Spl i t t ings 19 2.1 N M R Spectra 26 2.2 Smoothed Order Profiles 27 2.3 Bi layer Thickness vs. Temperature 28 2.4 Difference Order Parameters : II 32 2.5 Membrane M o d e l for L ip id -Choles tero l M i x t u r e s 36 3.1 Red ig i t i zat ion of Isotropic Signal 49 3.2 Temperature-Dependent Isotropic Signals: a 50 3.3 Temperature-Dependent Isotropic Signals: b 51 3.4 Temperature-Dependent Isotropic Signals: c 52 3.5 Isotropic Frac t i on Versus Temperature. 1 53 3.6 Isotropic Frac t i on Versus Temperature: II 55 3.7 E lec t ron M i c r o g r a p h of P O P C : P O P S : C h o l e s t e r o l . A 57 3.8 E lec t ron M i c r o g r a p h of P O P C : P O P S : C h o l e s t e r o l . B 58 3.9 E le c t ron M i c r o g r a p h of P O P C : P O P S : C h o l e s t e r o l : C 59 3.10 E le c t ron M i c r o g r a p h of P O P C : P O P S : M B P 60 4.1 N M R Spectra Corrected For Relaxat ion Effects 70 4.2 Re laxat i on Exper iment : P i i n B j 71 4.3 Frequency-Dependent Re laxat i on Rate : P i 6 i n B2 74 4.4 N M R Spectra Corrected for Orientation-Dependent T2- Re laxat ion : B i layer B i 75 4.5 N M R Spectra Corrected for Orientation-Dependent T2- Re laxat ion : B i layer B2 76 4.6 T2 Re laxa t i on : AScD vs . A / ? ' 79 4.7 Tj.eff R e l a x a t i o n Spec t rum: D P P C - d 2 81 4.8 T2,ét R e l a x a t i o n Spectra : A d d i t i o n of Cholesterol to P O P C - d s i 1 83 4.9 r2,eff R e l a x a t i o n Spectra : A d d i t i o n of Cholesterol to P O P C - d a i II 84 4.10 r2,eff R e l a x a t i o n Spectra : B i ± P i e , P24 85 4.11 T2,éi R e l a x a t i o n Spectra : B j i P i e , P24 86 A . l E u l e r A n g l e Definitions 109 A . 2 Use of W i g n e r Ro ta t i on Matr i ces 114 A . 3 P a k e Doublet Spectrum W i t h Gauss ian Broadening 115 A . 4 Precession Diagrams 119 B . l Ca t i on -Exchange Chromatography. 135 B . 2 Absorbance at 280 n m vs. Frac t i on 136 B . 3 A l k a l i n e G e l Electrophoresis 139 Acknowledgement M y e r , f ami ly (a l l of you ) , alex, ed, m a r k , mike , r o b i n , n e i l , j u l i a , clare, cindy, Jennifer, theresas, andrew, m y r n a , dav id , peter, ne i l , k i m , michels , s y b i l , thomas, John I . , ken, don, wayne, m . moscarello, the physics softbaJl team (ed!), nserc, the ubc department of phys i c s , . . . and cynth most of a l l : thanks . Chapter 1 Introduction 1.1 R e a d e r - O r i e n t a t i o n . The fo l lowing thesis began w i t h a desire to obta in useful in format ion regarding certain biological processes impor tant to a part i cu lar medical disease and has involved, at various t imes, methods and ideas taken f rom biochemistry, neuroanatomy, classical and q u a n t u m physics. In fact, the goals defined early i n the process were eventually replaced - i n a predictable w a y - by more modest a n d realistic ones dictated by unresolved questions fundamental to the broader context of the work , and by obvious constraints upon t ime and resources. T h e mul t i -d i sc ip l inary nature of the project has enlisted the interests of an equally varied cohort of researchers. W h i l e there is no pretense here of neatly ty ing the various fields of s tudy together, probably an impossible task, an effort has been made to give appropriate representation i n this first chapter to several interests which have followed this work. In this regard the present chapter provides a g lobal overview of basic physical concepts pertinent to studies of l ip id -pro te in interactions using N M R , inc lud ing the mot ivat ion for the experimental routes eventually defined and pursued. T h i s chapter underlines the differences between funct ioning biological membranes and the enormously simpli f ied ones available to current exper imental methods. It is a selective review intended to be readable by both physicists and other researchers i n the biological sciences. For readers " fami l iar w i t h the field" no harm w i l l result f rom preceding direct ly to the last section of this chapter for a brief guide to the experimental work which forms the core of this thesis. T h e experimental chapters tie together three papers recently wri t ten on this work a n d , while referring at times to some didact ic mater ia l found i n the first A p p e n d i x they are, for the most p a r t , self-contained. A s such they may be profitably read independently. A p p e n d i x A contains a short review of some N M R essentials useful , f rom the physics viewpoint , to studies of membrane systems. Cer ta in work, in i t ia l ly central but u l t imate ly of peripheral importance , remains of sufficient interest as to have been inc luded i n the introductory discussion a n d , i n more de ta i l , i n A p p e n d i x B . 1.2 M o d e l M e m b r a n e s : General Considerations . Bio log i ca l membranes are structures present i n a l l cells, serving many functions there. M o s t impor tant of these is to isolate and contain the phys ica l constituents necessary to cell l i fe . C e l l membranes are barriers which are permeable to s m a l l uncharged molecules common to both the cell and the environment such as - especially - water , oxygen, and carbon dioxide. For most molecules the membrane is only selectively permeable or impermeable, thereby enabl ing controlled i o n exchange to create and mainta in essential concentration gradients. " R e a l " b io log-i ca l membranes, as dist inct f rom model systems, are complex structures composed of different classes of molecules which together permit a number of functions to be performed. These may be biochemical functions such as transforming energy f r o m the environment into a cell-useable form (i.e. metabol ism) or , as another example, t ransduc ing environmental s t imul i in to mean-ingful chemical signals. Other functions may be phys i ca l or s t ruc tura l i n nature, such as to provide a useful cellular shape or to endow the membrane barr ier w i t h the appropriate elasticity and flexibility i t needs to survive i n its environment. T h e p r i m a r y molecular components of the biological membrane are called lipids axid proteins. L i p i d molecules are amphiphiles, that i s , composed of two regions dist inct i n their solubil ity properties: a water-soluble (hydrophiUc) headgroup region, and a water-insoluble (hydrophobic) tail region. W i t h i n this generality, there are many different k inds of l ip ids - indeed , i n terms of present understanding, an anomalous number of such (for a l i s t see e.g. A l b e r t s et ai, 1983); the biological necessity for this incredible diversity is not clear, although funct ional ly relevant po lymorphism of l i p i d structures is probably an i m p o r t a n t consideration (Cul l i s et al., 1986). Th i s thesis w i l l be concerned w i t h only two classes of l i p i d s : phospholipids and sterols, which we take to be representative of the outer (plasma) membrane of eucaryotic cells. Shortened names for the phospholipids used i n this work are P O P C and P O P S . ^ These molecules, shown i n F igure 1.1 have a characteristic phosphate group as part of their structure. The hydrophobic region is composed of two fatty acyl chains: a 16 carbon pa lmit i c acid chain HEADGROUP glycerol backbone PC = phosphatidylcholine: (P03)"CHjCHjN*(CHj)j PS = phoaphatidylserine: (P0j)'CHjCH-NH3* COO" H2O ^HjC—( jH -CHj -0 X c = o )cH2 V;H2 EXAGGERATED HjC< HjC( * INTER-LIPID H,C<^  H,C >CH, >CH, H2C< HjC< H,C< HjC< H,C )CHj >CH, >CH, CH3 Lipid—water interface Bilayer Interior SPACING cholesterol palmitoyi chain H^c ^^ain PHOSPHOLIPID-CHOLESTEROL BILAYER REGION EXPANDED ABOVE lipid-WQter I interfoces u bilayer interior F i g u r e 1.1: Phospholipid-cholesterol Bi layer . T h i s cartoon depicts an expanded region of a phosphol ip id-cholesterol bilayer for the purpose of defining the l ip ids which wiU be used for experiments i n this thesis: P O P C , P O P S , and cholesterol. T h e spacing between the l ip ids i n the expanded picture has been exaggerated to a id v iewing. T h e a and /? carbons of the headgroup are respectively defined to be the carbons immediate ly to the right of the phosphate group. and an 18 carbon oleic ac id chain , which are bo th esterified to a (3 carbon) glycerol molecule, often cal led the glycerol backbone. 'These are technically referred to as l-palmitoyl-2-oleoyl-phosphatidylcholine and l-palinitoyl-2-oleoyl- phos-phatidylserine respectively. T h e most common equ i l ibr ium configuration for l ip ids i n biological membranes is as a fluid-bilayer. T h i s is arranged as two uni -molecu lar ly - th in "sheets" of l i p i d molecules w i t h their hydrophi l i c headgroups facing outward into the aqueous environment and the hydrophobic acy l chains, sandwiched between the headgroups, fac ing inwards towards each other. T h u s , the bi layer is a remarkably t h i n mater ia l composed of a b imolecular layer of o i l - ut ter ly insoluble i n water - whi ch has none the less been modified by evolut ionary processes not only to have a macroscopic water-solubi l i ty for 3-dimensional bi layer formations of appropriate topology, but also to be highly permeable to water. T h e bilayer is considered to be a two-dimensional " f l u i d " at relevant physiological temperatures. For this case , the i n d i v i d u a l l ip ids have relative conformational freedom of their acyl chains, rotat ional freedom of the entire molecule ( w i t h i n the viscous constraints imposed by the acy l chains and the l ip id -water interface), and thermal ly -driven l a t e r a l t ranslat ional freedom (diffusion) w i t h i n the surface formed by the bilayer. The bi layer also behaves as a true fluid i n the sense that i t has zero shear restoring force. For the type of l ip ids called d iacy l phospholipids (which w i l l concern us below) this fluid phase is called the L a pha,se. A s a condensed matter system there are considered to be at least three phases for aqueous solutions of P C phospholipids, the fluid L» phase and two sol id (gel) phases. T h e two lower temperature gel phases, called the Lpi and the Ppi ( " r ippled" ) phase, have latera l crystal l in i ty and h i g h conformational order of their acyl chains. T h e y differ by a periodic long-wavelength r ipple i n the bilayer surface of the Ppi phase. T h e acyl chains i n this phase are t i l ted at an angle to the bi layer normal . The transit ion between the Lpi and the P^/ phases is called either the pretransition or the subtransition (Lewis et al, 1987). T h e former name is used if , pr ior to the t rans i t ion , the acyl chains of the Lpi phase are i n their (metastable) configuration at a slight t i l t to the bilayer normal ; the lat ter name is used i f the Lpi phase is i n its completely ordered form w i t h its acyl chains -hexagonal ly p a c k e d - paral le l to the bi layer normal . The " t i l t e d " Lpi phase is metastable a n d , after several weeks below the pretransi t ion temperature, w i l l enter its ful ly ordered state. T h e higher temperature transi t ion between the gel Ppi phase and the fluid La phase, called the main transition, involves a mel t ing of both the acyl chains a n d the latera l crystal l inity . T h e fluid phase is the one common to functioning b i o l o^ca l systems and w i l l concern us exclusively i n this thesis. The carbon-carbon bonds i n the acyl chains of F igure 1.1 are, w i t h one exception, ro ta t i on -al ly unconstrained, result ing i n highly flexible acy l chains w i t h a large number of conformational degrees of freedom i n the phase. The exception is the so-called " c i s " double b o n d i n the oleic ac id that introduces a fixed bend i n that acy l chain at the idnth carbon. T h i s results i n a substant ia l ly lowered mel t ing point for oleic ac id (13.4 " C ) , as compared to the equivalent 18-carbon fatty acid having no cis double bonds (stearic ac id , 69.6 ° C ) , thereby al lowing such membranes to be i n the fluid phase at physiological temperatures. In effect, the presence of the fixed k i n k creates fluid-like disorder i n the chain packing. Thickness and fluidity are key concepts i n biological membranes. A sizeable proport ion of this thesis w i l l be spent upon considerations of these parameters. Thickness is impor tant i n order to increase the strength of the bi layer , to decrease ionic permeabil it ies , and to permit the accomodation of larger proteins - commensurate w i t h increased funct ional complexity - i n the bi layer , a point to which we w i l l re turn . F l u i d i t y is essential i n order to solvate proteins, to al low the bilayer to p lay a dynamic role i n trans-bilayer exchange processes {e.g. fatty ac id exchange for import or export ) , and to permit complex events such as endo/exocytosis to take place. T h e fluidity and thickness of a phosphol ip id bilayer are profoundly affected by inc lusion of l ip ids f r o m the second class mentioned - sterols - which are inc luded i n the model bilayers to be studied here. T h e most impor tant sterol to eucaryotes, and the one which w i l l be used i n studies here, is cholesterol. The structure of cholesterol is given i n Figure 1.1. It is a relat ively r ig id a m -phiphi l i c molecule w i t h a smal l headgroup (a single hydroxy l group) , and a part i cu lar ly uni form hydrophobic surface which tends to order neighboring acyl chains. It has been argued that the evolution o f cholesterol, which occurred w i t h the appearance of atmospheric oxygen approx-imate ly 1.5 X 10^ years ago, modified physical constraints upon p lasma (bilayer) membrane properties, so p lay ing a permissive role i n the appearance on earth of eucaryotic cells as we know them ( B l o o m and M o u r i t s e n , 1988). In any case i t is known that inclusion of physio-logical concentrations of cholesterol i n model membranes is associated w i t h several key events: e l iminat ion of the m a i n phase t rans i t ion i n phosphol ip id bilayers (V i s t and Davis , 1990; Need-h a m and Evans , 1988) and i n erythrocyte membranes ( M a r i v i g l i a et ai, 1987); increased acy l chain or ientational order (Lafleur and B l o o m , 1990) and therefore, by relations which w i l l be-come apparent i n Chapter 2, increased bilayer hydrophobic thickness (Seelig and Seelig, 1975; Ipsen et al, 1990; N e z i l and B l o o m , 1992); decreased permeabi l i ty and decreased area per l i p i d , and a greatly increased tension at w h i c h vesicle lysis occurs (i.e. increased bilayer cohesion) (Needham et al., 1988). It is remarkable that such events occur upon addit ion of cholesterol and yet the translat ional and rotat ional diffusion constants remain relatively unchanged by the ordering and thickness-increasing effects. T h i s is suggestive of another role for cholesterol i n ma inta in ing low microviscosity ( M a r a v i g l i a et ai, 1987; B l o o m and M o u r i t s e n , 1988), probably due to the relat ively smooth surface the cholesterol molecule presents to the acyl chains. T h u s , cholesterol strengthens the bi layer and at the same t ime increases or maintains its f luidity. T h e phase d iagram for a phosphol ipid/cholesterol mix ture was only recently determined and a theoret ical model now exists i n good agreement w i t h experiment (V i s t and Davis , 1990; Ipsen et al., 1987). Since then a s imi lar phase diagram has been determined for the P O P C : C h o l e s t e r o l system (Thewalt et a/.,1991) as shown i n Figure 1.2^. T h e impor tant point to note is the r i ch phase behavior : there are so-called solid-ordered (so), liquid-ordered (lo), and liquid-disordered (Id) phases as well as coexistence regions between gel state l ip ids and f luid state l ipids having different fixed concentrations of cholesterol. A l l the experiments w h i c h w i l l be described in this thesis for bilayers w i t h cholesterol were performed w i t h samples at temperatures characteristic of the lo phase region. There are a l i m i t e d number of three dimensional topologies for stable l i p i d structures w i t h i n an aqueous environment. These a l l satisfy the need to exclude the hydrophobic part of the l ip ids ^This figure was kindly provided by J. Thewalt. s o Id lo so + Lo lAl - 1 5 1 1 1 1 1 1 1 O.OO 0.10 0 . 2 0 0 . 3 0 ^ C H O L E S T E R O L Figure 1.2: P O P C : C h o l e s t e r o l Phase D i a g r a m . T h e phase diagram for P O P C : c h o l e s t e r o l mixtures is shown here as obtained using N M R difference spectroscopy. D i s t inc t phases are ev-ident : l iquid-disordered (Id), l iquid-ordered (lo), solid-ordered (so), and a coexistence region (so + lo). Exper iments using cholesterol-containing membranes i n this thesis were restricted to the 3 0 % cholesterol region at temperatures of > 5 ° C , i.e. the lo region. (F igure courtesy of J . Thewal t , unpublished data. ) f rom contact w i t h water. T h i s may be achieved i n several ways: i n a micelle configuration wherein the acyl chains face inward to form a sol id sphere w i t h the headgroups interfacing water at the surface of the sphere (therefore, these tend to be smal l structures) ; i n one of two hexagonal configurations wherein either the acy l chains face a l l inward to f i l l a cy l indr i ca l space, w i t h the headgroups on the surface of the cyl inder facing outward towards the water ( H / ) , o r the acyl chains face a l l " o u t w a r d " f rom cylinders which have the headgroups on the inside surface of the cyl inder and water f i l l ing the cylinders ( H / / phase) ^; i n a lamellar configuration consisting of b i layer stacks w i t h a hydrated space between the headgroups of neighboring bilayers; i n a vesicle configuration wherein the bi layer forms a closed sphere w i t h water inside and outside the sphere (as i n a cell) ; or into more difficult- to-describe, and less common, cubic configurations. There are m a n y factors determining the l ikely topology which l i p i d bilayers w i l l adopt , inc luding variations i n the acyl chains or i n the headgroup of the l ip ids , as wel l as hydrat ion and presence of ions i n the aqueous environment; for a good review see (Cu l l i s et ai, 1986). There has also been the suggestion that l ip ids i n association w i t h appropriate ions may facil itate formation of intermediate non-bi layer structures dur ing such processes as endo / exocytosis ( G u l i k et al., 1967; C u l l i s and de Kru i j f f , 1979). A t the h igh water concentrations discussed i n the experimental chapters to follow, only closed spherical vesicles or large uni lamel lar vesicles ( L U V ' s , about .5 ^ m i n diameter) are expected. In fact , most samples have been prepared as so-called mul t i lamel lar vesicles ( M L V ' s ) ( B a n g h a m et al., 1965; M a y e r et al., 1985). These are onion-like arrangements of successively larger vesicles, w i t h a hydrated region between bilayers, which are variable i n size i n the range of about 1 0 - ^ - 1 0 " ^ cm). T h e force act ing between bilayers i n M L V ' s is a superposition of electrostatic. V a n der WaaJs, hydrat ion-repuls ion, and fluctuation forces ( M a r s h , 1989). The interbilayer hydrat ion force for an egg-lecithin-water system has been determined to be repulsive and exponential ly decaying w i t h distance f rom the bilayer surface (Rand) . T h e resultant interbilayer thickness of water i n 'In both cases the cylinder axes form a two-dimensional hexagonal lattice. A typical cylinder axis has a diameter of about 4 nm (Tate and Gruner, 1989). M L V ' s consisting of P C l ip ids is between about 25-40 A ( H u i et al, 1980; Reiss -Hussan, 1967) and this water is known to rap id ly permeate M L V ' s ( H u i et ai, 1980; CuUis and Hope , 1980). One must here consider these numbers only as estimates, especially for the samples containing cholesterol, a n d / o r the negatively charged P O P S , for which one expects a greater hydra t i on . L i other terms, and for P O P C molecules i n par t i cu lar , one expects to have about 4.3-22 water molecules per l i p i d i n the hydrat ion range of 10-50 w t % (Bechinger and Seelig, 1991). We t u r n now to the second major constituent of real b i o l o ^ c a l membranes: proteins. These may be s t ruc tura l or biochemical i n funct ion. In general, there are two classes of prote in which are d irect ly associated w i t h the l i p i d bilayer: so-called extrinsic and intrinsic proteins. Examples of each type w i l l be discussed i n subsequent experimental sections of this thesis. Intr insic proteins are amphiphi l i c molecules which are s imultaneously solvated by b o t h the hydrophobic por t ion of the bilayer and by the aqueous media external to the headgroup regions. T h u s , intr ins i c proteins have central regions which are hydrophobical ly matched to the bi layer and corresponding hydrophi l i c regions which together anchor the prote in to the bi layer interior and exterior . In biological systems the respective hydrophobic regions of bilayer and protein tend to be matched i n length i n such a way as not to change the ordering properties of the acyl chains ( M o u r i t s e n and B l o o m , 1984; B l o o m and S m i t h , 1985; B l o o m et ai, 1991). T h e effects of hydrophobic length matching and mismatching between integral amphiph i l i c polypeptides i n P O P C and P O P C : C h o l e s t e r o l membranes w i l l be explored i n deta i l i n Chapter 2. E x t r i n s i c proteins m a y or may not be amphiphi les . T h e y may par t ia l l y penetrate the l i p i d bi layer ( i .e . one-sided penetration) but are generally considered to be extrinsic to the bilayer. Therefore, they are commonly po lar or charged molecules which interact electrostatically w i t h the bi layer or w i t h parts of intr insic proteins which extend into the aqueous region. Some exper imental interest i n this thesis - and a p r i m a r y mot ivat ional one - is associated w i t h a par t i cu lar extr insic protein called myelin basic protein ( M B P ) , used here as an i l lus t ra t i on . M B P , also called basic protein or encephalitogenic prote in , is an intracel lular extrinsic pro-tein found i n certain b r a i n cells (oligodendrocytes) which produce the l ipidacious mater ia l called myelin found i n the white matter of m a m m a l i a n brains. M B P is of medical interest since a certain demyel inat ing disease^ w h i c h is s imi lar to mult ip le sclerosis, and used as a model of th i s , may be exper imental ly induced i n animals by inject ion of M B P into the s M n (Stewart et al., 1985). It is we l l established that M B P plays a role i n mult i lamel lar bilayer stabi l izat ion (see for instance, Moscare l lo et al. 1986; Magg io and Y u , 1989; P a l i and H o r v a t h , 1989). A t neutral p H M B P has 30 posit ively charged amino ac id residues, out of a t o ta l of 170 amino acids, of which 26 ± 5 are b o u n d to l ipids i n the bi layer (Boggs et ai, 1980). In so lut ion , M B P is considered to have t e r t i a r y s t ructura l dimensions defined by an ell ipsoid w i t h major and minor axes of 150 A and 15 A respectively ( E p a n d et al., 1974), and i t is known that conformational changes may take place as a funct ion of the l i p i d composit ion of bilayers w i t h which M B P interacts (Boggs et al., 1981). The procedure we used to extract this prote in from human b r a i n white matter is detai led i n A p p e n d i x B . Otherwise , M B P wiU be used i n this thesis only to i l lustrate an unusual phenomenon -membrane vesicle eruptions - i n Chapter 3. In a membrane composed of l ip ids , extrinsic and intr insic proteins, membrane homogeneity is not necessarily expected: heterogeneity may occur due to dispersive thermal interactions ( f luctuations) , screened io iuc interact ions, covalent protein-protein interact ions, or cytoskeletal-protein interact ions (discussed below) (Sperotto et al., 1989). These mechanisms may be connected w i t h phenomena such as protein- induced la tera l phase separation ( e.g. protein-protein aggregation to enhance enzyme funct ioning) ; or the preferential association of protein w i t h a specific l i p i d type (Warren et ai, 1975); or, as a s t ructura l example, the association of a h igh density of proteins i n regions of exo- and endo-cytosis (coated pits) (Goldstein et ai, 1979). There are several features which have so far been excluded f rom this discussion of biological membranes. In par t i cu lar , real biological membranes are usually composite materials which , i n add i t i on to the prote in - l ip id structures already discussed, include a mechanical ly supportive substructure of proteinacious biopolymers which allows the external p lasma cell membrane to ^Experimental allergic encephalitis. be maintained i n mechanical ly stable shapes. T h i s part of the membrane, which may be a few to a hundred times the thickness of the bi layer , is often called the subsurface cortex. W h i l e the attachment of the subsurface cortex to the f lu id bilayer is not ful ly understood i t is known that i t has int imate connections to other filamentous networks w i t h i n cells which together form a k i n d of dynamic , continually modif ied, scaffolding for the cell as a whole, called the cytoskeleton. T h e role of the cytoskeleton is complex and w i l l not be discussed further. Another component of the biological membrane is the glycocalix, an extracel lular "forest" of peptidoglycan molecules extending f rom the fluid bilayer to create a very rough external surface wh i ch , among other things, is useful as a cell identifier to provoke recognit ion - or not - of a given cell by other cells (e.g. immune cells). A related feature is the asymmetr ic d is tr ibut ion of l i p i d types across the bilayer ( C h a p m a n et al., 1986), a good example being the intra/extracel lulax phosphol ip id headgroup assymetries seen i n different cell types (Zwaal and Hemker , 1982), the importance here being that extracel lular l ipids are antithrombogenic (i.e. do not promote a hemostatic c lo t t ing response) while intracel lular l ip ids are h ighly thrombogenic. Other intra /extrace l lu lar asymmetries include d is tr ibut ion and types of proteins, as wel l as i on gradients w h i c h establish typ i ca l electric field gradients of 10^ V / m across the bilayer. Amongst other things , the trans-membrane potent ia l may affect l i p i d dynamics and structure (as seen by flourescence anisotropy, Lakos et a/ . , 1990). In complex organisms the cell may also be embedded into many extracel-l u l a r structures (e.g. collagen networks) such as al low mechanical /b iochemical coordination of actions between large or smal l groups of cells. W e note last ly that the fluid bi layer contains many unmentioned l ip ids such as g lycol ipids , sphingomyelins, and their derivatives, as wel l as glycoproteins, l ipoproteins, fatty acids, etc. wh i ch w i l l not be discussed further i n this thesis. T h e biological membrane as a finished product has many remarkable and poor ly understood features which are outside the scope of this document ; as an example, note that the red b lood ceU membrane is considered to be on the order of 100 times softer than latex rubber and yet is approximately 10* times as strong! In summary , the bilayer represents a beaut i fu l , s imple, and sophisticated solution to the problem of iso lat ing a cell while at the same t ime re ta in ing the necessary components o f the environment from which i t evolved. It should at this point be clear that the systems s tudied i n this work, having as they do only 1-3 different l ip ids p lus , at most , a single prote in , are simple models representative of the current state of knowledge regarding substantial ly more complex structures. 1.2.1 Nuclear M a g n e t i c Resonance N M R rudiments relevant to the experimental sections are discussed m a i n l y i n A p p e n d i x A or as the need arises; we w i l l make o idy a few introductory comments here. A n atomic nucleus w i t h intr ins ic spin angular momentum ^I, of a rb i t rary or ientat ion, has a colinear magnet ic moment fi = 7^.1, where 7 is the gyromagnetic ra t i o and h is P l a n k ' s constant. Macroscopic nuclear magnet ism arises when a magnetic field H o is appl ied to a sample consisting of m a n y such nucle i : the magnetic field couples to the magnetic moments and removes the energy level degeneracy associated w i t h the spat ia l degrees of freedom for each of the spins fj, (Zeeman effect). In equ i l i b r ium, at la t t i ce temperature T , populat ion differences between the magnetic energy levels results i n a net macroscopic magnetizat ion M which m a y be described by B o l t z m a n n ' s law for a sample of N spins: M^N-ih J2 me'^'^l e"^"^ = XoH^, (1.1) m=—I m=—l where is the stat ic nuclear susceptibil ity i n the high temperature approx imat ion , and is Bo l t zmann ' s constant (Cur ie ' s L a w ) . T h e low value of Xo - 10"^ — 10~* less than that for N electrons i n the same field - encouraged the development of resonance methods for observing nuclear magnet ism. Nuclear magnetic resonance refers here to the absorption of electromagnetic radiat ion w h i c h occurs at only certain (resonant) frequencies for a given system of spins. Since st imulated emission and absorption rates are ident ica l , net absorpt ion by the sample requires populat ion differences between available energy levels (such as produced by H Q above). T h e delivery of electromagnetic radiat ion of appropriate wavelengths, 0(2-10^ m ) , and subsequent detection of this typ i ca l l y employs a coi l containing the sample (spin system) being studied as part of an electric c ircuit tuned for the frequencies of interest. Other detection methods are described elsewhere ( A b r a g a m , 1961). A b s o r p t i o n of rad iat ion perturbs the equ i l i b r ium populat ions of the energy levels as t r a n s i -tions into higher energy states occur. Interactions of the spins w i t h their environment, called the lattice, restores the equl ibr ium populat ions after i r r a d i a t i o n , w i t h i n some characteristic t ime Ti, cal led the spin-lattice relaxation time. If i r rad ia t i on is persistent a point of saturation is eventually reached where further absorption can only occur as spin-lattice re laxation restores popu la t i on differences, thereby transferring energy to the latt ice . Sp in - sp in interactions are also common. For the case of strong coupling, magnetization can be quickly transferred between spins resul t ing i n an equi l ibr ium at a spin temperature different f rom that of the lat t i ce . The timescaJe for establishing thermal equi l ibr ium between spins wi thout energy transfer to the latt ice is cal led the transverse relaxation time, T2. Phys ica l ly , there may be mul t ip le mechanisms contr ibut ing to the observed relaxation times for each of T i and T2; such cases w i l l be described i n more detai l i n Chapter 4. 1.2.2 M o t i v a t i o n : M e d i c a l Connections Studies of l i p i d systems discussed so far are t ight ly constrained by the s impl ic i ty of the model systems be ing used. A s described above, these studies are most often restricted to parametr iz ing near- ideal membrane systems composed of at most a few l ip ids and - less often - a single prote in . Due to the s m a l l amount of x-ray or neutron diffraction da ta available for l i p i d systems, there is ignorance even as to many simple features of topologicaUy relevant membrane structures - such as bilayer thickness or the distance of an extr insic protein from the bi layer. N M R is l i m i t e d i n this regard because, for l i p i d systems i n the La phase, i t is a mesoscopic measurement* ( B l o o m *Able to probe distances on the length scale of about 100 nm. et ai, 1991) associated w i t h the fact that latera l diffusion, constants may be o n the order o f 10"^^ m^/s which means l ip ids diffuse a distance « y/ADrs « 45 n m dur ing a typ i ca l N M R measurement requir ing TS ~ 50/xs to record a spectrum. For integral proteins, the s i tuat ion is even worse: to date only two biological ly relevant Integral proteins have had their fu l l t e r t i a r y structure determined (XJnwin and Henderson, 1983;Deisenhofer et al, 1986), apparently due to difficulties i n preparing good 3-D crystals for such proteins. W h i l e there have been some medical ly useful spin-offs from studies of simple l i p i d systems, for the greater part , these systems are being studied for their own merits as physical ly interesting structures. F r o m the viewpoint of c l in ica l medicine, the present state of knowledge excludes most med-ica l ly interesting l i p i d systems. A n impor tant example of this , and one that has concerned us , is the myelin sheath wh i ch surrounds nerve cell axons i n the m a m m a l i a n b r a i n , so p e r m i t t i n g saltatory conduction of nerve imptdses at a higher velocity t h a n i n unmyel inated axons. F i g -ure 1.3 depicts the major l i p i d and protein components of h u m a n mye l in . There are a couple of features wor th not ing about this : the h igh cholesterol concentration is typ ica l of many h u m a n cells (e.g. red blood cell membranes contain 50 % cholesterol); the so-called galactocerebroside lipid is pathognomonic of the oligodendrocyte cells which produce mye l in ; and the protein com-posit ion of myel in is unusually simple w i t h 50-55 % of (integral) proteo l ip id protein ( P L P ) and 30-35 % (extrinsic ) mye l in basic protein ( M B P ) . M B P and P L P both have postulated roles i n the formation and maintenance of myelin and i ts pathology (Wood and Moscarel lo , 1984). T h e apparant ab i l i ty of these proteins to cause experimental autoimmune encephalomyelitis ( E A E ) (Stewart et ai, 1991), is associated w i t h a worldwide effort to understand their structure and function i n hopes of determining the etiology of mul t ip le sclerosis. In general t e r m s , ^ H - N M R has played a sigruficant role i n characteriz ing l i p i d behavior i n bilayer systems (Seelig and Seelig, 1980; D a v i s , 1983; B l o o m and S m i t h , 1985; B l o o m et ai, 1991). It has also been used more specifically i n M S related research to study the effect of M B P on the bilayer (S ix l and W a t t s , 1982; S ix l et ai 1984). Other nuclear species have also been used to study basic proteins and membranes by N M R ; examples include protons (^H) (Persaud AO wt% H,0 MYELIN 75 wt% Lipid 28 % Galoctolipid 1% myelin associated glycoprotein 5% Wolfgram protein 5 0 - 5 5 % proteolipid protein (PLP) —mostly Lipophilin 3 0 - 3 5 % myelin basic protein (MBP) 39 % Phospholipids -galoctocerebroside -sulfatide -phosphatidylcholine -phosphatidylserine -phosphotidylethanolamine -sphingomyelin -phosphatidyl inositols F i g u r e 1.3: M y e l i n C o m p o s i t i o n . T h i s table i l lustrates the l i p i d and protein composit ion of human myel in ( A l t m a n and D i t t m e r , 1984). Note that the major i ty compo-nent by weight is the l i p i d part . T h e l i p i d composit ion is complex but the prote in composit ion is relatively s imple. et al., 1988); phosphorous (^^P), to determine phase-behavior (Fraser et al., 1989; Deber et ai, 1986); and carbon (^^C), for h igh resolution s t ruc tura l studies (Mendz et ai, 1986) and to study the interact ion of M B P w i t h charged l ip ids (Deber et ai, 1986). Other techniques which have been especially useful to characterize M B P and i ts interations w i t h l ip ids include electron sp in resonance (Persaud et ai, 1989; P a l i and H o r v a t h , 1989; Sto l lery et ai, 1980; Boggs et ai, 1980), which has supported a minor role for the hydrophobic regions of M B P i n b ind ing neighboring bilayers; and l i q u i d x-ray diffraction and freeze-fracture electron microscopy, used to investigate the ultrastructure of l i p i d dispersions i n the presence and absence of M B P ( Moscare l lo et ai, 1986; Inouye et ai, 1989), i n part i cu lar to investigate possible roles for M B P i n mul t i - lamel lar s tabi l izat ion (Fraser et ai, 1986). Other techniques used include photolabel l ing (Boggs et ai, 1988) and Fourier transform infrared spectroscopy (Surewicz et ai, 1987). A characteristic feature of almost a l l the l i p i d models used i n these studies is the absence of cholesterol, an essential component of mye l in . Recent advances have resulted i n an increased abi l i ty to meaiungly interpret changes i n N M R spectra associated w i t h the b ind ing of ions and charged proteins i n the region of the l i p i d headgroup (Seelig and M c D o n a l d , 1987; Seelig et ai, 1987; R o u x et ai, 1989). Such techniques have helped encourage recent studies of prote in - l ip id interact ions, e.g. m e l i t t i n ( K u c h i n k a and Seelig, 1989; Dempsey et ai, 1989) and spectr in ( B i t b o l et ai, 1989). A s previously noted, V i s t and Davis ( V i s t and Dav is , 1990) have now worked out the phase behavior for a b inary m i x t u r e of phosphol ip id and cholesterol. These studies, as wel l as the experimental work of ( R o u x and B l o o m , 1990) which looks at the effect of cation b inding at the bilayer upon the quadrupolar splitt ings of headgroup-deuterated l ip ids , together provide hope for differentiating effects due to cat ion b ind ing from those due to protein b inding. The l ong term goal motivating our experiments has been to reconstitute a model myel in membrane ( M M M ) containing appropriate concentrations of aU the constituents shown i n F i g -ure 1.3, and to study this system using N M R i n order to characterize M B P ' s interact ion w i t h M M M . Considering the urgency associated w i t h a human disease such as M S the hope is that - at least - gross features of the M M M system may be determined which usefully increase medical understanding of M S despite l ikely inabi l i t ies to ful ly interpret every deta i l of the data . However, we recognized from the outset several issues which needed to be addressed pr i o r to experimention w i t h M M M ' s . In par t i cu lar , one issue involved the unfortunate exclusion of cholesterol f rom most of the published work on M B P - l i p i d interactions. T h i s is i n sharp contrast to the profound known effects of h igh cholesterol concentrations i n phosphol ip id bilayers and dictated that our i n i t i a l studies must investigate simpler model systems w h i c h at least included cholesterol. A n o t h e r issue was the relative difficulty of prepar ing proteo l ip id protein - wh i ch , along w i t h the dearth of effects noted for the interact ion of integral proteins w i t h phase acy l chains i n general , suggested the need for fundamental research into the effect of model integral polypeptides upon phospholipid-cholesterol bilayers. T h e s tudy of these more fundamental issues w i l l be the m a i n concern this thesis. T h u s , the long-term experimental studies we have proposed which are most direct ly related to the model myel in system are o idy per ipheral ly discussed (see A p p e n d i x B ) . A l t h o u g h we have chosen to avoid extensive discussion of these experiments, we w i l l now briefly present some results of these studies i n order to underline the above discussion and to permit in t roduct ion of the experimental chapters. E x a m p l e : M B P - P h o s p h o l i p i d Interactions by N M R M B P was added serially to membranes composed of: P O P C : P O P S (5 : l ) (m:m) or P O P C : P O P S : C h o i (5 : l :2 .6) (m:m:m) up to 50% by weight. T h e N M R experiments were performed at temperatures of 20 and 37 [°C]. Measurements of T 2 and T i were made before and after each addi t ion of M B P . Different experiments used deuter ium labels on either the choline headgroup, the serine headgroup, or the p a l m i t o y l chain of P O P C . Th i s research extended earlier ^ H N M R studies of the effects of M B P i n model bilayers ( S i x l and W a t t s , 1982; S i x l et al., 1984) to include the presence of cholesterol. In general, the addit ion of M B P resulted only i n smal l changes to the quadrupolar splitt ings of a l l l i p i d species. For P O P C this is consistent w i t h the weak b ind ing of M B P to these l ip ids (Boggs et al., 1982) but for P O P S there is a s imi lar effect which is not necessarily expected on the basis of the electrostatic interact ion between i t and M B P . For b o t h headgroups there is a decrease i n order (quadrupolar spl itt ings) w i t h the addi t ion of cholesterol, indicat ing less constrained m o t i o n of the headgroup probably due to the increase i n effective area per molecule i n the headgroup region. A s a s imple i l lus trat ion of the importance of cholesterol. F igure 1.4 shows powder-type spectra for several P 0 P C - d 4 headgroup deuterated versions of the above bi layer i n the presence and absence of cholesterol and increasing M B P content at 21°C. W e see i n F igure 1.4 two _] I I i _ c b a - 1 — I — I — I - - | — I — I — 1 — r -- 3 0 - 2 0 •10 0 10 F r e q u e n c y , kHz 20 30 F i g u r e 1.4: M B P - i n d u c e d Isotropic L i n e . T h i s figure demonstrates three N M R spectra of headgroup deu-teriated P O P C i n a P 0 P C - d 4 : P 0 P S : C h o l e s t e r o l sample w i t h no M B P (a); w i t h 25 w t % M B P (b); and w i t h 50 w t % M B P (c). A d d i -t i on of about 25 w t % of the posit ively charged myel in basic protein ( M B P ) results i n increased isotropic intensity whi le further addi t ion up to 50 w t % does not effect the isotropic intensity further. spl i t t ings , associated w i t h two equivalent deuterons on each of the a lpha and beta positions (see F igure 1.1) of the choline headgroup. These spl i tt ings (divided by two) are p lotted against the amount of M B P i n F igure 1.5. ^ It is observed here that the a lpha pos i t ion deuterons are 1 0 1 8 H o 4 H o â 2 H a b o -0 5 1 0 1 5 A m o u n t o f M B P A d d e d , m g Figure 1.5: M B P and P O P C Headgroup Quadrupolar Splitt ings. Quadrupo lar splittings are p lotted versus the amount of M B P added to the sample for deuteration at the a pos i t ion of the P C head-group (a) or at the /? posit ion (b). T h e various symbols rep-resent P O P C : P O P S bilayers (molar rat io =5:1) at 21 °C ( A ) ; P O P C : P O P S : C h o l e s t e r o l bilayers (molar ra t i o =5:1:2.6) at 21 " C (o) and at 37 °C (•). T h e straight lines are least squares fits to the data . more affected by the presence of M B P than those i n the be ta pos i t ion , and that this effect is eliminated when cholesterol is present. A model calculation ( R o u x et al., 1989) to interpret the impl icat ions of these results for the average posit ion of M B P ' s charged groups is possible but w i l l not be pursued here. ^Actually, "dePaked" spectra (Sternin et al, 1983) were used to calculate the splittings. Another interesting feature, innocuously represented by the isotropic lines seen i n the spectra of F igure 1.4, w i l l now be discussed since the attempt to understand this result is a s tart ing point for the second experimental chapter (Chapter 3). M e m b r a n e E r u p t i o n s A s the l i p i d systems of the last section were studied, and especially u p o n addi t ion of choles-terol to the membrane, a nagging feature was the presence of a n isotropic l ine w h i c h tended to reversibly increase or decrease i n intensity as a funct ion of temperature . T h i s was nagging because the membranes are composed of roughly 15% P O P S and the fract ion of the t o ta l s ignal i n the isotropic l ine at higher temperatures was of this magnitude . Since we were interested i n the interact ion of M B P w i t h P O P S , i t being the negatively charged l i p i d , and previous workers h a d conjectured that P O P S prefers a membrane of h igh curvature (Gruner et ai, 1985), i t seemed possible that large amounts of P O P S were i n some smal l vesicles. Further study, using headgroup deuteriated P O P S proved this to be not the case; however, the feature of reversibil -i t y was an in t r i gu ing observation which required further explorat ion . T h i s involved more and sl ightly different experiments (discussed i n detai l i n Chapter 3) , inc lud ing freeze-fracture elec-t ron microscopy, and resulted i n recognition of a novel connection between micromechanical properties of b i layer membranes and the use of N M R to measure these. A n t i c i p a t i n g Chapter 3, the phenomenon of membrane eruptions was seen, for the first t ime "knowing ly " by N M R . It is enough to note here that this involves ejection of membrane away from the parent vesicle, but s t i l l connected w i t h the parent vesicle. It is especially interesting that a protein can cause eruptions to occur, b o t h i n general terms and i n regards to myelinogenesis (and, therefore, pos-sibly M S pathogenesis). Such eruption-l ike behavior is a possible phys ica l mechanism whereby a neuroblast ( randomly) selects the populat ion of neurones which it is to myelinate; that i s , the process of early myel inat ion may part ia l ly be a protein-mediated thermodynamic effect of the bilayer membrane. However, this suggestion is hypothet i ca l a n d , i n any case, is properly applied on ly i n relat ively simple systems. 1.3 S u m m a r y . A number of experiments liave been performed w h i c h are useful as background for studies of M B P - l i p i d interactions i n M M M systems. One series of experiments, which demonstrated the first clear observations of changes i n perdeuteriated acy l chain quadrupolar splitt ings (for l ip ids i n the L a phase) attributable to the presence of a n integral polypeptide , is detailed i n Chapter 2, a long w i t h some of the impl icat ions of these results relat ing to the geometry of cholesterol i n phosphol ip id bilayers. A l s o i n Chapter 2, the N M R d a t a is interpreted i n a way which allows certain unusual connections to be made w i t h micromechanical measurements of bi layer mechanical properties. A n o t h e r such "connect ion" is explored i n Chapter 3 wherein w i l l be found details of electron microscopic and recently reported ^^P N M R and N M R observations of membrane "e rupt i ons " (Nez i l et al, 1991). Chapter 4 addresses some important questions ar is ing i n Chapter 2 as regards orientation-dependent T2 re laxat ion causing spectral d istort ion i n quadrupolar echo spectra. A method now used i n our laboratory to generate spectra of re laxat ion rates, and spectra which have been corrected for orientation-dependent (frequency-dependent) re laxation effects is described. C h a p t e r 4 concludes on a speculative note by us ing this method to describe orientation-dependent re laxat ion effects i n the perdeuteriated acyl chains of the l i p i d and integral -protein- l ip id systems of C h a p t e r 2 as a fruit ful area for further study. W e reiterate: A p p e n d i x A contains a discussion of some N M R rudiments used herein but , as each of the experimental chapters is self-contained, no continuity w i l l be lost i n exc luding A p p e n d i x A from perusal . F i n a l l y , A p p e n d i x B includes a rough outline of the overal l experimental program for N M R studies of M B P - l i p i d interactions i n M M M as weD as the detai led methods we used for recovery of M B P from human tissue. C h a p t e r 2 Effects of Integral Polypeptides on Bi layer Thickness 2.1 C h a p t e r Overview. ^ D e u t e r i u m (^H) N M R was used to study bilayer hydrophobic thickness and mechanical prop-erties when cholesterol a n d / o r synthetic amphiph i l l i c polypeptides were added to deuterated P O P C l i p i d bilayer membranes i n the l iquid-crystal l ine (fluid) phase. Smoothed acyl chain o r i -entat ional order profiles were used to calculate bilayer hydrophobic thickness. A d d i t i o n of 30 m o l % cholesterol to P O P C at 25 °C increased the bi layer thickness from 2.58 to 2.99 n m . T h e peptides were chosen to span the bilayers w i t h more or less mismatch between the hydrophobic peptide length and membrane hydrophobic thickness. T h e average thickness of the pure l i p i d bilayers was significantly perturbed upon addi t ion of peptide only i n cases of large mismatch , being increased (decreased) when the peptide hydrophobic length was greater (less) than that of the pure bi layer , consistent w i t h the "mattress" model of protein l i p i d interactions (Mour i tsen and B l o o m , 1984.) T h e experimental results were also used to examine the combined influence of the polypeptides and cholesterol on the orientational order profile and thickness expansiv-i ty of the membranes. A detailed model for the spat ia l d i s t r ibut ion of P O P C and cholesterol molecules i n the bilayers was proposed i n order to reconcile the general features of these mea-surements w i t h micromechanical measurements of area expansivity i n closely related systems. Exper iments to test the model were proposed. ^This chapter closely follows a previously published paper (Nezil and Bloom, 1992). 2.2 Introduct ion . Orienta t i ona l order parameters of carbon-deuterium ( C D ) bonds i n the hydrophobic mi l i eu of model membrane l ip ids are important as they reflect the acy l chain ordering and disordering which dominates the thermodynamics of the gel -to- l iquid crystal l ine (main) phase transit ion ( C h a p m a n , 1975). D e u t e r i u m nuclear magnetic resonance ( ^ H - N M R ) has been used to deter-mine the var iat ion of the magnitude of the acy l chain or ientat ional order parameters |5c7i)(n)| w i t h carbony l posit ion n , often called the acy l chain "order profi le"(Seelig and Seelig, 1977; M a n t s c h et ai, 1977; Seelig and Seelig, 1980). It is we l l known that |5CD ( « )| is sensitive to changes i n cholesterol concentration, temperature, and headgroup subst i tut ion . A more recent empir i ca l observation (Lafleur et a/ . , 1990) is that , as each of these parameters is varied, the shape of the order profile changes i n a manner that depends only on a single independent pa -rameter , e.g. the average value of |5CD(W)| over the acyl chain , and not on which of the three perturbat ions is used to change |5'CD(«)I-For an acy l chain containing N carbon atoms, {|5cD!) = ^ | : i 5 c D ( n ) | . (2.1) A semi -empir i ca l re lat ionship has been found to exist for fluid membranes between (|5CD|), the b i layer hydrophobic thickness d, and its m a x i m u m thickness when the acy l chains are i n the a l l - t rans conf iguration, dg: rf=do(a(|5cD|)+/3), (2.2) where the constants a and /? satisfy the constraint ^a+ff = 1 (Ipsen et al., 1990). T h e fact that E q 2.2 is consistent w i t h available measurements of (|5CD|) using ^ H - N M R , and d using x-ray di f fract ion, suggests that ^ H - N M R may be used to determine mechanical properties of b iomem-branes ( B l o o m et ai, 1991). In this context, the observation that natura l ly occurring integral membrane proteins i n fluid bilayers do not perturb (|5'CD|) has been interpreted theoretically, us ing the "mattress" model of prote in- l ip id interactions (Mouri tsen and B l o o m , 1984), as being due to the match ing of hydrophobic regions of l ipids and proteins v i a evolutionary processes i n order to produce strain-free bilayers ( B l o o m and M o u r i t s e n , 1988). We now present the results of some experiments which test the concepts described above. In par t i cu lar , we compare the hydrophobic match ing of pure P O P C bilayers (referred to as Bi), and bilayers containing 30 m o l % cholesterol (^ 2), to two a -he l i ca l integral membrane peptides of different hydrophobic lengths: L y s 2 -G ly -LeUm - L y s 2 -A la -amide , w i t h m =16 or 24 (Davis et al, 1983; Huschi l t et ai, 1985), to be called P i e and P24 respectively. T h e monounsaturated P O P C is representative of the dominant l ipids i n the p lasma membranes of eucaryotic cells having high cholesterol concentrations (Alberts et ai, 1989; B l o o m and M o u r i t s e n , 1984; B l o o m et a/.,1991). U s i n g the relationship between hydrophobic bilayer thickness and or ientat ional order ex-pessed i n E q n 2.2, we shal l show that the shorter peptide P i e is wel l matched to the t h i n bilayer Bi but too short for the " t h i c k " bilayer B^, while the longer peptide P24 is wel l matched to B2 but too long for Bi; these results are as antic ipated by the mattress model . However, a more detailed analysis of the order profile and the temperature dependence of < \SCD\ > indicates subtleties i n the spat ia l correlations of the l i p ids , peptides , a n d sterols i n these mem-branes. A model w iU be proposed which addresses some of these issues. Further measurements of the type reported here, combined w i t h X - r a y , neutron dif fraction and micromechanical mea-surements, w i l l be required to provide a more detailed picture of the manner i n which l ip ids , sterols, and proteins (or peptides) are organized i n membranes. 2,3 E x p e r i m e n t a l Procedures . 2.3.1 Mater ia ls . Perdeuteriated pa lmit i c ac id was prepared by s tandard methods i n our laboratory. A v a n t i Po lar L i p i d s ( A v a n t i Po lar L i p i d s , B i r m i n g h a m , A L ) used this mater ia l to produce the single-chain perdeuteriated l - pa lmi toy l -2 - oleoyl-phosphatidylcholine ( P O P C - d a i ) used here. Cholesterol was purchased from S igma (Sigma, St. Lou i s , M O ) . T h e amphiph i l i c cationic peptides P i e and P24 were synthesized by previously published methods (Davis et ai, 1983). 2.3.2 Sample P r e p a r a t i o n . The sample preparat ion procedure was a sl ightly modified version of already published methods (Huschilt et ai, 1985). T h e modif icat ion s imply involved measuring membrane components us-ing dry weights rather than by t i t ra t i on and , after add i t ion of the buffer (800 fA of 5 0 m M Hepes, l O O m M N a C l , and p H = 7 . 4 , using deuterium depleted water f rom S igma) , the sample then u n -derwent four cycles of freezing i n l i q u i d nitrogen followed b y warming to room temperature. The samples were then centrifuged at 90,000 r p m and 25 °C for one hour i n a microBeckman centrifuge, and the pellet was transfered to an N M R tube. T h e amount of P O P C - d a i used was typica l ly about 30 m g . T h e P O P C - d a i i C h o l e s t e r o l samples contained 30 m o l % cholesterol and pept ide - l ip id samples contained 3.5 m o l % peptide. T h e P O P C - d a i samples contained 4.8 m o l % peptide. 2.3.3 N u c l e a r M a g n e t i c Resonance. The ^ H - N M R experiments were performed on a home-built spectrometer operatmg at 46 M H z for deuterons (Stern in , 1985). A quadrupolar echo sequence was used: 90ir-T-90j,-r-echo, w i t h r =60 ^s and a repeat t ime of 150 ms. T h e 90° pulse length was 4.0 /xs. Spectra were recorded w i t h a 2 / is dwell t ime and at least 50,000 transients collected for s ignal averaging. Signals were detected i n quadrature w i t h phase cyc l ing (Davis , 1979; Ranee and B y r d , 1983), and temperature was controlled using a B r u k e r model BV-TIOOO temperature controller (Bruker Instruments , Inc. , B i l l e r i c a , M A ) . 2.4 Resul ts . Figure 2.1 presents the ^ H - N M R spectra and their dePaked forms, obtained at 25 °C for the various cases of pept ide - l ip id hydrophobic match ing and mismatch ing i n the P O P C - d a i (Bi) and P O P C - d 3 i : c h o l e s t e r o l (^2) samples. C o m p a r i n g the unperturbed bilayers (i.e. no pep-tide) we observe the fami l iar dramatic increase i n the quadrupolar spl itt ings which occurs w i t h the add i t i on of cholesterol to a pure phosphol ip id system. We also note that addit ion of the -60 - 4 0 - 2 0 0 20 40 60 requency, kHz 2H NMR Spectra . ^ H - N M R spectra (above), and dePaked spectra (below), f rom quadrupolar echo experiments w i t h r = 60/is at 25 °C for various cases of hydrophobic m a t c h / m i s m a t c h . The upper 3 spectra i n each case show bilayer B i ( P O P C - d a j ) w i t h no peptide added (a); w i t h 6.3 m o l % P i 6 (b); w i t h 4.8 m o l % P24 (c). T h e lower three spectra i n each case are for bilayer B2 ( P O P C - d a i x h o l e s t e r o l 7:3 M : M ) w i t h no peptide added (c); w i t h 3.5 m o l % peptide P24 (d) ; and w i t h 3.5 m o l % peptide P i e (d). T h e vert ica l dashed lines are for v i sua l a id F i g u r e 2.1: only. (relatively) weU-matched peptide to each of B i and B2 ( i .e. , samples B i P i e and B2P24 respec-t ively) has relat ively l i t t l e effect on the spectrum compared to the cases of mismatch (B1P24 and B 2 P i 6 ) - For the latter cases we see that adding P i g decreases the quadrupolar splitt ings of B2 while add ing P24 results i n increased splittings for B i . T h e smal l isotropic peak i n F igure 2.1 c is insignif icant. T h e comments of the last paragraph also apply to the dePaked spectra of F igure 2.1 ;how-ever, the spectral differences of interest are more pronounced. W e use these dePaked spectra to calculate the smoothed order profiles p lotted i n Figure 2.2. T h i s figure demonstrates that O 2 4 6 8 10 12 14 16 C a r b o n P o s i t i o n , n F i g u r e 2.2: Smoothed O r d e r Profiles. Smoothed acy l chain or ientat ional order profiles calculated from the dePaked spectra of F igure 2.1. Parts a (bilayer B2) and b (bilayer B i ) each display three order profiles corresponding to addit ion of peptide: no peptide (-f ); peptide P i e (o); and peptide P24 ( A ) . mismatch between hydrophobic lengths dp and di, for the peptides and l ipids respectively, is correlated w i t h a systematic increase (for dp > d/) or decrease (for dp < di) i n \ScD{n)\. Us ing E q n . 2.2, a corresponding increase or decrease i n the l ip id-pept ide bi layer hydrophobic l ength , dip, is obtained. There is relat ively l i t t le change i n | 5 C D ( W ) | u p o n addi t ion of a match ing peptide (dp « di). Simi lar order profiles were obtained at several temperatures for samples Bi and B2, and for the corresponding cases of greatest mismatch : B1P24 a-nd B2P16, respectively. T h e thicknesses i n these cases, as calculated f rom E q . 2.2, are p lo t ted as a funct ion of temperature i n F igure 2.3. The sol id lines are l inear least squares fits to the da ta w i t h the fol lowing slopes ( in uiuts of 3 6 I 1 _ 3 2 -in cu c: " u 30 - I 2 8 -O CL O -fe 2 6 -2 4 ~T 1 1 n 5 10 1 5 2 0 T e m p e r a t u r e , T 2 5 3 0 F i g u r e 2.3: Bi layer H y d r o p h o b i c Thickness vs. Temperature . Bi layer hydrophobic thickness versus temperature for samples Bi ( A ) , BiP24{o), B2 (•), and B2P1G (+); and l inear least squares fits to this data . Â / ° C ) : -0 .05 ± 0.01 for Bi; -0 .06 ± 0.01 for i ? iP24 ; -0 .11 ± 0.01 for ^ 2 ; and -0 .10 ± 0.01 for 52P16. B2P16, respectively. 2.5 Discussion. 2.5.1 N M R T i m e and Distance Scales. It is wel l k n o w n that any spectroscopic technique has some intr insic t ime scale TS associated w i t h i t . In the case of N M R i n fluid membranes, TS > 10""* s (Devaux, 1983; Seelig and Seelig, 1980; B l o o m and S m i t h , 1985), w h i c h is approximately equal to the inverse of the spectral w i d t h . Because of the relat ively large latera l diffusion constant i n flmd membranes (typical ly , D w 4x10"^^ m^s"^), the distance diffused by molecules dur ing TS, LJ, « {ADTSY^^ « 400A , is quite large and represents an intr ins ic distance scale for N M R i n fluid membranes ( B l o o m et al., 1991). For this reason, the spectra described below should be interpreted as averages over domains hav ing a size greater than several hundred Angstroms , which is more t h a n ten times greater t h a n the average separation of neighbouring peptide molecules. T h u s , the N M R spectra only provide in format ion on the average change i n bilayer hydrophobic thickness, due to the pept ide - l ip id interact ion , and not on the correlation length of the peptide-induced per turbat ion of the bilayer chacteristics. W e w i l l not discuss here the information on correlation length provided by peptide- induced orientation-dependent spin-spin relaxation effects. It is k n o w n that such effects do not modi fy significantly the interpretat ion given below of the spectral changes induced by the presence of the peptide molecules (Nez i l et al., 1991) as w i l l be discussed i n Chapter 4. 2.5.2 Orientational O r d e r and Bi layer Thickness . The calculated bilayer hydrophobic thickness (see E q . 2.2) for each of the smoothed order profiles of F igure 2.3 is l i s ted i n Table 1. There is good agreement for the calculated thickness of pure P O P C - d a i , 25.8 Â , w i t h the published value of 26 Âfor (buffered) D P P C i n the L a -phase (Lewis and E n g e l m a n , 1983). Some in format ion on electron density profiles for egg PC-cholestero l mixtures is available from X - r a y diffraction experiments ( M c i n t o s h et ai, 1989). These samples are s imilar to P O P C - c h o l e s t e r o l mixtures since most of the egg P C molecules Bilayer Calculated Thickness, A Type no peptide P i P2 B i ( P O P C - d a i ) 25.8 25.8 26.4 B2 ( P O P C - d 3 i : C h o l . ) 29.9 28.6 29.8 Table 2.1: Bi layer H y d r o p h o b i c Thickness . B i layer hydrophobic thickness at temperature T = 2 5 ° C for the various bi layer types described i n the text . W e have used E q n 2.2 to calculate d w i t h do = 39.4 A , as calculated by Marce l j a for D P P C (Marce l ja , 1974). also consist of a single, mono-unsaturated acy l chain . T h e X - r a y dif fraction measurements on a 33 m o l % cholesterol mix ture at 21 " C gives a headgroup separation of 40 A . T h i s is i n agreement w i t h our measurement of a bilayer thickness of 29.9 A f o r 30 m o l % cholesterol at 25 °C i n Table 2.1 al lowing a reasonable thickness of 5 A f o r the headgroup region. These correlations encourage further consideration of the the impl icat ions of our N M R measurements and we proceed here under the assumption that E q n 2.2 is va l id for such mixtures . A n i m p o r t a n t consequence of E q n 2.2 is that the well established increase i n (|5CD|) upon addi t ion of cholesterol means that cholesterol appreciably increases the the phase average bilayer hydrophobic thickness. Table 2.1 l ists this increase as 4.1 A f o r add i t ion of 30 m o l % cholesterol to a P O P C bilayer at 25 °C . T h e peptides used here have a well defined, r i g i d , a- hel ical structure w i t h hydrophobic lengths of dp « 2 4 A for P i e and dp « 36 A f o r P24 (Davis et al, 1983; Huschi l t et al., 1985). C o m p a r i n g dp w i t h the unperturbed thicknesses, di, of the peptide-free bilayers i n Table 2.1, we see t h a t , i n a l l cases, dp d\, i.e. only different degrees of mismatching are considered here. In general, the addi t ion of peptides w i t h di > dp (di < dp) results i n a decreased (increased) average thickness of the bi layer, as expected. The magnitude of mismatch is not exact ly correlated w i t h the resultant change i n thickness: for the case of greatest mismatch , dp - « l O A for P24 i n Bi, the change i n thickness is -|-0.6 A ; yet, for the lesser degree of mismatch di — dpK 6 A for P i e i n B2, the thickness change is -1.3 A . Thus , the perturbat ion due to mismatch is not symmetr ica l w i t h respect to the sign of the mismatch : the " shor t " peptide i n the " t h i c k " bilayer is more effective t h a n the " l ong" peptide i n the " t h i n " bilayer i n changing the bi layer thickness. W e beleive this asymmetry is l ikely related to physical considerations of the pept ide - l ip id interact ion (below), rather t h a n to questions of peptide solubil i ty which have been addressed elsewhere (Davis et al., 1983). T h e results g iven here for peptide P24 i n bilayer Bi are s imi lar to those obtained i n previous studies on peptides i n phosphol ipid or potass ium-palmitate bilayers (Huschilt et ai, 1985), but our study of peptides i n B2 represents the first results on matching i n membranes containing large amounts of cholesterol. T h e approximate matching of P i e to Bi and P24 to B2, and mismatch of P i e to B2 and P24 to Bi, is i n qual i tat ive agreement w i t h the predictions of the mattress model ( B l o o m and M o u r i t s e n , 1984). In order to interpret our results quantitat ively other considerations become impor tant inc lud ing thermal ly excited thickness fluctuations of the bilayers (see e.g. Brochard and L e n n o n , 1975; B l o o m et al., 1991) and the flexible coupl ing of the posit ively charged lysines (at neutra l p H ) to the peptide backbone v i a four methylene groups. It seems to us that the m a i n features of the l ip id-pept ide interact ion , inc lud ing the lack of symmetry associated w i t h mismatch , is l ike ly to be interprétable i n terms of reasonable phys ica l models i n which the phys ica l considerations described above are inc luded. For example , the lack of symmetry w i t h respect to the sign of the mismatch can probably be explained i n terms of the flexible coupling of the posit ive charges of the lysines. T h e four methylene groups of P i e i n the B 2 P i e membrane are probably completely extended and the P i e peptide oriented para l le l to the bilayer normal i n order that the charges reach the water region. In the case of the B1P24 membrane the P24 peptide, being too long for the thickness of B i , can t i l t relative to the surface n o r m a l . 2.5.3 U n u s u a l Features of the Results . There are two m a i n features of our results which are unusual and indicat ive of subtleties i n the arrangement ( "packing") of the P O P C , cholesterol, and peptide molecules i n the bilayers and that w iU require further experimental investigation to clarify. T h e first feature concerns the shape of the order profiles, | 5 C D ( " ) | versus n: the three-component bilayers differ markedly from either the one-component ( P O P C ) or two-component ( P O P C x h o l e s t e r o l and P O P C : p e p t i d e ) bilayer systems studied here. Th i s is seen f rom F i g -ures 2,2 and 2.4. Whereas the change i n |5'cr»(«)| upon addi t ion of cholesterol to the pure P O P C bilayer monotonicaUy decreases for increasing n ^, the corresponding change i n \ScDin)\ upon add i t i on of P i e to B2 goes through a m a x i m u m near n = 12. These features are especially evident i n F i g u r e 2.4 which is based on measurements of the order parameter , |5'czj(n,T)|, at several temperatures between 5°C and 25°C. In F igure 2.4, we have plotted the var iat ion w i t h n 1 i i \ 1 r 2 4 6 8 10 1 2 1 4 1 6 C a r b o n P o s i t i o n , n F i g u r e 2.4: Difference O r d e r Parameters : II. T h e difference order parameter , AS'^'^(n,T) (see text) has been averaged over the temperature range 5-25 °C for various cases: 7 = 5 2 , * = fli (a); 7 = BiP24,S = B i (b); 7 = B z P i e , * = B^ (c). The long-dashed lines represent AS^'^(n,T) at temperature T = 25°C while the other dashed lines are for T = 5°C. similar result applies to temperature changes (Lafleur et al., 1990). chain pos i t ion n of the "difference order parameter" A 5 ' ^ ' * ( n , T ) : A5 '^ '^ (n ,T ) = | 5 j ^ ( n , r ) | - \S'cD(n,T)\, (2.3) where the superscripts 7,6 specify the two different samples for which the difference i n order is being demonstrated. T h e dashed lines i n F igure 2.4 represent the difference order profiles at the highest (25 °C) and lowest (b^C) temperatures used while the sol id symbols represent the average difference order profile over this temperature range. It is perhaps worth n o t i n g that the n = 12 posit ion on the acyl chain roughly corresponds to the methylene pos i t ion to which cholesterol is predicted to penetrate into the bi layer (based upon the all -trans configuration for the acy l chains near the cholesterol). T h e d a t a i n F igure 2.4 suggest that the change i n the equ i l ibr ium thickness upon perturbat ion of the thick bilayer by the short pept ide is correlated w i t h an increasing acyl chain disorder. T h e change is m a x i m a l i n the region near the hydrophobic terminat ion of the cholesterol molecules. T h e presence of cholesterol and the short pept ide i n a phosphol ip id mix ture together represent two competing forces effecting the thickness of the bi layer : the results of F igure 2.4 suggest that the influence of the peptides i n m a k i n g the membrane thinner cannot be p ic tured s imply as a cancellation of the th ickening effect of the cholesterol molecules. T h e second feature that requires interpretat ion is that the expansivity of the bilayer h y -drophobic thickness, i.e. àd = {l/d){dd/dT), is increased ( in magnitude) by a factor of approximately two (see F igure 2.3) upon add i t i on of cholesterol, independent of pept ide i n -clusion. The values of \àd\ for the four samples are given ( x l O ~ ^ °C~^) : 2.1 ( B i ) , 2.4 (B1P24), 3.6 (B2), and 4.1 ( B 2 P i 6 ) - T h i s is to be compared w i t h the results for the area expansiv-i ty = {l/A){dA/dT) which , according to micromechanical measurements (Needham et ai, 1988), is always substantial ly decreased vLTpon the add i t i on of cholesterol. For example , i n Table 1 of Needham et al. (1988), i t is seen that for D M P C at 35 ° , = ( 4 .2±0 .2 ) x l O ' ^ " C " ^ while a sample of D M P C : c h o l e s t e r o l containing 40 m o l % cholesterol gives ÙA = (2.3) X 10~^ °C~^ at 35 °C. T h i s is difficult to reconcile since the volume expansivi ty d y = (l/V){dV/dT) is usual ly expected to be extremely smal l i n relat ion to the area expansivity, i.e. m a k i n g the identi f ication V = Ad, and àv « 0 these simple considerations i m p l y OA « —àd, i n contradict ion w i t h our results and the results of (Needham et al, 1988) which taken together show that upon add i t i on of cholesterol the change i n \àd\ is increased while the change i n |à^| is decreased. In order to interpret these unusual features of our experimental results, we propose a s imple , but speculative, model for characterizing the spat ia l d i s t r ibut ion of phosphol ipid and cholesterol molecules i n bi layer membranes composed of such l ip ids . W e then describe some experiments that are capable of test ing the model . We emphasize that we are presently unable to compare the ac tual magnitudes of ÙA and àd since we have no micromechanical measurements of à A i n the P O P C and P O P C : cholesterol samples used here for the measurements. Rather , we are t r y i n g to deal w i t h the comparison of the changes induced i n jà^l and \àj\ by cholesterol, i.e. the observation that |à<i| increases while \àA\ decreases upon the addi t ion of cholesterol. W e believe that this represents a real anomaly that must be explained i n terms of changes i n the geometrical d i s t r ibut ion of cholesterol i n the l i p i d bi layer as the temperature is varied. 2.5.4 M o l e c u l a r P a c k i n g Considerations. It is clear that some drastic over-simplif ication of molecular packing has been made i n re lat ing the membrane volume V to the product of membrane thickness d, as determined f rom < | 5 C D | > measurements using E q n 2.2 , w i t h membrane area A, as obtained from micromechanical mea-surements (Needham et al., 1988). A l t h o u g h A is unambiguously the sum of the projections of the areas of a l l the phosphol ipid and cholesterol molecules on the membrane surface, the quant i ty d is an effective phospholipid hydrophobic thickness (a distance approximately equal to the average separation of the glycerol backbones of the phosphol ipid molecules of the two leaflets of the membranes) . In wr i t ing V = Ad, i t is i m p l i c i t l y assumed that the cholesterol molecule maintains a constant depth i n the membrane relative to the glycerol backbone of the phosphol ip id molecule as the temperature and peptide concentration are varied. Another ques-t ionable assumpt ion , imp l i c i t i n neglecting changes i n ay relative to changes i n ÙA and a^, is that there are no temperature-dependent packing problems associated w i t h the different shapes of the phosphol ip id and cholesterol molecules. A l s o , the micromechanical measurements used to determine ÙA are performed on uni lamel lar vesicles under tension whi le the measurements of àd are performed on mult i lamel lar vesicles i n their re laxed state. A central feature of the model we now propose is that the average posit ion of the cholesterol molecules relative to the phospholipid-water interface is al lowed to vary w i t h temperature . W i t h this model , we are able to interpret qual i tat ively the observation that ÙA + àd ^ 0 in phospholipid-cholesterol mixtures i n terms of a non-negligible volume expansivity à y and the variat ion w i t h temperature of the smal l f ract ion of the cholesterol that is on average transferred outside the bi layer . 2.5.5 M e m b r a n e M o d e l For L ip id -Choles tero l M i x t u r e s . Suppose that the membrane is composed of Ni, phosphol ip id and Nc cholesterol molecules of average cross-sectional areas AL and Ac, and volumes Vi and Vc, respectively. T h e n , i f a fract ion / of each cholesterol molecule protrudes, on average, beyond a l ip id - i i xed reference point (e.g. such as the pos i t ion of the glycerol backbone w i t h i n the membrane) into the aqueous region (see F igure 2.5), we may write equations for the t o t a l membrane area A and volume V i n terms of the above quantities and the apparent phosphol ip id thickness ^ d: A = NLAL + NcAc, (2.4) and V = Ad-\- fNcVc. (2.5) It is then easy to show that the assumption of smal l p ro t rud ing cholesterol volume (fNcVc <. V) gives df " ^ NcVc ^^"^ ~ - ('-'^ A very rough estimate of df/dT may be made for j d y | < |à^ - | -Qd | f rom our measured values of àj and representative measurements of d ^ f rom micromechanical measurements (Needham et We assume here that Eqn 2.2 is valid. H2O headgroup_ ^ e g i o n Q Q Q Q Q Q Q ^ ^ c h y d r o p h o b i c reg ion QOÛQOQ-h p i d -c h o l e s t e r o l . , ' " ° } ^ ' ' mo lecu le i n t e r f a c e s (avg. posit ion) headgroup regi âroOœDaJOGODOODŒO H2O Figure 2.5: M e m b r a n e M o d e l for L i p i d - C h o l e s t e r o l M i x t u r e s . D i a g r a m showing a cholesterol molecule i n a phosphol ip id bilayer used for proposed theoretical model (see text ) . T h e cholesterol is de-p ic ted i n its average posit ion w i t h respect to the l i p i d water interface. Zc is the length of the cholesterol molecule hav ing area Ac] / is the f ract ion of the cholesterol molecule pro t rud ing f rom the hydrophobic inter ior ; and d is the hydrophobic thickness of the bi layer. al., 1988). T h e exper imental observation that the changes i n expansivity i n going f rom Bi to B2 corresponds to |Aà^| < |AQd| yields (for NL/NC = 7 /3 , VC/VL « 0.6 and ÙA+àd » -10-^/°C) df/dT « +0 .5%°C~^ . T h i s smal l displacement of the cholesterol molecules relative to the phosphol ipids , corresponding to about 0 .07A/°C should be detectable w i t h specially designed neutron dif fraction experiments, as described below. W e note that the increased protrus ion of cholesterol molecules f rom the membrane surface w i t h increasing temperature can be interpreted i n a n a t u r a l way as a consequence of the increase i n latera l pressure on cholesterol f rom the neighboring phosphol ip id molecules as the temperature i n increased. T h e exper imental observations could also be understood i n principle i f df/dT = 0 prov id ing that the excess volume associated w i t h the packing of mixtures of phosphol ipid and cholesterol molecules changes w i t h temperature such that à y w -|- w - 1 0 ~ " ' / ° C . It seems unl ikely that à y < 0 so that the interpretat ion i n terms of a non-zero value of df/dT is favoured. T h e mode l described above draws attention to the desirabi l i ty of correlating the results of N M R experiments w i t h those of micromechanical experiments such as those developed by Evans and his col laborators ( B l o o m et al., 1991; Needham et al., 1988). In relat ion to the studies reported here, micromechanical experiments on P O P C : c h o l e s t e r o l mixtures are planned ( E . E v a n s , personal communicat ion) but have not yet been carried out . Other measurements, such as X - r a y diffraction to determine the electron density var iat ion i n the bilayer, w i l l also be needed i n order to test the model just described. Espec ia l ly useful would be neutron diffraction experiments s imi lar to those previously carried out to determine the spat ia l d istr ibut ion of different segments of the acy l chains and polar headgroups of phosphol ip id molecules i n bi layer membranes ( B i i l d t et al., 1979; Zaccai et ai, 1979). These experiments exploit contrast methods using p a r t i a l l y deuterated molecules and would make i t possible to measure changes i n the relative posit ions of phosphol ip id and cholesterol molecules i n membranes. 2.6 C o n c l u d i n g R e m a r k s . In this paper, measurements of the or ientat ional order profile of the pa lmi toy l chains of P O P C have been used to explore several aspects of the hydrophobic thickness of P O P C . Increased average chain or ientat ional order < \SCD\ > was observed upon addit ion of 30 % cholesterol i n agreement w i t h many previous observations (see e.g. Laf leur et aL, 1990) and this was inter-preted quantitat ively i n terms of increased bi layer hydrophobic thickness d us ing a previously developed l inear relat ionship, E q . 2.2, between d and < \SCD\ >• T h e influence of amphiph i l i c polypeptides of different hydrophobic lengths on the average or ientat ional order of pure P O P C bilayers and those containing 30 % cholesterol was found to be i n qual i tat ive agreement w i t h the predictions of the "mattress model of pro te in - l ip id interact ions" (Mour i tsen and B l o o m , 1984). T h i s represents the first experimental check of the mattress model i n membranes containing cholesterol and serves to conf irm, at least qual itat ively , the u t i l i t y of E q n 2.2 for mixtures of phosphol ipids and cholesterol. T h e exper imental results were also used to examine the combined influence of the po lypep-tides and cholesterol on the or ientat ional order profile and thickness expansivity of the m e m -branes. W h e n the thickness expansivity was compared to publ ished area expansivity measure-ments of re lated, but not ident ica l , systems i t was found necessary to take into account details of the manner i n which l i p i d and cholesterol molecules are geometrically arranged (packed) i n the bi layer i n order to reconcile the different types of mechanical measurements. In part i cu lar , w i t h the present interpretat ion of the orentational order i n terms of bilayer thickness, i t is necessary to explain why the magnitude of the thickness expansivi ty is increased upon add i t i on of cholesterol while the area expansivity is decreased. In order to test whether the model pro-posed for this reconci l iat ion is correct, i t would be necessary to carry out other experiments -especially X - r a y and neutron diffraction measurements - on l ipid-cholesterol mixtures . T h e fact that cholesterol doubles the rate of thermal expansivi ty of the bilayer hydrophobic thickness may well have interesting consequences i n real biological systems: e.g. since perme-abi l i ty is a decreasing funct ion of bilayer thickness, therefore, presence of cholesterol implies a 2.6. Concluding Remarks. 39 more r a p i d phys i ca l response of the bilayer permeabi l i ty to changes i n temperature. T h i s could be bio logical ly advantageous by prov id ing a cell w i t h increased isolat ion from its environment at vulnerable t imes of lowered temperature when m a n y enzyme-related cel lular functions - whi ch also have a strong temperature dependence - become inactive. C h a p t e r 3 Vesicle E r u p t i o n s 3.1 C h a p t e r Overview ^. T h e analysis of Chapter 3 allowed comparisons to be made between the thickness expansivi ty measured using N M R and the area expansivity as obtained f rom micromechanical measure-ments . T h e use of N M R to estimate membrane mechanical properties i s , perhaps surprisingly, an unusual feature of the experiments just described. It has more often been the case that these two fields were pursued w i t h relatively l i t t l e overlap. T h i s approach is g iv ing way to one that is more inclusive of the many receiit advances i n our understanding of bi layer systems f rom the micromechanica l , thermodynamic , and spectroscopic persectives. In this vein we have chosen to inc lude here another example of N M R ' s usefuUness i n obta in ing a novel estimate of à A i n phos-pho l ip id systems which are s imi lar to those studied i n Chapter 3. T h i s work arose i n a n a t u r a l way through following-up observations of an unusual feature i n the spectra of phospholipids and cholesterol when these are mixed i n a rat io typ i ca l of of myel in . T h e picture developed f rom these experiments w i l l also be used to interpret a previously unexplained l ineshape feature k n o w n to accompany the addit ion of myel in basic prote in to phosphol ipid mixtures . W e now give a n expl ic i t overview of the results of this chapter. and ^^P N M R , and freeze-fracture electron microscopy, were used to study spontaneous vesiculat ion i n model membranes composed of P O P C : P O P S w i t h or wi thout cholesterol. T h e N M R spectra indicated the presence of a central isotropic l ine the intensity of whi ch is reversibly and l inear ly dependent upon temperature i n the L a phase, w i t h no hysteresis when cyc l ing be-tween higher and lower temperatures. Freeze-fracture microscopy showed smal l , apparently ^This chapter closely follows, with slight modifications, a previously published paper (Nezil et al., 1992). connected vesicles which were only present when the samples were frozen (for freeze-fracture) f rom an i n i t i a l temperature of 40-60 °C, and absent when the samples were frozen f r o m an i n i t i a l temperature of 20 °C. Ana lys i s of mot iona l narrowing was consistent w i t h the isotropic lines being due to la tera l diffusion i n - and t u m b l i n g of - sma l l vesicles (diameters « 50 n m ) . These results were interpreted i n terms of current theories of shape fluctuations i n large u n i l -amellar vesicles w h i c h predict that smal l daughter vesicles may spontaneously " e rupt " f rom larger parent vesicles i n order to expel the excess area created by thermal expansion of the bi layer surface at constant volume. A s s u m i n g that a l l the increased area due to increasing t e m -perature is associated w i t h the isotropic l ines, the N M R results allowed a novel estimate of the coefficient of area expansion i n mult i lamel lar vesicles ( M L V ' s ) which is i n good agreement w i t h micromechanical measurements upon giant uni lamel lar vesicles of s imi lar composit ion. Exper iments performed on uni lamel lar vesicles w h i c h had been placed upon glass beads con-firmed that àA determined i n this way is unchanged compared to the M L V case. A d d i t i o n of the h igh ly posit ively charged (extrinsic) myel in basic prote in ( M B P ) to a P O P C : P O P S system showed that membrane eruptions of the type described here occur i n response to the presence of this pro te in . 3.2 Introduction. N M R spectra for isotropic l iquids are characterized by complete mot iona l averaging of d ipolar , quadrupo lar and anisotropic chemical shift (tensor) interactions. For this reason, a l l struc-t u r a l l y / c h e m i c a l l y equivalent spins i n isotropic l iquids give rise to a single central peak which w i l l only be split by orientationally averaged indirect spin-spin interactions. B y contrast, the or ientat ional order of many l i q u i d crystals , such as the L ^ phase of phosphol ip id bi layers, gives rise to non-zero motionaUy-averaged values of the tensor interact ions. Nevertheless, i t is not uncommon for N M R spectra of l i p i d systems i n the L» phase to exhibit a lineshape character-ist ic of isotropic mot ions . Such N M R signals may often be a t t r ibuted to arti facts of the sample preparat ion such as produc t i on of smal l vesicles or micelles (e.g. by subject ing the sample to freeze-thaw cyc l ing) , s m a l l background amounts of deuterium (^H) nuclei i n the buffer, or chem-i c a l degradation of phosphol ip id molecules result ing i n an isotropic mot ion for some fract ion of the sample; alternatively the signal could be due to the presence of cubic phases ( C u l l i s a n d de Kru i j f f , 1979; T i l c o c k , 1986), which give rise to the same type of mot ional averaging of the ten-sor interactions as for isotropic l iquids . In any case, i f the intensity i n the isotropic l ine is smal l relative to the spectral features being studied, these effects are usual ly ignored as be ing insignif -icant . W e recently observed, and studied i n deta i l using N M R and freeze-fracture electron m i -croscopy, an isotropic l ine from a mixture of P O P C ( l -palmitoyl -2-o leoyl -phosphatidylchol ine) , P O P S ( l -palmitoyl -2-oleoyl -phosphatdylserine) and cholesterol. T h i s l ine had the unusual fea-ture that i ts intensi ty was reversibly and l inear ly dependent upon temperature: w i t h increased (decreased) temperature the intensity increased (decreased) w i t h no hysteresis apparent when cyc l ing between higher and lower temperatures. E lec t ron microscopy revealed the presence of connected vesicular structures which had some characteristics s imi lar to the vesicle shape fluctuations called " b u d d i n g " and "ves iculat ion" ( M i a o et al, 1991;Seifert et al, 1991; W o r t i s et al, 1991). B u d d i n g is the name given to the adiabatic and spontaneous " e rupt i on " of a satell ite vesicle f rom a parent vesicle when the satellite remains connected to the parent by a smal l tube of bi layer membrane. Successive satellite product ion m a y subsequently produce bead-l ike strings of vesicles. Such unusual shapes are also known to occur i n red b lood cells [e.g. see Deu l ing and He l f r i ch , 1977). T h e shape of a vesicle w i t h fixed surface area and enclosed volume, is de-termined by the m i n i m i z a t i o n of the tota l bending energy of the bi layer. A d i a b a t i c vesiculation may occur for a given l i p i d composit ion when the satellite vesicles produced have a curvature closer to the spontaneous curvature for those l ip ids as compared to their curvature i n the parent vesicle. M a n y factors determine whether vesiculation w i U occur inc lud ing temperature, buffer, and membrane composit ion , especially the presence of charged l ip ids . T h e m a i n purpose of this chapter is to i l lustrate the phenomenon and the use of N M R spectroscopy as a method which is complementary to more standard methods used to study membrane mechanical properties 3.2. latroduction. 43 ( B l o o m et ai, 1991). Observations w i l l also be presented w h i c h indicate that such membrane eruptions can occur upon addi t ion of a h ighly posit ively charged protein (myel in basic prote in , M B P ) to the bilayers studied here. In model systems the spontaneous product ion of smal l vesicles ( 0 (40 nm) ) has been pre-viously observed for hand vortexed dispersions of myelin l ip ids (excluding cholesterol) (Fraser et ai, 1986), mixtures of phosphatidylchol ine-phosphatidic ac id dispersed i n water (< 60 n m ) upon adjustment of p H (Gains and Hauser , 1983), and for mixtures of long-chain lecithins (acyl chain lengths > 14 carbons) mixed w i t h 20 m o l % short chain lecithins (6-8 carbons per acy l chain) (Gabr ie l and Roberts , 1984). However, none of these cases reported reversibil ity ^ ( in the thermodynamic sense) nor were adequate explanations provided for the phenomena. Other interest i n smal l and large uni lamel lar vesicles (i.e. S U V ' s and L U V ' s ) has been aroused by the possibi l ity of us ing such vesicles to encapsulate drugs for (potential ly) site-specific delivery to target organs ( B l u m e and Cevc , 1990; M a d d e n et ai, 1990), and several techniques have been developed for U L V fabrication such as by sonication of mul t i lamel lar vesicles ( M L V ' s ) ( H u a n g , 1969), the French pressure cell ( M i l n e r et ai, 1950; H a m i l t o n et ai, 1980), extrusion through polycarbonate membranes (Olson et ai, 1979; Barenholtz et ai, 1979; Hope et ai, 1985), and by other methods ( B a t z r i and K o r n , 1973; Bruner et ai, 1976; Szoka and Paphadjopoulos , 1978; M i m m s et ai, 1981). Spontaneous vesiculation i n h u m a n erythrocytes has also been observed for a variety of triggering mechanisms. L i m i t e d examples of these include incubat ion w i t h sonicated d imyris -toylphosphatidylchol ine vesicles (Frenkel et ai, 1986; Bi i t iko fer et ai; 1987), increased intracel -lu lar calc ium ( A l l a n and Thomas , 1981), A T P depletion ( L u t z et ai, 1977), and u p o n addit ion of a variety of amphiphiles (Hagerstrand and Isomaa, 1989) for exocytotic events; and w i t h , for instance, treatment of ghosts w i t h A T P (Birchmeier et ai, 1979) for endovesiculation. In general, the size of the vesicles produced i n these experiments seems to be i n the range 200 n m - 1 iim, which is too large to result i n the isotropic lines seen i n the experiments described here 'Addition of myelin basic protein was found to inhibit vesiculation in the case of myelin lipids (Fraser et al, 1986). (below). In order to understand the origin of an isotropic N M R absorption spectrum for b i layer systems we first discuss a part i cu lar example f rom deuter ium (•^H) N M R which we w i l l find useful and w h i c h , aside f rom certain specifics of the interact ion itself, is representative of other nuclear species as wel l . 3.2.1 Some Useful T h e o r y In first order per turbat ion theory, the interact ion between the electric quadruple moment of a deuterium nucleus and the (approximately) axia l ly symmetr i c charge d istr ibut ion of a carbon-deuterium ( C D ) bond gives a doublet N M R spectrum having a sp l i t t ing of 2u} given b y u = UQ{P2{cose)), (3.1) where 0 is the instantaneous, time-dependent angle between the C D bond direct ion a n d the external magnet ic field, P2{x) = (3a;^ - l ) / 2 is the Legendre po lynomia l of order two , and UQ/2ir w 125 k H z is the m a x i m u m value of u> i n the absence of any reorientational m o t i o n of the C D b o n d (Dav is , 1979). T h e average {) is taken over mot ions that are "fast on the N M R t imescale" , i.e. characterized by correlation times TQ satisfying M^TQ = I.OQTQ/5 « 1. For fast conformational and reorientational molecular motions about the local membrane normal n, w h i c h is the local axis of symmetry for the fast molecular motions i n fluid membranes, and slow changes of the angle /? between n and the external magnetic field, we obta in u = u)qScDP2{cos^), (3.2) where Sen = l/2{3œs'^9 — 1) is the or ientat ional order parameter for the carbon-deuterium bond and 6 is the instantaneous angle between the C D bond and n. T h e t ime dependence of is only slow on the N M R timescale for vesicles of large enough radius R that the combined effects of reorientation i n a m e d i u m of viscosity rj, and molecu-lar diffusion w i t h diffusion constant D, expressed i n terms of the correlation times Tr and respectively, satisfy the condit ion that MirTy > 1, where ( B l o o m et ai, 1978): ± = i + l = J ^ + f . (3,3) TV TV U iTTTjR^ ' T h e effective residual second moment M^r of the mot ional ly averaged N M R spectrum is and the average is taken over /3 G [0, TT] for the powder lineshape (Davis , 1983). A s the vesicle size is decreased, Ty decreases r a p i d l y so that eventual ly the above inequal i ty is violated and one no longer obtains the superposit ion of doublets normal ly associated w i t h E q n 3.2. For vesicles smal l enough that the opposite l i m i t , M^rTy •< 1, is satisfied, the ' quadrupolar splitt ings are mot ional ly averaged to a single isotropic, Lorentz ian l ine having fu l l w i d t h at h a l f - m a x i m u m 6 that is related to i ts spin-spin re laxat ion t ime T2 by the equation ( c f . A b r a g a m , 1961; B l o o m et al., 1978) TT^ = ^ = M2r7V = | ( W Q 5 C C ) V (3.5) where S is the f u l l w i d t h at one-half m a x i m u m of the experimental ly obtained (approximately Lorentz ian) l ineshape, and T2 is the spin-spin relaxation time (see, for instance, A b r a g a m , 1961; B l o o m et al., 1978). T h i s simple model w i l l be used to show that the isotropic lines noted i n our N M R spectra may indeed residt f rom smal l vesicles of the type we have seen us ing freeze-fracture electron microscopy. 3.3 E x p e r i m e n t a l Procedures . 3.3.1 Materia ls Perdeuteriated pa lmi t i c acid was prepared by standard methods i n our laboratory. A v a n t i Po lar L i p i d s ( A v a n t i Po lar L i p i d s , B i r m i n g h a m , A L ) used this m a t e r i a l to produce the single-chain perdeuteriated l - p a l m i t o y l - 2 - oleoyl-phosphatidylcholine ( P O P C - d a i ) used here; they also synthesized the undeuterated P O P C and P O P S used here. Cholesterol was purchased f rom S igma (S igma, St . L o u i s , M O ) . Headgroup deuteriated P O P C was prepared by condensing P O P A and deuteriated choline bromide (Merck , Sharp , and D o h m ) according to previously described methods ( R o u x et al., 1983). T h e nomenclature for the deuteriated choline headgroup is given: -{POÀ)~C"H2C'^H2N'^{CH3)3 = P C , where a , / î denote specific carbon atoms i n the headgroup. Spherical ly supported vesicles (SSV ' s ) consisting of P O P C - d a i : P O P S : Cholesterol (as above) as single bilayers supported upon spherical glass beads of .5 fim size were prepared according to the methods of (Bayer l and B l o o m , 1989). 3.3.2 Sample Preparat ion T h e sample preparat ion procedure was a sl ightly modif ied version of publ ished methods (Huschi l t et al., 1985). T h e modif icat ion s imply involved measur ing membrane components using dry weights rather than by t i t r a t i o n and , after addit ion of the buffer (800 / i l of 5 0 m M Hepes, l O O m M N a C l , and pH=7 .4 , using deuter ium depleted water f rom Sigma) , the sample then underwent four cycles of freezing i n l i q u i d nitrogen followed by w a r m i n g to room temperature (hereafter called freeze-thawing) to equi l ibrate solute d is tr ibut ion (Mayer et al., 1985). T h e samples were then centrifuged at 90,000 r p m and 25 °C for one hour i n a m i c r o B e c k m a n centrifuge, and the pellet was transfered to an N M R tube. A l l samples composed of P O P C : P O P S : c h o l e s t e r o l were i n the mole rat io 5:1:2.6. The P 0 P C : P 0 P S samples were i n the mole rat io 5:1. M y e l i n basic prote in ( M B P ) was prepared by extract ion from isolated bovine myel in using established meth-ods (Lowden et ai, 1966) and was stored i n the lyophi l l i zed form. The amount of P O P C - d a i used i n a sample was typ ica l ly about 30 mg. 3.3.3 Freeze-Fracture Electron M i c r o s c o p y Cryof lxat ion a n d Freeze etching Standard freezing methods were used (Steinbrecht and Z iero ld , 1987; Robards and Sleytr , 1985; and P l a t t n e r and B a c h m a n n , 1982). T h e sample was raised to a temperature of either 20, 40 or 60 "C on a Balzers (F i i r s tentum Liechtenstein) gold specimen holder, then frozen i n l i q u i d propane at about the temperature of l i q u i d N2. Freeze etching was performed i n a Balzers 400 Freeze-etch device. T h e sample, at a temperature of about 100 ° C , was cut w i t h a l i q u i d N2-cooled knife . T h e microtome was mainta ined at -170 ' 'C . T h e etch t ime for a l l preparations was 1 minute . T h e vacuum was mainta ined at about lO" '^ torr . Repl icat ion P l a t i n u m / c a r b o n was evaporated using an electroidc gun . T h e shadowing angle was 45°. T h e f i l m thickness was about 1.5 n m and was measured w i t h a quartz crysta l oscillator positioned i n the specimen plane. To increase the mechanical s tabi l i ty of the repl ica a carbon film of about 10 n m was placed on the sample. T h e replicas were floated on a 5% solution of sodium dodecyl sulfate. E l e c t r o n M i c r o s c o p y RepUcas were examined i n a J E O L 1200 E X scanning transmission microscope i n the conven-t i ona l transmiss ion mode using 80 k V accelerating voltage. 3.3.4 N u c l e a r Magnet ic Resonance T h e ^ H - N M R experiments were performed on a home-built spectrometer operating at 46 M H z for deuterons (Stern in , 1985). A quadrupolar echo sequence was used: 90a;-r-90y-r-echo, w i t h r =60 fis and a repeat t ime of 150 ms. T h e 90° pulse length was 4.0 fis. Spectra were recorded w i t h a 2 fis dwel l t ime and at least 50,000 transients collected for signal averagng . Signals were detected i n quadrature w i t h phase cyc l ing (Davis , 1979; Ranee and B y r d , 1983), and temperature was controlled using a B r u k e r model BV-TIOOO temperature controller. Phosphorus (^^P) N M R was studied using a Bruker W P - 2 0 0 spectrometer operat ing at 81 M H z . U p to 1000 transients were accumulated using a 15 fis 90° pulse l ength , a Is repeat t ime , and a 20 k H Z sweep w i d t h . Broad -band proton decoupling was used. 3.3.5 D e t e r m i n a t i o n of Isotropic Intensity T h e method is i l lustrated here for the case of headgroup deuteriated P 0 P C - d 4 i n P O P C : P O P S : c h o l e s t e r o In F igure 3.1 is shown a spectrum for this sample (lower spectrum) which has an isotropic com-ponent. In the upper spectrum the digit ized signal for the isotropic part has been removed manual ly by redig i t iz ing the centre points (by eye). The isotropic fract ion / is defined as the rat io of the area of the isotropic part removed divided by the area beneath the ac tual spectrum. 3.4 Results . 3.4.1 N M R Figures 3.2, 3.3, 3.4 show representative N M R spectra for the cases of headgroup deuteriated P 0 P C - d 4 and pa lmi toy i chain deuteriated P O P C - d s i using ^ H N M R , and phosphorus ^^P N M R , respectively, for P O P C : P O P S : c h o l e s t e r o l mixtures . T h e temperature at which each spectrum was recorded is noted on the left (right) side of the figure for increasing ( decreasing) temperature between consecutive spectra. T h e p r i m a r y feature to note is that i n each case an isotropic s ignal appears w i t h increasing ( decreasing) intensity for higher (lower) temperatures. The method described above (see F igure 3.1) for characterizing the fract ion / i n the isotropic part of the s ignal is relatively easily appl ied for the case of headgroup deuteriated sample (Figure 3.2), and for cases using ^^P N M R (Figure 3.3), as compared to the chain deuteriated sample (F igure 3.4), since there is less error i n defining the frequency range over which the isotropic part of the signal is found. T h e ^^P N M R spectra are characterist ic of l ip ids i n a J I J 1 I I I 1 1 1 1 1 I 1 1 1 1 1 L I , , , , 1 , , , , ^ , , , , 1 , 1 . . 1 - 2 0 - 1 0 ^ 0 , , , 10 20 Frequency, kHz Figure 3.1: Redigit izat ion of Isotropic Signal . N M R spectrum of headgroup-deuteriated P O P C - d 4 : P O P S : C l i o l e s t e r o l (5:1:2.6) m :m:m at 40 " C showing the presence of a central isotropic signal (a); and the appearance of the same spectrum when the central region has been digital ly removed (b) i n order to determine the fraction of the t o t a l spectral intensity which is i n the isotropic s ignal . T h e isotropic component of the spectrum m a y be represented as a superposit ion of two (Lorentzian) N M R signals of equal area, one due to each of the deuteriated carbonyl groups (see text ) . 60 40 30 21 °C 40 21 °C ~ r 1 1 1 1 1 1 1 r -20 - 1 0 20 requency, kHz Figure 3.2: Temperature-Dependent Isotropic Signals: a . Spectra obtained at various temperatures are shown for the case of headgroup-deuteriated P O P C - d 4 : P O P S : C h o l e s t e r o l by N M R (this figure); for P O P C : P O P S : C h o l e s t e r o l by ^ i p N M R (Figure 3.3); and for chain-deuteriated P 0 P C - d 3 i : P 0 P S : C h o l e s t e r o l (Figure 3.4). T h e molar rat io of these membrane constituents for aU cases was 5:1:2.6 respectively. The temperature at which each spectrum was recorded is shown on the left side of the figure for increasing temper-ature between successive spectra and on the r ight side for decreasing temperature between successive spectra. Th i s capt ion applies to this figure and each of Figures 3.3, and 3.4. -10 -5 0 5 10 Frequency, kHz Figure 3.3: T e m p e r a t u r e - D e p e n d e n t I s o t r o p i c S i g n a l s : b . F igure showing isotropic intensity i n ^^P N M R spectra. See caption of F igure 3.2 for details. Figure 3.4: Temperature -Dependent Isotropic Signals: c. Figure showing isotropic intensity i n N M R spectra. See caption of F igure 3.2 for details. bilayer structure (Cul l i s and de Kru i j f f , 1976; 1978). These spectra, and similar data for the case of the "^^P N M R , have been used to determine the isotropic fract ion and , i n Figure 3.5, this is p lotted versus the temperature for the various samples. A l l the da ta for this figure were obtained by ^^P N M R except the l ine label led b 15 2 5 3 5 4 5 5 5 6 5 T e m p e r a t u r e , °C Figure 3.5: Isotropic Fract ion Versus T e m p e r a t u r e . I. T h e isotropic fraction / of the tota l N M R spectral inten-sity is p lotted against the temperature T for various samples: P O P C : P O P S : C h o l e s t e r o l i n the mole rat io 5:1:2.6 (a,b,c); and P O P C : P O P S i n the mole rat io 5:1 (d,e). These samples also dif-fer w i t h respect to their deuteriation and i n whether or ^^P N M R was used to observe them: no deuter iat ion, by ^^P N M R (a); headgroup-deuteriated P 0 P C - d 4 , by N M R (b); chain-deuteriated P O P C - d a i , by ^ i p N M R (c); no deuter iat ion, by ^^P N M R (d); and chain-deuteriated P O P C - d a i , by ^^P N M R (e). T h e least-squares fits shown have slopes, i n units of 10~^°C"^, given by 3.2 ± 0.2 (a); 3.2 ± 0.1 (b); 2.1 ± 0.2 (c); 1.1 ± 0.3 (d); and 0.26 ± 0.03 (e). whi ch was obtained using N M R for the headgroup-deuteriated sample. In a l l cases there was found to be no significant difference between two measurements w h i c h were made at the same temperature for a given sample, independent of the recent thermal history i n the phase (i.e. no hysteresis). Therefore, for s impl ic i ty i n Figure 3.5, average values have been used when more than one measurement is made at a given temperature. T h e var iat ion i n the isotropic intensity between 20-50 " C was i n the range of about 1-10 %. T h e first th ing to note is that the response of the isotropic fract ion to variat ion i n the temperature is l inear as shown by the least squares fits (straight lines i n F igure 3.5.) T h e slopes df/dT are l isted i n the capt ion t o F igure 3.5. A n o t h e r feature is t h a t , except for sample a , a l l the samples have s imi lar values for / at the lowest temperature studied, converging to / = 1 % at about 20° C . T h e addi t ion of cholesterol to the P O P C : P O P S sample, as represented by cases of a , b , and c, is correlated w i t h increased values of the slope df/dT as compared to the cases d and e (no cholesterol). There also appears to be a somewhat pecul iar feature: df/dT decreases depending upon whether the pa lmi toy i chain is perdeuteriated, independent of the presence of cholesterol; e.g. i n F igure 3.5 compare d w i t h e (no cholesterol), or compare c w i t h either a or b (cholesterol present). T h i s effect is not seen when i t is the headgroup which is deuteriated (compare a w i t h b) . We believe that this result is l ike ly due to translocat ion of the p a l m i t o y i and oleoyl chains, known to be up to 2 0 % i n the P O P C - d a i prepared for these experiments (Lafleur et al., 1989), which could alter acyl chain packing i n the bi layer. A l l the cases represented i n F igure 3.5 were obtained w i t h M L V samples whose thermal histories inc luded a freeze-thawing stage. Before N M R was performed each sample was removed from a freezer (at about -10°C) and allowed to equil ibrate at r oom temperature for at least 12 hours. Thereafter , the equi l ibrat ion t ime at each temperature was about one hour before performing the N M R . In order to estimate the importance of the M L V nature of the samples as a contr ibut ing factor to the intensity of the isotropic s igna l , a chain-deuteriated sample containing P O P C - d 3 i : P O P S : c h o l e s t e r o l ( in the same proport ions as the other samples) was prepared on 0.5 ^ m glass beads as spherically supported vesicles (SSV ' s ) (Bayer l and B l o o m , 1989). It is k n o w n that these are uiulamel lar vesicles of precisely defined spherical shape w i t h an approximately 1 - 1 . 5 n m thick layer of buffer between the bead and the inner leaflet of a bi layer . Freeze-fracture electron microscopy was not possible o n this sample due to the presence of the beads. I n F igure 3.6 the isotropic fract ion versus temperature is p lo t ted for M L V and the S S V samples w h i c h were otherwise ident i ca l . F igure 3.6 shows that the response is again l inear 9 -_l 1 1 1 ^ p 5 15 2 5 3 5 ^ 4 5 5 5 T e m p e r a t u r e , C Figure 3.6: I s o t r o p i c F r a c t i o n V e r s u s T e m p e r a t u r e : I I F i g u r e 4 . T h e isotropic fraction / is p lo t ted as a funct ion of tem-perature for chain-deuteriated P 0 P C - d 3 i : P 0 P S : C h o l e s t e r o l when i n the form of single bilayers formed upon 0.5 /xm glass beads (a) (by N M R ) ; and i n the form of M L V ' s which have undergone four freeze-thawing cylcles (b) (by ^^P N M R ) . F i l l e d symbols mean decreasing temperature between successive measurements whi le open symbols mean increasing temperature. w i t h a slope w h i c h is about the same for bo th samples {i.e. (2.0 ± 0.2) x 10~^ " C " ^ for the M L V sample, b i n Figure 3.6; and (1.7 ± 0.2) x 10~^ " C " ^ for the U L V sample); however, the figure indicates that the U L V sample has an isotropic fract ion which is increased over that for the M L V sample by a positive constant. 3.4.2 Freeze-Fracture Microscopy In F igure 3.7 is shown a typ i ca l micrograph for P O P C : P O P S : c h o l e s t e r o l (5.0:1.0:2.6); the sam-ple had an i n i t i a l temperature of 20 °C before being frozen i n the l i q u i d propane. The fracture faces seen through the bilayers of the M L V ' s are as expected for samples which have previously undergone freeze-thawing cycles (Mayer et al., 1985) and are not unusual . T h e size d i s t r i -bu t i on of vesicles ranges from diameters of about 50 n m to several microns . A l s o note that smal l vesicles tend to appear singly and are more or less isolated f rom the M L V structures. A s imi lar micrograph w i t h no significantly different features was obtained for P O P C : P O P S samples wi thout cholesterol (data not shown). A t higher i n i t i a l temperatures (40°C - 60°C) the d is tr ibut ion of M L V ' s appears to be unchanged but a new feature is apparent which is typ ica l of the whole sample: l ong tube-l ike structures connected to vesicles are seen to extend from the outer bilayers. T w o examples are shown i n F igure 3.8 and 3.9. In F igure 3.8 is shown a higher power (100k magnif ication) view of a membrane "erupt ion" consisting of a vesicle w i t h a diameter of about 50 n m which is located at the end of a tube of about .5 fim i n l ength . In F igure 3.9 is shown a typ i ca l series of apparent ly connected, or at least l inear ly associated, vesicles. Close inspect ion of the smaller vesicles shows some fracture surfaces characteristic of M L V structure. It has been noted by others ( S i x l et al., 1984) that a low intensity isotropic l ine appears i n N M R spectra upon addi t ion of > 30 w t % M B P to a s imi lar system of l ip ids ( D M P C : D M P S exc luding cholesterol). W e have also observed this phenomenon for the P O P C : P O P S samples studied here , as was seen i n F i g u r e 1.4. T h e freeze-fracture microscopy shown i n F igure 3.10 for the addi t ion of M B P to a P O P C : P O P S (5:1) sample again indicates the presence of l ong bead-l ike strings of smal l vesicles; i n this case, even when the sample has an i n i t i a l temperature of on ly 20 " C before being frozen i n l i q u i d propane. T h e vesicles i n this case have a tendency to cluster together, as seen i n the upper left corner of the micrograph. T h e same result is found when M B P is added to the P O P C : P O P S : c h o l e s t e r o l sample of F igure 3.7 except that the c lumping effect is absent and , a l though strings of bead-like vesicles are seen, the lengths of these on average appear longer and have fewer vesicles contained Figure 3.7: E l e c t r o n M i c r o g r a p h o f P O P C : P O P S : C h o l e s t e r o l . A . Freeze-fracture electron micrograph for P O P C : P O P S : C h o l e s t e r o l (5:1:2.6)(m:m:m) showing typ ica l M L V ' s . Th i s sample was frozen in l iqu id propane f rom an in i t ia l temperature of 20 " C . The bar rep-resents 200 nm. Figure 3.8: E l e c t r o n M i c r o g r a p h o f P O P C : P O P S : C h o I e s t e r o l . B . Freeze-fracture electron micrograph for P O P C : P O P S : C h o l e s t e r o l (5:1:2.6)(m:m:m) showing a high-power v iew of an erupt ion or erupt ion- l ike event. The sample was frozen in l iqu id propane f rom an in i t ia l temperature of 60 "C. The bar represents 200 n m . Figure 3.9: E l e c t r o n M i c r o g r a p h o f P O P C : P O P S : C h o l e s t e r o l : C . Freeze-fracture electron microscopy for sam-ples of P O P C : P O P S : C h o l e s t e r o l (5: l :2 .6)(m:m:m). Th is micrograph shows a higher power view of an event typ ica l for samples cooled f rom higher in i t ia l temperatures. The in i t ia l temperature pr ior to cool ing for this sample was 40°C. The bar represents 200 n m . wi th i n them. F igu re 3.10: E l e c t r o n M i c r o g r a p h o f P O P C : P O P S : M B P . Freeze-fracture electron micrograph (for freezing f rom an in i t ia l tem-perature of 20°C) for a sample composed o f P O P C : F O P S i n the mo-lar rat io 5:1 wh ich has had about 50 wt% myel in basic protein ( M B P ) added to i t . T h e bead-l ike str ings of smal l vesicles characterist ic of this sample are absent in corresponding micrographs for s imi lar sam-ples wh ich lacked M B P (not shown but s imi lar to F igure 3.7. The bar again represents 200 n m . 3.5 D I S C U S S I O N T h e methods used here to determine the isotropic f ract ion / are exceedingly s imple. W h i l e the N M R establishes the presence of isotropic mot ions, this technique alone is incapable of determin ing the precise nature of the structures which might be associated w i th such a mot ion . However, certain points may st i l l be made on the basis of the N M R , data . F i rs t ly , the reversible nature of the isotropic intensi ty as a funct ion of temperature immediate ly rules out bo th the unwanted presence of D 2 O i n the buffer a n d / o r chemical degradation of phospholipids, as wel l as r u l i n g out a constant presence of micelles or S U V / L U V ' s formed i n the sample preparat ion , as possible explanations for the isotropic intensity. Secondly, the ^^P N M R clearly shows a bi layer signature which argues against any major presence of hexagonal ( H / / ) phase l i p i d orgaidzation (Cu l l i s and de Krui j f f , 1976,1978). A l s o , P S and P C l ip ids are known to be bilayer stabi l iz ing and they tend not to form non-bilayer phases (Ti l cock , 1985). It is conceivable that cholesterol could inc l ine the system towards such structures but the freeze-fracture microscopy argues against this interpretat ion since there is no evidence of cubic phases be ing present, nor is there evidence of inverted micelles. The only significantly different feature i n the micrographs w h i c h is temperature dependent is the presence of the apparently connected regions of smal l vesicles described above. It is wel l -known that cooling rates i n l i p i d systems of the type studied here, using a l i q u i d propane b a t h kept at approximately the temperature of l i q u i d ni trogen, are on the order o f about -10^ " C / s (Plattner and B a c h m a n n , 1982). Therefore, the cooling t ime required i n our experiments for the sample to go f rom the fluid to the gel phase is expected to be between 20- 60 ms . Since eruptions i n giant uni lamel lar vesicles have been typ ica l ly observed to have durations on the order of seconds and longer (personal observations of eruptions seen on video recordings made by E . Evans) i t i s , therefore, not surpris ing that the electron microscopy is able to detect the presence of vesicles which in i t ia l l y erupted at the higher temperature and then were, subsequently, "frozen i n " . T h e h igh resolution of the spectrum for the headgroup deuteriated sample allows a further check. Close inspection of the spectrum given i n F igure 3.1 suggests that the isotropic l ine seen there is actually a superposit ion of two Lorentz ian l ineshapes, as would be expected for m o t i o n a l narrowing of the two pairs of spectroscopically dist inct deuterons at the a and /3 positions of the choline headgroup. T h e predicted w i d t h , according to the model suggested i n the i n t r o d u c t i o n , may be determined. N o t i n g that the characteristic vesicle size produced has a radius on the order of i l « 25 n m then, using E q n . 3.3 w i t h 77 = 10"^ Poise as the viscosity of water, D = 5 x l 0 ~ * cm^/s as the diffusion constant ( B l o o m et al. , 1991), and a temperature T « 50°C, we find Tr « 40/xs and w 20^s , wh i ch gives ry « 13/is. A l s o , E q n . 3.4 m a y be used to determine Mir for the a and j3 carbon positions to obta in M^r = 3 .7xl0*s~^ and Af^^ = 6.2xl0''^s~^. These values for Ty,M^r,^T^^M^^ satisfy MirTy < 1. U s i n g E q n . 3.5 we can now predict the f u l l - w i d t h at one ha l f m a x i m u m , S, of the Lorentz ian lineshapes w h i c h would result f rom isotropic mot i ona l averaging of the a and j3 quadrupolar splitt ings a n d find: 6a = M2fTy j-K = 1.5 k H z and Sp = 260 H z . These values agree favourably w i t h the approx imate widths of 1.6 k H z and 380 H z for the a and /3 positions respectively, as measured d irec t ly off the isotropic peak i n F igure 1, suggesting that the isotropic N M R lines are consistent w i t h the vesicles seen us ing electron microscopy. In these experiments l ip ids move between anisotropic and isotropic structures reversibly w i t h temperature . If the s impl i fy ing assumption is made that a l l the extra membrane area induced by increasing the temperature goes into the isotropic structures, and i f the area per l i p i d is approx imate ly the same i n the lamellar and vesicular regions, then i t is easy to show that the coefiicient of areal expansion àj^ ( B l o o m et al., 1991) is related to the intensity of the central peak b y 1 dA df T h e d a t a of F i g u r e 3.5 for the P O P C : P O P S : c h o l e s t e r o l samples gives dfjdT « (2 - 3) X 10 -^ °C~^ which is remarkably close to the value of « 2 X 10~^ " C " ^ obtained by (Needham et al., 1988) for mixtures of D M P C and cholesterol. In any case, i t is known that the avai labi l i ty of excess area for large-scale t h e r m a l undulat ions i n L U V ' s can result i n an unstable vesicle surface which has a tendency to spontaneously erupt into satellite vesicles connected by microscopic umbiUcal tubes (Evans and Rawicz,1990). It should be kept i n m i n d that the l i p i d mixtures being compared have different molecular compositions and different mechanical forms: m u l t i -lamellar vesicles ( M L V ' s ) i n our measurements and giant uni lamel lar vesicles ( G U V ' s ) i n the micromechanical measurements (Needham et al , 1988). Nevertheless, we believe that the order of magnitude agreement between df/dT and ÙA is significant and indicates that the constraints imposed by the stacked lamellae of the M L V ' s do not signif icantly l i m i t this vesicular-type of area expansion. Unfortunate ly i n this case, the process of vesiculation is generally described for L U V ' s and we know of no theoretical description of budd ing or vesiculation occuring i n M L V ' s (where steric considerations may be important ) . T h e least squares fits i n F igure 3.5 show that the add i t i on of 30% cholesterol to bilayers composed of P O P S : P O P C increases df/dT by about 2 x 10-^°C~^ for b o t h the chain-deuteriated P O P C , f rom (0.26 ± 0.03) x 1 0 - ^ ° C - i to (2.1 ± 0.2) x 1 0 - 3 ° C - ^ and for the non-deuteriated P O P C , f rom (1.1 ± 0 . 3 ) x l O - ^ ^ C " ^ to (3.2 ± 0 . 2 ) x l O ' ^ ^ C ' ^ T h i s suggests that the eruptions occur more readi ly i n the presence of cholesterol than i n i ts absence. Th i s result is not necessarily expected o n the basis that the increased bending stiffness associated w i t h cholesterol add i t i on might be expected to inh ib i t the process of vesiculation by m a k i n g regions of higher curvature less accessible i n terms of energetics. However, i t may be that cholesterol somehow lowers the energy barr ier to vesiculat ion, perhaps due to its abi l i ty to rap id ly " f l ip- f lop" between the two leaflets of the bi layer . Th i s could allow for l oca l fluctuations of increased curvature so prov id ing a focus for the erupt ion event. A n o t h e r question concerns whether the l i p i d composi t ion is identical i n bo th the parent and the daughter vesicles. For instance, considerations of l i p i d po lymorphism would preferentially locate the (charged) P O P S i n vesicles of higher curvature compared to P O P C . The presence of M B P m a y also influence the l i p i d d i s t r ibut ion . In the case considered i n F igure 3.10 the ves iculat ion may by due to M B P ' s expected tendency to associate preferentially w i t h negatively charged l ip ids (Chiefetz and Moscarel lo , 1985; P a l i and H o r v a t h , 1989), such as P O P S (Boggs et al., 1977; S m i t h and M c D o n a l d , 1979), possibly result ing i n perturbations f rom ideal m i x i n g of the l i p i d s present a n d , therefore, permi t t ing a local ized var iat ion of the bulk l i p i d composit ion which cou ld promote vesiculation. However, charge of the l ip ids is expected to be only one of m a n y factors (buffer, p H , etc.) which need to be studied i n association w i t h vesiculation effects. F i g u r e 3.6 suggests that df/dT « ( 2 . 0 ± 0 . 2 ) x I Q - ^ ^ C " ^ i n the P O P C - d 3 i : P O P S : c h o l e s t e r o l samples, independent of whether these are M L V ' s or L U V ' s on glass beads. However, there is s t i l l a constant difference i n / between these two samples which needs to be expla ined . Unfortunately , the difference i n the t h e r m a l histories of these two samples (the M L V sample underwent 4 feeze-thawing cycles i n the i n i t i a l sample preparation) does not permit definitive comments t o be made regarding the apparent relative increase i n the absolute intensity of the isotropic peak for the L U V sample; i t m a y be that stresses associated w i t h the freeze-thawing procedure do not relax on the t ime scale of about 12 hours which was used as an equi l ibrat ion t ime i n these experiments. 3.6 C o n c l u d i n g R e m a r k s . T h e work described here shows that some l ip ids i n the M L V systems studied undergo a temperature-dependent and reversible change i n the degree of mot iona l averaging of their N M R spectra, consistent w i t h spontaneous vesiculat ion - or the M L V analogue of this - occurr ing i n response to changes i n temperature. T h e novel method i l lustrated here for est imating the coefficient of area expansion f rom N M R measurements gives results i n agreement w i t h ex ist ing microme-chanical measurements for ÙA (Needham et al., 1988) i n s imilar systems. A l t h o u g h we have chosen to i l lustrate these effects w i t h a rather specialized ternary l i p i d system it should be made clear we believe this phenomenon to be common to many l i p i d systems and has probably been observed i n passing, but not interpreted, by spectroscopists before now. M u c h work is presently being done to c lari fy the physics under ly ing 3-dimensional membrane conformations ( L i p o w s k i , 1991; Wor t i s et al., 1991; Seifert et al., 1991; M i a o et ai, 1991; Evans and R a w i c z , 1990; M u t z and Hel f r i ch , 1989; and Sackman et al., 1986). The significance of spontaneous eruptions of the type described here remains to be demonstrated for the larger communi ty interested i n membranes - especially the biological and medical side. In this regard, the add i t i on of the highly posit ively charged M B P to the P O P C : P O P S sys-t em has been inc luded to i l lustrate the point that membrane eruptions/vesiculat ions can occur i n response to the presence of a prote in . T h e potent ia l biological importance of proteins inf lu-encing the erupt ion process should not be underest imated: the possibi l i ty of cel lular (genetically determined) control of eruptions, a lthough i n present experimental terms h i g h l y speculative, is a worthwhi le consideration even at the outset of emerging experimental programs to study these events. For example, the l oca l in i t ia t i on of surface eruptions i n bi layer subsystems w i t h i n the cell could contribute to our understanding of such things as ceU-ceU contacts and transport of cel lular materials . C h a p t e r 4 Future Direct ions : Relaxat ion-Spectra 4.1 Overview ^ Close inspect ion of the d a t a i n F igure 2.1 indicates a change i n the shape of spectra upon add i -t i o n of integral polypeptides, especially evident for the addi t ion of P j e to the P O P C : C h o l e s t e r o l bilayer (B2). ^ In Chapter 2 we suggested these changes were due to effects which the integral peptides have upon the or ientat ional order of the acy l chains. T h i s is not , however, the only conceivable explanat ion . We wiU discuss i n this chapter whether or not these apparent ordering effects, correlated w i t h the add i t i on of peptides, could arise from artifacts due to or ientat ion-dependent re laxat ion distort ing the spectral shape d u r i n g the t ime - a b o u t 100 / i s - necessary to aquire a quadrupolar-echo spectrum. We w i l l f ind t h a t , while there are strongly or ientat ion-dependent re laxat ion effects due to the peptide , a correction method we have developed permits separation of the dynamic versus the ordering effects. Relaxat ion-spectra are novel and their use for interpret ing dynamics i n the systems studied here is l imi ted . T h e chapter ends w i t h a short discussion which carries these analyses to a l i m i t e d conclusion ( in the present context) and suggestive of directions for further experiments. T h e spectral-correction procedure which we now discuss is an empir i ca l method of general u t i l i ty i n ana lyz ing N M R relaxat ion phenomena i n l iquid-crystal l ine systems for which the ^ H - N M R spectra are inhomogeneously broadened. T h e analysis is theoretically justif ied for cases where the t o t a l spectral intensity of the system, at each frequency, may be considered to be a superposit ion of spectral intensities from several subsystems, each of which independently ^The CMly parts of this chapter are a slightly modified version of part of a previously published paper (Nezil et al, 1991). 'We will continue to use the notation developed in Chapter 2 for describing the various combinations of lipids and polypeptides. undergoes exponential re laxat ion. It i s , otherwise, of empir i ca l use i n construct ing b o t h a "re laxat ion spectrum," which compares relaxation as a funct ion of frequency across the ^ H - N M R spectrum, and a theoretical spectrum corrected for spectral d istort ion caused by re laxat ion of the quadrupolar echo at a non-uni form rate across the spectrum. T h e method and its usefulness w i U be i l lustrated for re laxat ion d a t a acquired for the integral pept ide - l ip id systems of C h a p t e r 2. The method has also been used to test theoretical predictions concerning the dependence of re laxat ion rates upon quantities such as the or ientat ional order parameter of the carbon-deuterium b o n d , 5cD> a n d / o r the angle /3' between the bilayer n o r m a l and the external magnet ic field (Nez i l et al., 1991). D e u t e r i u m N M R of l i p i d bi layer systems commoiUy results i n inhomogeneously broadened spectral l ines. T h e present work has, i n the m a i n , been developed for such cases as a too l to do two things: f irstly, to al low us to construct theoretically correct spectra i n situations where relaxation effects are sufficiently strong and frequency dependent that they distort spectra acquired by quadrupolar echo ^ H - N M R experiments; and , secondly, as a method for describing orientation-dependent re laxat ion effects. W h i l e the latter part of this chapter concerns i tsel f w i t h some interesting results for re laxation spectra acquired for pept ide - l ip id systems, the complex nature of these systems is prohibit ive i n terms of extensive analysis , and the results must therefore be considered pre l iminary , not definitive. T h e novelty of the simple methods developed here warrants this presentation as an example of their use. 4.2 N u m e r i c a l M e t h o d s . The l i n e w i d t h of an inhomogeneously broadened ^ H - N M R spec t rum, w i t h spectral intensity f{i/) at frequency i/, is (by definition) due to differences i n the resonant frequencies of i n d i v i d u a l spins but not t o interactions between equivalent spins. A n equ i l i b r ium system described by f(v) can therefore be considered a collection of independent subsystems,denoted by the index i, which each contribute spectral intensity / , ( i / ) to the t o t a l spectral intensity. For ^ H - N M R powder spectra of l ip ids in a fluid b i layer , the quadrupolar spl i t t ing of a deuteron depends u p o n only two things: the value of SCD which characterizes spectroscopically dist inct deuterons; and the angle 13', already defined, which may have one or two values for a given value of w and 5 C D (see A p p e n d i x A ) . Therefore, the range of subsystems i contr ibut ing to the t o ta l spectral intensity at a given frequency extends over each value of ^ C D ? and over one or two values of /9 for each of the values of 5 C D • To inc lude re laxat ion , we consider only spin systems characterized by exponential re laxat ion towards e q i i i l i b r i u m at each frequency for each subsystem i at that frequency. In this case, the time-dependent spectrum, f{y,t), is a superposit ion of exponentials at each value of v, and the deviat ion f rom f{u, oo) (equil ibrium) m a y be wr i t t en : F{u, t) = f{u, t) - f{u, oo) = f; Bi{u) e-^lTi{^) (4.1) »=i where Bi{v) is the change i n spectral ampl i tude for the i * ' ' subsytem, after per turbat i on , f rom i ts e q u i l i b r i u m value; T,(i /) may represent either the spin- latt ice relaxation t ime , T\, or the spin-spin re laxat ion t ime , T2, for the i * ' ' subsystem at the frequency u; and M is the number of subsystems contr ibut ing to the spectral intensity at frequency v. In an N M R experiment the frequencies and measurement times are discrete and E q . [ 4.1] becomes: n^hh) = '^""'^ j = h...N k=l,...L (4.2) «•=1 where the tk's are times between the perturbat ion f rom equ i l ibr ium and the aquisit ion of the exper imental spectra i n a re laxation experiment. B y prescribing the M values of Tj(i / j ) a priori to be fixed constants spanning the reasonably expected range of relaxation times then, for each fixed i/j, E q . [ 4.2] is a system of L equations for the M unknown 5, ( i / j ) ' s . For P O P C - d a i , the number of subsystems, M, theoretically contr ibut ing at a given frequency is at most 30 b u t , i n order to provide a good set of relaxation times for T,-, we usual ly take M ~ 100 or 200. For instance, i n one of the systems studied, Ti{uj) was assigned values at 10 fis intervals from 10 to 2000 us. In the fol lowing experimental section, at each frequency 1/ we find a solution of E q n 4.2 for the re laxat ion functions Bi{vj), i = l , . . . A f , usually composed of one to three isolated de l ta functions, w h i c h is a least squares fit to the spectral amplitudes obtained f rom a re laxat ion series of spectra. T h e formulat ion is general and i t is possible to construct spectra f rom other classes such as piecewise-constant or smooth ( W h i t t a l l and M a c K a y , 1989). B o t h the nonnegative least-squares a lgor i thm ( N N L S ) (Lawson and Hanson , 1974) and l inear programming ( L P ) techniques (Gass , 1969) give solutions of the required f o rm. W e use N N L S here. In our N M R experiments we coUect da ta for N = 2048 frequency po ints ; and the solution to E q . [ 4.2] is then determined for that subset of these points which contains the spectral in format ion . T h e s tat i s t i ca l relevence of f i t t ing to a sum of exponentials is a complex prob lem outside the scope of the present discussion. Some aspects of this topic are discussed w i t h respect to N N L S elsewhere ( W h i t t a l l and M a c K a y , 1989). T h e fact that most of the 5 , ( i ' j ) ' s are zero is a property of the N N L S a lgor i thm. To parametrize the relaxation funct ion Bi(i/j), i= 1 , . . . M , at each frequency i/j, we choose the weighted harmonic average re laxat ion t i m e , Teff(i'j): where Tet[{j/j) may, for instance, refer to the T i - r e laxat i on t ime , TiefcÇuj) ( s imi lar ly for Ti^-or T2-relaxat ion t imes) . P l o t t i n g T~^{vj) as a function of frequency creates a "re laxat ion spec t rum" of re laxation rates. Other characteristics such as the first moment , least upper b o u n d , degree of smoothness, or a plot of the relaxation funct ion for every frequency may be examined as required. T h e frequency spectrum at zero t i m e , free of distort ion due to re laxation dur ing the receiver dead t i m e , i s : M n ^ i , 0 ) = ^ 5 . ( 1 / , ) j = l,...N. (4.4) «•=1 In the fo l lowing examples, we examine b o t h the trends i n characteristics of the relaxation spectrum w i t h frequency, and the frequency spectrum at zero t ime . (4.3) 4.3 Relaxat ion in P e p t i d e - L i p i d Systems. 4.3.1 E x a m p l e : O r d e r i n g Effect of P i e in Bi layer B 2 . In. F igure 4.1 is found the ^ H - N M R spectra for bilayer B i (a); bi layer B2 (c) and for bi layer B2 w i t h the (mismatched) peptide P16 added (e) for the quadrupo lar echo occurring at 120^s. a ^—-b c ^ e ^ -60 -40 -20 0 20 40 60 F r e q u e n c y , kHz F i g u r e 4.1: N M R Spectra Corrected For Relaxat ion Effects. ^ H - N M R quadrupolar echo spectra w i t h r = 60/is recorded at T = 25C for mult i lamel lar dispersions of P O P C - d g i (a); P O P C - d a i plus 30 m o l % cholesterol (b,c); and P 0 P C - d 3 i : C h o l e s t e r o l : P i e i n the molar ratios 6.0:2.6:0.3 (d,e). Spectra c and e are experimental spec-t r a . Spectra b , and d are the derived spectra for c and e respectively, after correction for T'2-relaxation effects occurr ing i n the t ime 2 r be-fore the echo is recorded. T h e dashed lines are arb i t rar i ly drawn at 16 k H z to a id v iewing . T h e spectra label led b and d i n this figure are f itted spectra which w i l l be discussed below. C o m p a r i s o n of the spectra w i t h and without P i e clearly shows a difference between quadrupolar splittings at larger frequencies, which we have tentatively at tr ibuted to the influence of the peptide. Determinat i on of the smoothed orientational order profiles as i n Chapter 2 shows the change i n i^cD upon addi t ion of peptide to the P O P C - d a i i C h o l bi layer to be between —13% at carbon 15 and - 2 0 % at carbon 11 (see F igure 2.2). F igure 4.2 shows a subset of the Fourier transformed F I D 's ( r < 100/is) for the P O P C -d 3 i : C h o l : L i 6 sample, whi ch indicates frequency-dependent re laxat ion: the larger spl i tt ings de-cay faster t h a n the smaller spl i t t ings . T h e corresponding plot for P 0 P C - d 3 i : C h o l wi thout J I 1 1 1 I I I 1 1 1 1 I I I I 1 I 1 I I J I I i I 1 1 L - 6 0 - 4 0 - 2 0 0 20 40 60 F r e q u e n c y , kHz Figure 4.2: R e l a x a t i o n E x p e r i m e n t : P i i n B 2 . Series of relaxation spectra for the sample P 0 P C - d 3 i : c h o l e s t e r o l : L i 6 used as the input data (F(t',-,ijk) i n E q n 4.2) i n the construction of the re laxat ion spectrum and the theoretical spectrum at < = 0. T h e t ime r between the i n i t i a l and refocussing pulses of the quadrupolar echo pulse sequence is l i s ted at the left of the figure. Note that relaxation is occurring at a faster rate for larger spl itt ings t h a n for smaller spl itt ings. peptide (not presented) shows a s imi la j frequency dependence which is , however, qual i tat ive ly different as w i l l be discussed below. Frequency dependent r 2 - re laxat ion has been observed i n D P P C - d a i (B loom and S t e r n i n , 1987) and i n other l ip ids (Per ly et ai, 1985) and it should be obvious that such or ientat ion-dependent behavior can result i n significant distort ion of the ac tual frequency spectrum (Speiss and Si l lescu, 1981). Therefore, the question: do the apparent effects seen i n the spec trum l e above reflect " true changes" i n the order of the prote in - l ip id system or are these effects manifestations of spectral d istort ion due to frequency dependent relaxation which has already occurred at the t ime the quadrupolar echo is recorded? To approach this question, for each spectrum i n the re laxat ion experiment series,the first moment was calculated and these values were then l inear ly extrapolated as a funct ion of 2 r to r = 0. T h e results of this extrapolat ion are quoted i n Table 4.1 as M^^*'^ for samples B2 and B 2 P i 6 - Table 4.1 also contains s imi lar data for the other samples of Chapter 2 to be discussed shortly. B y this measure, there is seen to be a 10% decrease i n the extrapolated first moment B i B1P16 B1P24 B2 B2P24 B2P16 M f ^ " - k H z k H z M ^ ^ k H z 48.5 ± 0.9 47.4 ± 0.6 52.6 ± 0.5 77.5 ± 1.0 74.4 ± 0.5 68.7 ± 1.2 51.1 ± 0.5 46.7 ± 1.0 55.3 ± 0.5 75.3 ± 0.5 74.9 ± 1.0 67.2 ± 0.5 49.8 ± 0.7 47.1 ± 0.8 54.0 ± 0.5 76.4 ± 0.8 74.7 ± 0.8 68.0 ± 0.9 Table 4.1: R e l a x a t i o n o f F i r s t M o m e n t . Table showing the first moments: M f * ' ' , obtained by extrapolat ion of A f 1 as a funct ion of r to r = 0 for a series of re laxation spectra; A f f , obtained by tak ing the first moment of the calculated spectrum which is corrected for orientation-dependent relaxation effects; and Aff^*, which is the ar i thmet i c av-erage of Afi^' ' ' ' - and A f f u p o n add i t i on of Lie to the P 0 P C - d 3 i : C h o l bi layer. Huschi l t et a/ . , in a s imi lar system but i n the absence of cholesterol,show that such an ordering effect is not observed i n the first moment (Huschilt et al, 1985). T h e results here and i n (Huschilt et al., 1985), are consistent w i t h the "mattress mode l " of M o u r i t s e n et al. (Mour i tsen and B l o o m , 1984; Ipsen et al, 1990), as discussed i n Chapter 2. However, we now emphasize that the apparent changes seen i n the spectra of F i g u r e 4.1 for addi t ion of Pie are subtle and the ad hoc method of extrapolat ing the first moment may be questioned. A more satisfactory demonstrat ion of the influence of the peptide on the orientational order parameter is provided by the N N L S fit described above. T h e zero t ime spectrum ( F ( i / j , 0 ) of E q n 4.2) is p lo t ted i n Figure 4.1 for P O P C - d a i : C h o l {B2 , b) and for P O P C - d s i : C h o l : P i 6 (B2P16, d). Direct v i sua l comparison of the two spectra immedia te ly indicates a residual difference i n the spectral shape after correction for relaxation re lated spectral d is tort ion , which we now just i f iably a t t r ibute to an ordering effect of the peptide. T h e first moment calculated direct ly f rom F{uj,0), M f , is also given i n Table 1, and this demonstrates a change i n i l / f ' o f —11% upon add i t i on of the peptide, consistent w i t h the change i n M^^*''^ already discussed. A s an i l lus t ra t i on we may tentatively characterize the spin-spin relaxation i n F igure 4.3 by p l o t t i n g the relaxation rate T^lfi against frequency for P O P C - d a i i C h o l w i t h pept ide P i e (crosses) and wi thout P i e (circles). (We w i l l give a more complete representation of T2 , e / / below.) T h e cutoff frequency i n this plot is determined by the low signal to noise ra t i o for data at larger frequencies. W i t h o u t peptide i n the membrane , the central part of the spectrum relaxes faster t h a n the extremeties and , excluding the m e t h y l group, this effect is roughly l inear , w i t h a slope of m = - ( 2 . 5 ± 0.2)xl0~^, such that r 2 « 200/xs centrally and r 2 « 350/is at larger frequencies. W i t h the addit ion of L i e , the basic l inear features of the plot are the same but now the slope, mpgp = (3 .7±0 .2 )x l0~^ , has changed sign. T h u s r 2 is now shorter for larger frequencies and longer centrally. The range of T2 values across this re laxation rate spectrum is roughly the same as i n the absence of P i e . F r o m these results i t immediate ly follows that a model invo lv ing at least two motions is necessary to expla in the effect of the peptide. To summarize , we have demonstrated that the add i t i on of the Lie peptide to the membranes composed of P O P C : C h o l i n the molar proportions 6.0 : 2.6 produces two effects: f irstly, there is a systematic decrease i n acyl chain or ientat ional order down the sn-1 chain and , secondly, a systematic change i n r 2 across the spectrum. A l t h o u g h these two effects are superimposed at the t ime of the quadrupolar echo, they may be separated by the technique described here. O 4 S 12 16 20 24 F r e q u e n c y , k H z Figure 4.3: F r e q u e n c y - D e p e n d e n t R e l a x a t i o n R a t e : P i e i n B2. T h e re laxat ion rate,T^gjf, is p lotted as a funct ion of frequency for P 0 P C - d 3 i : c h o l e s t e r o l (o) and for P 0 P C - d 3 i : c h o l e s t e r o l : P i 6 (+) . In this figure the left ha l f of the fuU spectrum has been reflected onto the right hal f and the average value of the two points then plotted against frequency. T h e sol id lines indicate least square fits of the d a t a to straight l ines. 4.3.2 Re laxat ion -Corrected Spectra for B 1 / B 2 ± Pept ides . In Figures 4.4 and 4.5 these experiments are extended for bi layer B i and B 2 , respectively, for the other combinations of match ing and mismatching discussed i n Chapter 2. T h e figures c learly show that the conclusions of Chapter 2 are unchanged after correct ion for spin-spin re laxat i on , though i t would appear that the ordering effects seen before correction are s l ightly reduced after the correction. So far we have considered re laxat ion effects only as a "di f f lctdty" to - 3 0 - 2 0 - 1 0 O 10 F r e q u e n c y , kH; 20 30 F i g u r e 4.4: N M R Spectra Corrected for Orientat ion-Dependent r 2 -Relaxat ion : Bi layer B i . •^H N M R spectra are given for the sample B i (sol id l ine ) , B1P24 (dou-ble l ine ) , and B i P i e (dashed l ine) . These spectra indicate t h a t , even after correction for orientation-dependent sp in - sp in relaxation (see t ex t ) , there are residual spectral differences w h i c h can be interpreted as conformational-ordering of acy l chains due to the add i t i on of the peptides. T h e short peptide (P ie ) is seen to be s l ightly too short for this bilayer while the l ong peptide is s l ight ly too long . be resolved i n order to interpret other, more interesting, results . B u t the re laxat ion studies i I I I I I I L F r e q u e n c y , kHz Figure 4.5: N M R Spectra Corrected for Orientat ion-Dependent T2-Relaxat ion : Bi layer B 2 . N M R spectra are given for the sample B2 (cholesterol present, sol id l ine ) , B2P16 (double-line), and B2P24 (dashed l ine) . S imi lar ly to F igure 4.4, these spectra indicate t h a t , even after correction for orientation-dependent spin- sp in re laxat ion (see text ) , there are resid-u a l spectral differences which can be interpreted as conformational-ordering of acyl chains due to the add i t i on of the peptides. In this case addi t ion of the long peptide (P24) is seen to match the bilayer hydrophobic thickness while the short peptide (P ie ) is too short. undertaken here are interesting for their own sake and we w i l l now consider these effects i n more detai l . 4.4 Orientat ion-Dependent Relaxation. Per turbat i on theory of re laxat ion i n l i p i d systems is h igh ly model-dependent, through the corre-la t i on funct ions, ^ ( r ) , associated w i t h the molecular fluctuations responsible for the re laxat i on (for example , see Jeffrey, 1981; Seelig and Seelig, 1980). It has been established that i m p o r t a n t motions affecting re laxat ion of deuter ium nuclei on phosphol ip id chains i n l i q u i d crysta l l ine bilayers include motions which are fast on the ( N M R ) timescale of 10~® s, i . e. TC < T M ^ 10~* s, usually associated w i t h conformational reorientations of the chain (Seelig and Seelig, 1980); and also slow mot ions , TC >- TM, possibly due to la tera l diflFusion of the l ip ids along curved surfaces ( B l o o m and Stern in , 1987). Therefore, to model such systems one generally needs to consider the complex anisotropic environment; angular excursions of the acy l chain a n d con-straints u p o n th is ; the d i s t r ibut i on of vesicle sizes ( in M L V systems such as those presented here); and ordering effects of membrane constituents such as, i n the cases we have been consid-er ing , cholesterol and proteins. T h e orientation dependence predicted by any such mode l can be experimental ly tested and the method we have developed here for parametr iz ing re laxat ion may i n pr inc ip le be used to test such orientation-dependent effects i n a more thorough way. A s noted elsewhere, the method most commonly used to study orientation-dependent re laxat ion rates usual ly measures these for only certain angles using single crystals (Tang et al., 1980) or oriented l i p i d samples ( l iquid crystals) ( B o n m a t i n et ai, 1990; Auger et al., 1990; J a r r e l l et al. 1988). In the case we wish to consider here, that of perdeuterated chains and their result ing N M R spectra when peptides are added to the system, we are faced not only w i t h the diff icul-ties associated w i t h many overlapping Pake doublets, but also w i t h the added compl icat ion of changing order parameters. These features greatly l i m i t our our interpretive abil ity. In the fol lowing, we present a s imple approach which clarifies these difficulties. In the simplest p ic ture , for a stat ionary d is tr ibut ion of frequencies (i.e. equi l ibr ium) and assuming a Gauss ian pliase d i s t r ibut ion , then i n the short correlation t ime regime {M^T^ 1) the A n d e r s o n Theory allows us to write for the re laxat ion t ime Ti, T^^ = M2TC, where TC is the correlation t ime for the motion and M2 is the contr ibut ion to the second moment associated w i t h the spin-dependent interactions that are modulated by the mot i on . Suppose that a new mot i on is introduced so that T2 T î " ^ T a " If this m o t i o n influences a part of the spin-dependent interactions having a second moment AM2 then = AM2TC (4.5) where AM2 = (Aa;)^. F r o m A p p e n d i x A , we may wr i te the quadrupolar sp l i t t ing 2a; = 2irAu so that u = uqScDi^cos'^P' - l ) / 2 (4.6) where U>Q = 2Tn'Q. Equat ions 4.5 and 4.6 suggest that contributions to A(T2~^) m a y be p ic tured i n terms of changes i n w, i.e. OJ — > u) + Au. These may be due to changes i n the loca l or ientat ional order {SCD — * SCD + ^SCD)^ which we w i l l ca l l mechanism A , a n d / o r changes i n the or ientat ion of the local surface n o r m a l relative to the magnetic field direct ion (i .e. f3' —>^ p' -h A / ? ' ) , mechanism B : Au = "^{AScDi^cos^P' - 1) + SCDI-^X^COS-'P' - l ) ]A/3 ' } . (4.7) If the changes i n SCD a-nd j3' are uncorrelated, then the orientation dependence of T j "^ may be wr i t t en i n the form T2-' = {Ti')o + A{T,-'). T h e n , us ing E q n 4.5, ^ = ( ^ ) o + A M 2 r c = ( Â ^ r c = ( ^ ) o + A ( ^ ^ ^ ^ ^ ) 2 - H W / 3 W ^ ^ ' (4.8) where we have defined A = U;1{ASCD)H''^ (4.9) and B = liK^^^l (4.10) T h u s , i n this v iew, TQ^^ and T(?^ are correlation times associated w i t h each of mechanisms A and B . Examples of these two mechanisms are depicted i n F igure 4.6. Exaggerated Curvature (A;S' Ra 0) Figure 4.6: T2 R e l a x a t i o n : ASCD v s . A/i,. T w o possible l i p i d configurations are shown i n order to depict sepa-rate contributions to T2 due to changes i n the order parameter when A / 3 ' = 0 ( A ) , and due to changes i n the angle /3' between the b i -layer normal h and the magnetic field H when ASCD = 0 ( B ) . In A the changes i n SCD may, for example, be considered to be due to inclusion of mismatching integral peptides i n the bi layer . In B the changes i n 0' may, for example, be due to diffusion of l ipids i n regions of high curvature. 4.4.1 Example :Headgroup-deuter iated D P P C In the case where SCD is constant i n E q n 4.8, so that only mechanism B contributes to the re laxat ion , we have ^ = (^^)o + 5 . i n 2 / ? W / 3 ' (4.11) T w o mechanisms have been proposed for such an orientation dependence of T2: cooperative motions i n the l i p i d bi layer , cal led "director fluctuations" (Watnick et ai, 1990), and diffusion of l ip ids along curved membrane surfaces ( B l o o m and Sternin,1987). Since the re lat ion between /?' and the quadrupo lar sp l i t t ing Au is well established (see A p p e n d i x A ) , then experimental determinat ion of the re laxat ion rate as a funct ion of frequency, i.e. the relaxation spectrum, permits the constants i n E q n 4.11 to be determined. T h u s , determination of the re laxat ion spectrum provides a check on these models. For the case of headgroup-deuteriated DPPC i n the LQ phase this dependence has been checked ( N e z i l et ai, 1991) and found to be i n remarkable agreement w i t h E q n 4.11 (mechanism B ) . These results are shown i n Figure 4.7 ^. F igure 4.7 a compares the ac tua l quadrupolar spectrum w i t h the re laxat ion spectrum; F igure 4.7 b compares the re laxat ion spectrum w i t h the spec trum w h i c h is predicted by E q n 4.11 for T2 (the inverse of E q n 4.11 is shown i n the figure). 4.5 F u t u r e directions: a qualitative discussion. U n l i k e the case just considered, we have no good way as yet to adequately expla in the changes i n re laxat ion about to be presented: these resTilts are inlcuded here only to emphasize the complex effects of adding even simple proteins to simple l i p i d systems. T h e results of Section 4.4, which proved useful i n mode l l ing r2 for the case of the DPPC headgroup deuteriated at a single posit ion (see F i g u r e 4.7), fa i l as such when there is a superposit ion of orientation-dependent intensities due to each of the fifteen deuteriated positions of the acy l chain. T h i s indicates the ^This figure was kindly provided by C. Morrison who is currently using these methods to study (especially) orientation-dependent T i relaxation. a F i g u r e 4.7: T2,efi R e l a x a t i o n T i m e S p e c t r u m : D P P C - d z . In Par t a is shown the T2,ejî re laxat ion t i m e spectrum (solid l ine) for headgroup-deuteriated D P P C - d 2 w i t h the ^ H - N M R quadrupo-lar echo spectrum superimposed (dashed l ine ) . In P a r t b the T^^efl relaxation t ime spectrum (solid l ine , as i n a) is shown w i t h the su-perimposed fit (dashed l ine) corresponding to E q n 4.11. In b o t h a and b the left hal f of the relaxation spec t rum was calculated and subsequently reflected to give the complete spectrum. need for an even simpler system i f the relaxation effects are to be understood. E v e n i f a model was available that permit ted deconvolution of overlapping signals , as is possible w i t h Depakeing methods for ordinary spectra, we would s t i l l be l i m i t e d by signal-to-noise and other associated problems associated w i t h the methods used here. For this reason, further consideration of these re laxat ion effects proper ly awaits the results of experiments currently underway w h i c h use hexamethylbenzene and oriented samples of singly-deuteriated D P P C ( C . M o r r i s o n a n d M . M o n c k , current research). None-the-less, since the re laxat ion-spectrum method had i t s first appl icat ion as appl ied to the systems studied i n this thesis, we have decided to include some of these re laxat ion spectra as examples of the method w i t h only a m i n i m u m of (qualitative) discussion. 4.5.1 A d d i t i o n o f C h o l e s t e r o l t o P O P C - d g i . A d d i t i o n of cholesterol results i n changes to bo th the distortion-corrected spectrum and the relaxation spectrum for P O P C bilayers, as shown i n F igure 4.8. Note that for bilayer B j the re laxat ion spectrum has been determined for aU regions of the intensity-spectrum; for B2 poor signal-to-noise prohib i ted this i n the v ic in i ty of the shoulders. Presence of 30 m o l % cholesterol generally increases the quadrupolar spl itt ings and flattens the plateau region of the intensity spec t rum (dotted lines i n F igure 4.8) commensurate w i t h the increase i n thickness (see Chapter 2). T h e relaxation spectra indicate an overall decrease i n the relaxation times Ti^eff when cholesterol is added. It is interesting that the shapes of these two relaxation spectra are much the same i n the regions for which there is corresponding data (i .e. i n the v ic in i ty of the edges associated w i t h the p lateau regions of the respective intensity spectra) . T h i s may be demonstrated ad hoc as i n F igure 4.9 where an arti f ic ial scal ing has been used to map the re laxat ion spectra onto each other: the frequency axis for bi layer B i was expanded by a factor of 1.54, and a constant re laxat ion t i m e of 210 fis was added onto T 2 , e / / for the bi layer B2. Such a l inear sca l ing is clearly not possible for the corresponding intensity spectra i n the plateau region. Figure 4.8: r2,eff R e l a x a t i o n S p e c t r a : A d d i t i o n o f C h o l e s t e r o l t o P O P C -dzi L T h e re laxat ion spectra for bilayers B i and B2 (solid lines) are com-pared w i t h eachother and w i t h their respective distortion-corrected spectra (dashed l ines) . There is an averall decrease i n Î 2 , e / / when cholesterol is added. T h e spectral shapes for the two relaxation spec-t r a are s imi lar w i th in the bounds of 90° edges (see F igure 4.9) Figure 4.9: T2,eS R e l a x a t i o n S p e c t r a : A d d i t i o n o f C h o l e s t e r o l t o P O P C -d s i I I . T h e shapes of the relaxation spectra for bilayers B i (single l ine) and B2 (double line) are compared w i t h eachother between the 90° edges associated w i t h their respective plateau regions (i.e. exc luding the shoulder regions). T h i s has been done by scal ing the abscissa by a factor of 1.54 when p l o t t ing for B i , and by add ing a constant factor of 210 fis to Î 2 , e / / for the bilayer B2. T h u s , the frequency axis i n this plot is correct only for bilayer B2 while the t ime axis is only correct for B i . 4.5 .2 A d d i t i o n o f P e p t i d e s . W e now qual i tat ive ly consider re laxation spectra determined for the various cases we have been studying here for addit ion of P i e or P24 to either of the bilayers B i or B2. I n F igure 4.10 is shown the three cases corresponding to bilayer B i . Focussing on the relaxation spectrum for F i g u r e 4.10: T2,ea R e l a x a t i o n S p e c t r a : B i ± P i e , P24 . Relaxat i on spectra are shown for the P O P C - d a i bilayer B i (solid line) when peptide P i e is added (double l ine) and when P24 is added (dashed l ine ) . T h e spectrum for B i shown here has been symmetrized i n order to emphasize s imilarit ies between it and the relaxation spec-t r u m shown i n F igure 4.7 a for headgroup-deuteriated D P P C . B i we see a shape w h i c h is reminiscent of the s imple re laxat ion spectrum for the headgroup-deuteriated D P P C , suggesting perhaps that the orientation dependence of T2 for this sample is just a superposit ion of the T2 spectra from the different carbonyl groups, a l l of which are affected by the same mechanism (the "sin^/îcoâ^/?" mechanism, B , according to the preceding discussion). W h e n either of the peptides are added significant changes occur i n the re laxat ion-spectral shape. In bo th cases the overall m a g n i t u d e of T2 is decreased and the peak values undergo a shift: towards larger frequencies for the mismatched peptide P24, and towards smaller frequencies for P i e - T h i s is most easily noted i n the frequency region corresponding to the termina l m e t h y l group or to the 90° edges of the p lateau region. T h e relaxation spectra for add i t ion of peptides seem more s imi lar to eachother, i n the magnitude of than either of them are to the r2 -spectrum for the unperturbed b i layer . However, the shape o f a l l three are s imilar , reminiscent of the headgroup deuteriated D P P C sample (above). T h e corresponding relaxation spectra for a d d i t i o n of peptides to the B2 bi layer are found i n F igure 4.11. For the case of the pure P O P C : c h o l e s t e r o l bilayer we see that addi t ion of the F igure 4.11: T2,eff R e l a x a t i o n S p e c t r a : B 2 ± P i e , P 2 4 ' Re laxat i on spectra are shown for the P O P C - d 3 i : C h o l e s t e r o l bilayer B2 (solid l ine) when peptide P i g is added (double l ine) and when P24 is added (dashed l ine ) . A d d i t i o n of P24 has very l i t t i l e effect upon the unperturbed relaxation spectrum while the addi t ion of P i g has a dramat i c effect. length-matched peptide P24 has almost no effect u p o n the unperturbed relaxation spec t rum. However, add i t i on of the short pept ide P i e to B2 results i n dramat ic changes both i n ampl i tude and shape. 4.6 C o n c l u s i o n . We have presented a method which allows empir ica l determination of a re laxation spectrum f rom inhomogeneously broadened spectra obtained i n a re laxat ion experiment. The method provides an improved empir i ca l representation of the observed relaxation which is more complete and v isual ly suggestive than hi therto . W e have used this method to determine spectra for the samples of C h a p t e r 2 which are corrected for d istort ion due to orientation-dependent spin-spin re laxat ion . T h e apparent effects u p o n the order of these systems, as explored i n Chapter 2, are essentially unchanged after correction for re laxat ion phenomena according to the methods described. However, i t is worth emphasizing that re laxat ion spectra are of interest i n the ir own right - their richness is only now beginning to be explored i n detai l - and , therefore, this aspect of the story t o ld here now awaits further experiments and understanding before i t can be properly continued. C h a p t e r 5 Bib l iography A b r a g a m , A . 1961. Pr inc ip les of Nuclear Magnet i sm. Oxford Univers i ty Press. A l b e r t s , A . , B r a y , D . , Lewis , J . , Raff, M . , R o b e r t s , K . , and J . D . W a t s o n . 1989. Molec-ular Biology of the Cell. Second E d i t i o n , G a r l a n d P u b l i s h i n g Inc. , New Y o r k , N . Y . A l l a n , D . , and P. Thomas . 1981. Ca^+-induced biochemical changes i n human erythrocytes and their relat ion to microvesiculation. Biochem. J. 198:433-440. A u g e r , M . , Carr ier , D . , S m i t h , I . C . P . , and H . C . J a r r e l l . 1990. E l u c i d a t i o n of mo-t i o n a l modes i n glycerol ipid bilayers. A N M R relaxation and lineshape study. J. Am. Chem. Soc. 112:1373-1381. B a n g h a m , A . D . , Standish , M . M . , and J . C . W a t k i n s . 1965. Diffusion of univalent ions across the lamellae of swollen pholphol ip ids . J. Mol. Biol. 13:238-252. B a r e n h o l z , Y . , A m s e l m , S., and D . Lichtenberg. 1979. A new method for propara-t i o n of phosphol ip id vesicles (liposomes) - French press. FEBS Lett. 99:210-214. Barnes , R . G . , and J . W . B l o o m . 1973. Deuteron quadrupole couplings i n deuterated g lyc ine . Molec. Phys. 25:493-494. B a t z r i , S., and E . D . K o r n . 1973. Single bilayer liposomes prepared without sonica-t i o n . Biochim. Biophys. Acta. 298:1015-1019. B a y e r l , T . M . , and M . B l o o m . 1989. Phys i ca l properties of single pholphol ip id bi layers adsorbed to micro glass beads. Biophys. J. 58: 357-362. Birchmeier , W . , Laxiz, J . H . , W i n t e r h a l t e r , K . H . , and M . J . C o n r a d . 1979. A T P -indnced endocytosis i n human erythrocyte ghosts. Character i zat ion of the pro-cess and isolation of the endocytosed vesicles. J. Biol. Chem. 254:9298-9304. B i t b o l , M . , Dempsey, C , W a t t s , A . , and P . F . Devaux. 1989. Weak interact ion of spectr in w i t h phosphatidylchol ine-phosphatidylserine mult i layers : a and ^^P N M R study. Febs. Letters. 224:217-222. B l o o m , M . , B u r n e l l , E . E . , M a c K a y , A . L . , N i c h o l , C P . , V a l i c , M . I . , and G . Weeks. 1978. Fat ty acy l chain order i n l e c i th in model membranes determined from proton magnetic resonance. Biochemistry. 17:5750-5762. B l o o m , M . 1979. Squishy proteins i n fluid membranes. Can. J. Phys.57: 2227-2230. B l o o m , M . , Dav i s , J . H . , and M . I . V a l i c . 1980. Spectra l distorsion due to finite pulse widths i n deuter ium nuclear magnetic resonance spectroscopy. Can. J. P/iys.58:1510-1517. B l o o m , M . , and I . C . P . S m i t h . 1985. Maidfestations of l i p id -pro te in interactions i n deuterium N M R . In : Progress in Protein-Lipid Interactions, (eds. A . Wat ts a n d J . J . H . H . M . Depont) . pp.61-68. Elsevier N o r t h H o l l a n d B iomed i ca l Press, A m s t e r d a m . B l o o m , M . 1987. N M R studies of membranes and whole cells. In E n r i c o Fermi Inter-n a t i o n a l School on the Phys ics of Magnet i c Resonance i n B io l ogy and Medic ine . Soc ieta I ta l iana d i F i s i c a , Elsevier Science Publ ishers , T h e Netherlands. B l o o m , M . , and E . S t e r n i n . 1987. Transverse nuclear sp in re laxat ion i n phophol ip id bi layer membranes. Biochemistry. 26:2101-2105. B l o o m , M . and O . G . M o u r i t s e n . 1988. T h e evolution of membranes. Can. J. Chem.66: 706-712. B l o o m , M . , Evans , E . , and O . G . M o u r i t s e n . 1991. P h y s i c a l properties of the fluid l ip id -b i layer component of cell membranes: a perspective. Quart. Rev. Biophys. 24:293-397. B l u m e , G . , A n d G . Cevc . 1990. Liposomes for the sustained drug release i n vivo . Biochim. Biophys. Acta. 1029:91-97. B o d e n , N . , and Y . K . Lev ine . 1978. Ca lcu lat ion of N M R sp in echo responses i n solids. J. Mag. Reson. 30:327-342. Boggs, J . M . , Moscare l lo , M . A . , and D . Papahadjopoulos . 1977. Biochemistry. 16:5420-5426. Boggs, J . M . , Stol lery, J . G . , and M . A . Moscarel lo . 1980. Effect of l i p i d environ-ment on the m o t i o n of a spin label covalently bound to myel in basic prote in . Biochemistry. 19:1226-1234. Boggs , J . M . , C lement , I . , M . A . Moscarel lo , E y l a r , E . H . , and G . H a s h i m . 1981. A n t i b o d y prec ip i tat ion of l i p i d vesicles containing mye l in proteins: dependence o n l i p i d composit ion. J. Immunol. 126:1207-1211. Boggs , J . M . et a l . 1982. L i p i d - P r o t e i n Interactions (Jost ,P . , C . , and G r i f f i t h , 0 . , H . , E d s . ) , V o l . n , C h p t . l ,Wi ley-Intersc ience , New Y o r k . Boggs , J . M . , Rangara , G . , and K . M . Koshy. 1988. Photo labe l l ing of myel in basic p ro te in i n l i p i d vesicles w i t h the hydrophobic reagent 3-(tri f louromethyl)-3-(m-[^25I]iodophenyl) diazine. Biochim. Biophys. Acta. 937:1-9. B o n m a t i n , J . M . , S m i t h , I . C . P . , J a r r e l l , H . C . , and D . J . S i m i n o v i t c h . 1990. Dynamics i n ordered l i p i d systems: cholesterol reorientation i n oriented bilayers. A N M R relaxation case study. J. Am. Chem. Soc. 112:1697-1704. B r a d y , G . W . , M u r p h y , N . , F e i n , D . B . , W o o d , D . D . , and M . A . Moscarel lo . zzz D A T E . The effect of basic myel in protein on mult i layer formation. Biophys. J. 34:345-350. B r i n k , D . M . , and G . R . Satchler. 1968. Angular Momentum. C larendon Press, O x f o r d . B r o c h a r d , F . , and J . F . Lennon . 1975. Frequency spectrum of the flicker phe-nomenon i n erythrocytes. J. de Physique 36:1035-1047. B r o w n , M . F . , Seelig, J . , and U . Haber len . 1979. S t r u c t u r a l dynamics i n phos-p h o l i p i d bilalyers from deuterium spin- latt ice re laxat ion t ime measurements. J . Chem. Phys. 70:5045-5053. B r u n e r , J . , S k r a b a l , P . , and H . Hauser . 1976. Single bi layer vesicles prepared w i thout sonication. Biochim. Biophys. i4c<a 455:322-331. B i i l d t , G . , G a i l y , H . U . , Seelig, J . , and G . Zaccai . 1979. Neutron diffraction studies on phosphatidylchol ine model membranes: head group conformations, / . Mol. Biol. 134:673-691. But iko fer , P . , Brodbeck , U . , and P . O t t . 1987. M o d u l a t i o n of erythrocyte vesicula-t i o n by amphiph i l i c drugs. Biochim. Biophys. Acta. 901:291-295. C h a p m a n , D . 1975. Phase transitions and fluidity of l ip ids and cell membranes. Q. Rev. Biophys.8:185. C h a p m a n , D . , Lee, D . C . , and J . A . H a y w a r d . 1986. Physicochemical studies of vesicles and biomembranes. Faraday Discuss. Chem. Soc. 81:107-116. Chei fetz , S., and M . A . Moscarello. 1985. Effect of bovine basic prote in charge micro -heterogeneity on protein-induced aggregation of uni lamel lar vesicles containing a m i x t u r e of acidic and neutral p h o s p h o l i p i d s . Biochemistry. 24:1909-1914. C u l l i s , P . R . , Hope , M . J . , and C . P . S . T i l c o ck . 1986. L i p i d po lymorphism and the roles of l ip ids i n membranes. Chem. Phys. Lipids. 40:127-144. C u l l i s , P . R . , and B . de Krui j f f . 1976. ^^P N M R studies of unsonicated aqeous dis-persions of neutra l and acidic phosphol ipids; effects of phase transit ions , p ^ H and divalent cations on the motion i n the phosphate region of the polar headgroup. Biochim. Biophys. A c f a 436:523-540. C u l l i s , P . R . , and B . de Kru i j f f . 1978. P o l y m o r p h i c phase behavior of l i p i d m i x -tures as detected by ^*P N M R ; evidence that cholesterol may destabilize bilayer structure i n membrane systems containing phosphatidylethanolamine. Biœhim. Biophys. Acta 507:207-218. C u l l i s , P . R . , and B . de Kru i j f f . 1979. L i p i d p o l y m o r p h i s m and funt ional roles of l ip ids i n biological membranes. Biochim. Biophys. Acta. 559:399-420. Dav i s , J . H . , Jeffrey, K . R . , B l o o m , M . , V a l i c , M . I . , and T . P . Higgs. 1976. Quadrupo -l a r echo deuteron magnetic resonance spectroscopy i n ordered hydrocarbon chains. Chem. Phys. Z/e«.42:390-394. D a v i s , J . H . 1979. Deuter ium magnetic resonance of the gel and l i q u i d crystal l ine phases of dipalmitoylphsphatidylchoUne. Biophys. 7.27:339-358. D a v i s , J . H . , Hodges ,R.S , and M . B l o o m . 19S2.Biophys. J.37:170-171. D a v i s , J . H . , C lare , D . M . , Hodges ,R.S. , and M . B l o o m . 1983. Interaction of a syn-thet ic amphiphi l l i c polypeptide and l ip ids i n a bilayer structure. Biochemistry.22:529^ 5305. D a v i s , J . H . 1983. T h e description of membrane l i p i d conformation, order and dy-namics by ^ H N M R . Biochim. Biophys. Acta. 737:117-171. Deber, C M . , Hughes P . W . , Fraser, P . E . , P a w a g i , A . B . , and M . A . Moscarel lo . 1986. B i n d i n g of normal and mult ip le sclerosis derived myel in basic prote in to phos-p h o l i p i d vesicles: effects on membrane headgroup and bi layer regions. Arch. Biochem. Biophys.. 245:455-463. De Gennes, P . 1974. The Physics of Liquid Crystals. Ox ford Univers i ty Press , L o n d o n . De ib ler , G . E . , Martenson , R . E . , and M . W . K i e s . 1972. Large scale preparat ion of mye l in basic protein f rom central nervous tissue of several m a m m a l i a n species. Preparative Biochemistry. 2:139-165. Dempsy, C , B i t b o l , M . , and A . W a t t s . 1989. Interact ion of me l i t t in w i t h m i x e d phopho l ip id membranes composed of D M P C and D M P S studied by deuter ium N M R . Biochemistry. 28:6590-6596. Derbyshire , W . , G o r v i n , T . , and D . Warner . 1969.A deuter ium magnetic resonance study of a single crystal of deuterated malonic ac id . Molec. Phys. 17:401-407. Deu l ing , H . J . , and W . Hel fr ich. 1977. A theioret ical explanation for the mye l in shapes of red b lood cells. Blood Cells. 3:713-720. Devaux, P . F . 1983. E S R and N M R studies of l i p id - p r o te in interactions i n m e m -branes. I n : Biological Magnetic Resonance, V o l . 5, pp 183-299. E d s . L . J . Ber l iner and J . Reuben. New Y o r k : P l e n u m Press . D i l l , K . A . , and P . J . F lory . 1980. Interphases of cha in molecules: monolayers and l i p i d b i layer membranes. Proc. Natl. Acad. Sci. i754.77:3115-3119. E d m u n d s , A . R . 1957. Angular Momentum in Quantum Mechanics. Pr ince ton U n i -versity Press , New Jersey E p a n d , R . M . , Moscarel lo , M . A . , Zirenberg E T A L . 1974. Biochemistry. 13:1264-E v a n s , E . , A n d D . Needham. 1987. Phys i ca l properties of surfactant bi layer m e m -branes: t h e r m a l transit ions, elasticity, r ig id i ty , cohesion and co l lo idal interac-t ions . / . Phys. Chem. 91:4219-4228. E v a n s , E . , and W . Rawicz . 1990. Entropy-dr iven tension and bending elasticity i n condensed fluid membranes. Phys. Rev. Lett. 64:2094- 2097. Fraser , P . E . , Moscare l lo , M . A . , R a n d , R . P . , and C M . Deber. 1986. Sponta -neous vesicularization of myel in l ip ids is counteracted by myelin basic prote in . Biochim. Biophys. Acta. 863:282-288. Fraser , P . E . , R a n d , R . P . , and C M . Deber. 1989. Bi layer -s tab i l i z ing properties of mye l in basic prote in i n dioleoyl-phosphatidyl-ethanolamine systems. Biochim. Biophys. Acta. 983:23-29. Frenkel , E . J . , K u y p e r s , F . A . , O p den K a m p , J . A . F . , Roelofsen, B . , and P. O t t . 1986. Effect of membrane cholesterol on dimyristoylphosphatidylchol lne- induced vesiculation of h u m a n red b lood cells. Biœhim. Biophys. Acta. 855:293-301. G a b r i e l , N . E . , and M . F . Roberts . 1984. Spontaneous format ion of stable uni lamel lar vesicles. Biochemistry. 23:4011-4015. G a i n s , N . , and H . Hauser. 1983. Character izat ion of smal l uni lamel lar vesicles pro-duced i n unsonicated phosphat id ic acid and phosphatidylchol ine- phosphatidic ac id dispersions by p H adjustment . Biochim. Biophys. Acta. 731:31-39. S.I .Gass, Linear Programming, M c G r a w - H i l l , N e w Y o r k , 1969 Go lds te in , J . L . , Anderson , R . G . W . , and M . S . B r o w n . 1979. Coated p i t s , coated vesicles, and receptor mediated endocytosis. Nature. 279:679-684. G r u n e r , S . M . , C u l l i s , P . R . , Hope , M . J . , and C . P . S . T i l c o c k . 1985. L i p i d polymor-ph i sm: the molecular basis of non-bilayer phases. Ann. Rev. Biophys. Chem. 14:211-238. G r u n e r , S . M . 1989. S tab i l i ty of lyotropic phases w i t h curved interfaces. J. Phys. Chem. 93:7562-7570. G u l i k - K r y z w i c k i , T . , R ivas , E . , and V . L u z z a t i . 1967. Structure et polymorphisme des l ipides: etude par diffaction des rayons x du système forme de lipides de mitochondries de coeur de boeuf et d'eau. / . Mol. Biol. 27:303-322. Haeberlen, U . 1976. High resolution NMR in solids, selective averaging . In Sup-plement 1, Advances i n M a g . Reson. (ed. J . S . W a u g h ) , Academic Press, New Y o r k , N . Y . Hagerstrand , H . , and B . Isomaa. 1989. Ves iculat ion induced by amphiphiles i n erythrocytes. Biochim. Biophys. Acta. 982: 179-186. H a m i l t o n , R . L . , J r . , Goerke , J . , G u o , L . S . S . , and M . C . W i l l i a m s . 1980. U n i l a m e l l a r liposomes made w i t h the French pressure cel l : a simple preparative and semi-quantitative technique. J. Lipid Res. 21:981-992. Hope , M . J . , B a l l y , M . B . , Webb , g. , and P . R , C u l l i s . 1985. Produc t i on of large u n i l -amellar vesicles by a r a p i d extrusion procedure. Character izat io of size d i s t r ibu -t i o n , trapped volume and abi l i ty to mainta in a membrane potent ia l . Biochim. Biophys. Acta. 812:55-65. H o u l t , D . I . , and R . E . R ichards . 1975. zzz Proc. Roy. Soc. 344:311-340. H o y l a n d , J . R . 1968. Ab initio bond orbi ta l calculations.I A p p l i c a t i o n to methane, ethane, propane, and ethylene. J. Am. Chem. Soc. 90:2227-2232. H u a n g , C . H . 1969. Studies on pholphatidylchol ine vesicles. Format ion and physical characteristics. Biochemistry. 8:344-352. Husch i l t , J . C . , Hodges, R . S . , and J . H . Davis . 1985. Phase equi l ibr ia i n an am-phiphi l i c pept ide-phosphol ipid model membrane by deuterium nuclear magnetic resonance difference spectroscopy. Biochemistry. 24:1377-1386. Inouye, H . , K a r t h i g a s i n , J . , and D . A . Kirschner . 1989. Membrane structure i n isolated and intact myel ins . Biophys. J. 56:129-137. Ipsen, J . H . , K a r l s t r o m , G . , M o u r i t s e n , O . G . , Wennerstrom, H . , and M . H . Zucker-m a n n . 1987. Phase equiUibr ia i n the phosphatidylcholine-cholesterol system. Biochim. Biophys. ^cia.905:162-172. Ipsen, J . H . , M o u r i t s e n , O . G . , and M . B l o o m . 1990. Relationships between l i p i d membrane area, hydrophobic thickness, and acy l chain or ientat ional order. The effects of cholesterol. Biophys. J.57:405-412. Jackson , J . D . 1975. Classical Electrodynamics, second edi t ion . J o h n W i l e y and Sons, New Y o r k . J a r r e l l , H . C , S m i t h , I . C . P . , J o v a l l , P . A . , M a n t s c h , H . H . , and D . J . Sminovi tch . 1988. A n g u l a r dependence of ^ H N M R relaxat ion rates i n l i p i d bi layers. J.Chem.Phys. 88:1260-1263. K.R.Je f f rey . 1981. Nuclear magnetic re laxat ion i n a sp in 1 system. Bull. Magn. Reson. 3:69-82. K u c h i n k a , E . , and J . Seelig. 1989. Interaction of m e l i t t i n w i t h phospharidylchohne membranes. B i n d i n g isotherm and l i p i d headgroup conformation. Biochemistry. 28:4216-4221. Laf leur , M . , F i n e , B . , Stern in , E . , C u l l i s , P . R . , and M . B l o o m . 1989. Smoothed or ientat ional order profile of the l i p i d bilayers by ^ H - nuclear magnetic resonance. Biophys. J. 56:1037-1041. Laf leur , M . , C u l l i s , P . R . , and M . B l o o m . 1990. M o d u l a t i o n of the or ientational order profile of the l i p i d acy l chain i n the La phase. Eur. Biophys. J. 19:55-62. Lakos , Z . , Somogyi , B . , Ba lazs , M . , M a t k o , J . , and S. Damjanov i ch . 1990. The effect of transmembrane potent ia l on the dynamic behavior of cell membranes. Biochim. Biophys. Acta. 1023:41-46. L a w s o n , C . L . , and R . J . Hanson Soving Least Squares Problems, P r e n t i c e - H a l l , E n -glewood Cl i f f s , New Jersey, 1974 L e w i s , B . A . , and D . M . Enge lman . 1983. L i p i d bilayer thickness varies l inear ly w i t h acy l chain length i n fluid phosphatidylchol ine vessicles. J. Mol. Biol. 166:203-210. Lewis , R . N . A . H . , M a k , N . , and R . N . M c E l h a n e y . 1987. A differential scanning calor imetr ic study of the thermotropic phase behavior of model membranes com-posed of phosphatidyl-cholines containing l inear saturated fatty acy l chains.Biochemistry. 26:6118-6126. L i n d b l o m , G . , Wennerstrom, H . , and G . A r v i d s o n . 1977. Translat ional dif fu-s ion i n model membranes studied by nuclear magneric resonance. J. Quant. C / i e m . l 2 , S u p p l . 2:153-158. L i p o w s k i , R . 1991. T h e conformation of membranes. Nature. 349:475-481. L o w d e n , J . A . , Moscare l lo , M . A . , and R . Moreck. 1966. Can. J. Biochem. 44:567. L u t z , H . U . , L i u , S . C . , and J . Palek . 1977. Release of spectrin-free vesicles f rom h u m a n erythrocytes dur ing A T P depletion. J. Cell Biol. 73:548-560. M a d d e n , T . D . , H a r r i g a n , P . R . , T a i , L . C . L . , B a l l y , M . B . , M a y e r , L . D . , Redelmeier, T . E . , Loughrey, H . C . , T i l c o c k , C . P . S . , Re in i sh , L . W . , and P . R . CulUs . 1990. T h e accumrdation of drugs w i t h i n large uni lamel lar vesicles exhib i t ing a proton gradient : a survey. Chem. Phys. Lipids. 53:37-46. M a g g i o , B . , and R . K . Y u . 1989. Interaction and fusion of uni lamel lar vesicles conta in ing cerebrosides and sulfatides induced by myel in basic prote in . Chem. Phys. Lipids. 51:127-136. M a n t s c h , H . H . , Sa i to , H . , and I . C . P . S m i t h . 1977. Deuter ium magnetic resonance. A p p l i c a t i o n s i n physics, chemistry, and biology. Prog Nucl. Magn. Reson. Spectrosc. 11:211-272. M a r a v i g l i a , B . , Dav i s , J . H . , B l o o m , M . , Westerman, J . , and K . W . A . W i r t z . 1987. H u m a n erythrocyte membranes are f luid down to -5 °C . Biochim. Biophys. Acta. 686:137-140. M a r c e l j a , S. 1974. C h a i n ordering i n l i q u i d crystals. H Stucture of bi layer m e m -branes. Biochim. Biophys. Acta. 367:165-176. M a t e u , L . , L u z z a t i , V . , L o n d o n , Y . , G o u l d , R . M . , Vossenberg, F . G . A . , and J . O l ive . 1973. J. Mol. Biol. 75:697-709. M a y e r , L . D . , Hope, M . J . , C u l l i s , P . R . , and A . S . Janoff. 1985. Solute d i s t r ibu -t ions and t rapping efficiencies observed i n freeze-thawed mul t i lamel lar vesicles. Biochim. Biophys. Acta. 817:193-196. M e n d z , G . L . , M o o r e , W . J . , and R . E . Martenson . 1986. N M R studies of basic prote in . X I I I . Assignment of histidine residues i n rabb i t , bovine, and porcine proteins. Biochim. Biophys. Acta. 871:156-166. M e r a l d i , J . P . , and J . Schl i tter . 1981. A stat is t i ca l mechanical treatment of acy l chain order i n phosphol ip id bilayers and correlation w i t h exper imental data . Biochim. Biophys. Acta. 645:193-210. M i a o , L . , Fourcade, B . , R a o , M . , and M . W o r t i s . 1991. E q u i l i b r i u m budding and vesiculat ion i n the curvature model of flidd l i p i d vesicles. Phys. Rev. A. In press. M i l n e r , H . W . , Lawrence, N . S . , and C . S . French. 1950. CoUoida l dispersion of chloroplast mater ia l . Science. 111:633-634. M i m m s , L . T . , Zamphig i , G . , N o z a k i , Y . , T a n f o r d , C , and J . A . Reynolds . 1981. Phospho l ip id vesicle formation and transmembrane prote in incorporat ion using o c t y l glucoside. Biochemistry. 20:833-840. Moscare l lo , M . A . , B r a d y , G . W . , Fe in , D . B . , W o o d , D . D . , and T . F . C r u z . 1986. T h e role of charge microheterogeneity of basic prote in i n the formation and maintenance of the mult i layered structure of myel in : a possible role i n mult ip le sclerosis. J. Neurosci. Res. 15:87-89. M o u r i t s e n , O . G . , and M . B l o o m . 1984. Mattress model of prote in - l ip id interactions i n membranes. Biophys. J. 46:141-153. M u t z , M . , and W . Hel fr i ch . 1989. U n b i n d i n g t rans i t ion of a biological model membrane. Phys Rev. Lett. 62:2881-2884. Needham, D . , M c i n t o s h , T . J . , and E . Evans . 1988. Thermomechanica l and transi -t i o n properties of d imyristoylphosphatidylchol ine /cholesterol bilayers. Biochem-istry. 27:4668-4673. Needham, D . , and E . Evans . 1988. Structure and mechanical properties of giant l i p i d ( D M P C ) vesicle bilayers from 20 °C below to 10 " C above the l i q u i d c rys ta l -crystal l ine phase transit ion at 24 °C . Biochemistry. 27:8261-8269. N e z i l , F . A . , M o r r i s o n , C . , W h i t t a l l , K . P . , and M . B l o o m . 1991. Re laxat ion- spectra i n mode l membranes using deuterium nuclear magnet ic resonance. / . Mag. Res. 93:279-290. N e z i l , F . A . , and M . B l o o m . 1992. Combined influence of cholesterol and synthetic amphiph i l i c polypeptides upon bilayer thickness i n model membranes. Biophys. J. 61:1176-1183. N e z i l , F . A . , B a y e r l , S., and M . B l o o m . 1992. Temperature-reversible eruptions of vesicles i n mode l membranes studied by N M R . Biphys. J. 61:1413-1426. O lson , F . , H a u t , C . A . , Szoka, F . C . , V a i l , W . J . , and D . Papahadjopoulos . 1979. Preparat ion of l iposomes of defined size by extrusion through polycarbonate membranes. Biochim. Biophys. Acta. 557:9-23. P a k e , G . E . 1948. Nuclear resonance absorption i n hydra ted crystals : fine structure of the pro ton l ine . / . Chem. Phys.l6:327-336. P a l i , T . , and L . I . H o r v a t h . 1989. Restr icted la te ra l diffusion of acidic l ip ids i n phopho l ip id vesicles aggregated by mye l in basic prote in . Biochim. Biophys. Acta. 984:128-134. Per ly , B . , S m i t h , I . C . P . , and H . C . Jarre l . 1985. A c y k cgaub dtbanucs i f ogiogitudtk-ethanolamines containing oleic acid and dihydrosterc idic ac id : ^ H N M Z R relax-a t i on studies. Biochemistry 24:4659-4665. Persaud , R . , Fraser, P . , W o o d , D . D . , and M . A . Moscare l lo . 1988. T h e glycosila-t i o n of h u m a n mye l in basis protein at threonines 95 and 98 occurs sequentially. Biochim. Biophys. Acta. 966:357-361. Persaud, R . , Boggs, J . M . , W o o d , D . D . , and M . A . Moscarel lo . 1989. Interaction of g lycosylated h u m a n mye l in basic protein w i t h l i p i d bilayers. Biochemistry. 28:4209-4216. P l a t t n e r , H . , and L . B a c h m a n n . 1982. Cryo f lxat ion : a too l i n biological u l t rastruc -t u r a l research. International Rev. of Cytology. 79:237-304. Ranee , M . , and R . A . B y r d . 1983. O b t a i n i n g high-fidelity sp in -1 /2 powder spectra i n anisotropic media : phase-cycled H a h n echo spectroscopy. / , Magn. Reson. 52:221-240. R i n t o u l , D . A . , and R . W e l t i . 1989. Thermotrop i c behavior of mixtures of glycosph-ingol ipids and phosphatidylchol ine: eff'ect of monovalent cations on sulfatide and galactosylceramide. Biochemistry. 28:26-31. R o b a r d s , A . W . , and U . B . S leytr . 1985. " P r a c t i c a l Methods i n E lec t ron Microscopy" . (ed. G a u e r t , A . M . ) Elsev ier , A m s t e r d a m , New Y o r k , Oxford . R o u x , M . , H u y n h - D i n h , T . , Igolen, J . , and Y . Pr igent . 1983. Simple preparation of l ,2 -dpalmitoyl -sn-glycero-3-phosphoric ac id and deuteriated choline derivatives. Chem. Phys. Lipids. 33:41-45. R o u x , M . , N e u m a n n , J . M . , Hodges, R . S . , Devaux , P . F . , and M . B l o o m . 1989. Conformat iona l changes of phosphol ip id headgroups induced by a catioidc inte-gra l pept ide as seen by deuter ium nuclear magnetic resonance. Biochemistry. 28:2313-2321. R u m s b y , M . G . . 1978. Organizat ion and structure i n central-nerve myel in. Biochem. Soc. Trans. 6:448-462. Ruocco , M . J . , and G . G . Shipley. 1982. Character izat ion of the sub- transit ion of hydrated D P P C bilayers. Biochim. Biophys. Acta. 684:59-66. S a c k m a n , E . , Duwe, H . , and H . Englehardt . 1986. Membrane bending elasticity and its role for shape fluctuations and shape transformations of cells and vesicles. Faraday Discuss. Chem. Soc. 81:281-290. S a n k a r a m , M . B . , Brophy, P . J . , and D . M a r s h . 1989. Spin label E S R studies on the interact ion of bovine spinal cord mye l in basic protein w i t h d imyr i s toy l -phosphatidyl -g lycerol dispersions. Biochemistry. 28:9685-9691. Schiff, L . I . Quantum Mechanics. 3'"'' ed i t ion . M c G r a w - H i l l Book C o m p a n y , New Y o r k , N . Y . Seelig, A . , and J . Seelig. 1974. T h e dynamic structure of fatty a c y l chains i n a phosphol ip id bilayer measured by deuter ium nuclear magnetic resonance. Bio-chemistry. 13:4839-4845. Seelig, J . 1977. Deuter ium magnetic resonance:theory and appl i cat ion to l i p i d mem-branes. Q. Rev. Biophys. 10:344-418. Seelig, A . , and J . Seelig. 1977. Effect of a single cis-double bond on the structure of a phosphol ip id bi layer. Biochemistry 16:45-50. Seelig, J . , and A , Seelig. 1980. L i p i d conformation i n model membranes and bio-logical membranes. Quart. Rev. Biophys. 13:191-61. Seelig, J . , and P . M . M a c D o n a l d . 1987. Phosphol ip ids and proteins i n biological membranes. ^ H N M R as a method to study structure , dynamics and interac-t ions. Accnts. Chem. Res. 20:221-228. Seelig, J . , M a c D o n a l d , P . M . , and P . G . Scherer. 1987. Phospho l ip id headgroups as sensors of charge i n membranes. Biochemistry. 26:7535-7541. Seifert, U . , B e r n d l , K . , and R . L i p o w s k i . 1991. Shape transformations of vesicles: phase diagrams for spontaneous curvature and bilayer coupl ing model . Phys. Rev. A. In press. S i x l , F . , and A . W a t t s . 1982. Interactions between phosphol ip id headgroups at membrane interfaces: a deuterium and phophorous nuclear magnet ic resonance and spin- label electron spin resonance study. Biochemistry. 21:6446-6452. S i x l , F . , Brophy , P . J . , and A . W a t t s . 1984. Selective prote in - l ip id interactions at membrane surfaces: a deuter ium and phosphorous nuclear magnet ic resonance study of the association of mye l in basic protein w i t h the bi layer headgroups of d imyr i s toy l phosphoatidylcholine and d imyr is toy l phosphat idylg lycero l . Bio-chemistry. 23:2032-2039. S m i t h , R . , and B . J . M c D o n a l d . 1979. Associat ions of myel in basic prote in proteins w i t h detergent micelles. Biochim. Biophys. Acta. 554:133-147. Speiss, H . W . 1978. i n N M R . Bas i c Pr inc ip les and Progress. ( D i e h l , O . , F l u c k , E . , and R . Kos fe ld , eds.) V o l . 15, pp . 55-214. Springer Ver lag , B e r l i n . Spiess, H . W . , and H.Si l lescu. 1981. So l id echoes i n the s low-motion region. J. Magn. Res. 42:381-389. Sperrotto , M . M . , Ipsen, J . H . , and O . G . M o u r i t s e n . 1989. Theory of prote in induced latera l separation i n l i p i d membranes. Cell Biophys. 14:79-95. Speyer, J . B . , Weber , R . T . , Das G u p t a , S . K . , and R . G . Gr i f f in . 1989. Aniso trop i c N M R spin latt ice re laxat ion i n phase cerebroside bi layers. Biochemistry. 28:9569-9574. Steinbrecht, R . A . , Z iero ld , K . 1987. "Cryotechniques i n biological electron m i -croscopy." Springer Ver lag , Heidelberg . S tern in , E . , B l o o m , M . , and A . L . M a c K a y . 1983. De-pake- ing of N M R spectra. J. Magn. Reson. 65:274-282. Stern in , E . 1985. D a t a aquis i t ion and processing: a systems approach. Rev. Sci. Instrum. 56:2043-2049. E . S t e r n i n , B . F i n e , M . B l o o m , C . P . S . T i l c o c k , K . F . W o n g , and P . R . C u l l i s . 1988. A c y l chain or ientat ional order i n the hexagonal H / / phase of phosphol ipid-water dis-persions. Biopyhys J. 54:689-694. Stollery, J . G . , Boggs, J . M . , and M . A . Moscarel lo . 1980. Var iab le interact ion of sp in -label led human myel in basic prote in w i t h different acidic l i p ids . Biochemistry.l9:12l9-1226. Stewart , W . A . , A l v o r d , E . G . , H r u b y , S., H a l l , L . D . , and D . W . Paty . 1985. E a r l y de-tect ion of experimental allergic encephomyelitis by magnetic resonance imaging . Lancet. 2:898. Surewicz , W . K . , Moscarel lo , M . A . , and H . H . M a n t s c h . 1987. Fourier transform i n -frared spectroscopic investigationof the interact ion between myel in basic protein and dimyristoylphosphat id lg lycero l bilayers. Biochemistry. 26:3881-3886. Szoka, F . , and D . Papahadjopoulos . 1978. Procedure for preparat ion of liposomes w i t h large internal aqueous space and high capture by reverse- phase evaporation. Proc. Natl. Acad. Sci. USA. 79:4198-4198. T a n g , J . , Sterna, L . , and A . P ines . 1980. Aniso trop i c spin- latt ice re laxation of deuterated hexamethylbenzene. J. Mag. Reson. 41:389-394. T a t e , M . W . , and S . M . G r u n e r . 1989. Temperature dependence of the sstructural dimensions of the inverted hexagonal ( H j / ) phase of phosphatidylethanolamine-containing membranes. Biochemistry. 28:4245-4253. T h e w a l t , J . , Haner t , C . E . , Linseisen, F . M . , F a r r a l l , A . J . , and M . B l o o m . 1991. Phase d iagram for membranes composed of mixtures of cholesterol and mono-unsturated phophol ip ids . Submi t ted to Acta Pharmaceutica Jugaslavica. T i l c o c k , C . P . S . 1986. L i p i d po lymorphism. Chem. Phys. Lipids. 40:109-125. Vega , S., and A . P ines . 1977. Operator formalism for double quantum N M R . J. Chem. Phys. 66:5624-5644. V i s t , M . R . , and J . H . Dav is . 1990. Phase equiUibr iao f cholesterol /d ipalmitoylphosphatidylchol ine mixtures : ^ H - N M R and differential scanning calorimetry. Biochemistry 29:451-464. W a r r e n , G . B . , Honslay, M . D . , Metcal f , J . C . , and N . J . M . B i r d s a l l . 1975. Cholesterol excluded from the phosphol ipid annulus surrounding an active calc ium transprt prote in . Nature. 235:684-687. W a t n i c k , P . I . , D e a , P . , and S.I. C h a n . 1990. Character i zat ion of the transverse re laxat ion rates i n l i p i d bilayers. Proc. Natl. Acad. Sci. USA. 87:2082-2086. K . P . W h i t t a l l , and A . L . M a c K a y . 1989. zzz J. Magn. Reson.84:lU. W o o d , D . D . , and M . A . Moscarel lo . 1984. Is the mye l in membrane abnormal i n mul t ip le sclerosis? / . Membrane Biol. 79:195-201. Wor t i s , M . , Seifert, U . , B e r n d l , K . , Fourcade, B . , M i a o , L . , R a o , M . , and R . K . P . Z i a . 1991. Curvature-contro l led shapes of l i p i d bi layer vesicles: budding , vesicula-t i o n , and other phase transit ions. Proceedings of the workshop on " D y n a m i c a l phenomena at interfaces, surfaces and membranes." ed. Beysens, D . , Boccara , N . , and G . Forgus. Les Houches, 18.2-28.2. Z w a a l , R . F . A . , and H . C . Henker . 1982. B l o o d cell membranes and ha«mostasis. Haemostasia. 11:12-39. Zaccai , G . , B i i l d t , G . , Seelig, A . , a n d J . Seelig. 1979. Neutron diffraction studies on phosphatidylchol ine model membranes.II C h a i n conformational and segmental disorder. J. Mol. Biol. 134:693-706. A p p e n d i x A H N M R in L i p i d Systems: Basics A . l Nuclear Magnet ic Resonance A . 1 . 1 Q u a d r u p o l a r H a m i l t o n i a n T h e incompletely averaged orientation-dependent tensor interactions of importance i n N M R include the anisotropic chemical shift ( A C S ) , the magnetic dipole-dipole ( M D D ) and , for spin > 1/2, the nuclear electric quadrupole ( N E Q ) interactions. For deuterons i n a field of 7.2 T , as i n our laboratory , the L a r m o u r frequency Vo « 46 M H z is large compared to the m a x i m u m quadrupo lar sp l i t t ing of about 250 k H z for ^ H i n C D bonds. For the membrane systems studied here, the quadrupolar sp l i t t ing is large compared w i t h either the dipolar interact ion between ^ H nucle i i n a methylene group ( m a x i m u m spl i t t ing about 4 k H z ) , or w i t h typ i ca l chemical shifts ( < 1 k H z ) . For these reasons we w i l l focus i n this chapter upon the N E Q interact ion as a first order perturbat ion of the nuclear Zeeman energy. W e first briefly review the N E Q interact ion . T h e classical charge distr ibutions />„(rn) and pe(re), for a nucleus and an electron at posi -tions Tn and re respectively, have an interact ion energy WE' U s i n g the add i t i on theorem for spherical harmonics Yim{9., <f>) (Jackson, 1975, pp.102) to rewrite the t e r m (|r„ - r d ) " ^ , then (A.1 ) (A .2 ) where the nuclear t e r m is ^ / m = / P n { T n ) r ' M 9 n , <l>n)d\n, (A .3 ) the electronic t e r m is = / ^e(re)rr('+l)n„.(ôe, ^e)d\e, (A .4 ) and we have assumed |re| > |r„| ^ . Introducing the q u a n t u m mechanical charge density operator Qn for the nucleus ?n(rn) = e^6(rn - p.), (A.5) t=i where the p,- are the coordinate positions of the Np protons and S is the D i r a c ^-function, we may then wr i te the quantum mechanical analogue of E q n A . 3 : ^ g i 2 | . y , „ ( 0 i , * . ) , (A .6 ) defined so that Aim =< '^im >, where i l , - , 0 , - , $ , - are the coordinates of the Np protons i n the nucleus, and e is the electron charge. S imi lar ly , for the Ne electrons at positions ri,Oi,(f>i B,m = - « \ / 2 ^ E ^ - ( A . 7 ) Aim and Bim are irreducible tensor operators of rank / and satisfy commutat ion relations w i t h the angular momentum operators Jz,J±: [Jz, Tim] = mhTim, and, [J±, Tim] = + I) - m(m ± l)hTim±i, (A .8 ) where Tim = Aim,Bim- A c c o r d i n g to the W i g n e r - E c k a r t ( W E ) theorem the m a t r i x elements for Aim and Bim, as well as those for any other irreducible tensor operator of fixed rank / , are propor t i ona l to the Clebsch-Gordon coefficients for the coupling of angular momenta. B y inspect ion , the / = 0 term i n E q n A . 2 represents the energy coupl ing of the nucleus to a point charge. T h e well-defined par i ty of stat ionary nuclear states requires that the diagonal m a t r i x ^VaKd since the quadrupolar coupling vanishes for s- electrons and only in such a case can |re| < |r„|. elements of Aim be vanishing for o d d /, wh i ch means that there is no permanent electric dipole moment for the nucleus. A l s o , known properties of the Clebsch-Gordon coefficients further restrict non-vanishing multipoles to satisfy the requirement that I <2I ( A b r a g a m , 1961). In par t i cu lar then , we note that a sp in 1 deuterium nucleus has a quadrupole moment (/ = 2). Since WE i n E q . A . 2 varies roughly as rpr7^'^^\ the large relative size of the electronic radius compared to the nuclear radius means that the effects of higher order mult ipoles may be ignored i n this thesis. Therefore, we now focus upon the H a m i l t o n i a n for the nuclear electric quadrupole interact ing w i t h an electric field gradient: = J2A2mB2m. (A .9 ) m T h e expl i c i t f o rm of the m a t r i x elements for the nuclear quadrupole moment operator A2m have been worked out i n Cartes ian coordinates (e.g. see Jackson, 1975, pp.137). Fo l lowing A b r a g a m (1961) the W E theorem allows .42m to be relaced by an irreducible tensor operator 02m w h i c h , for sp in I, has components _ eQ[3l] - Ijl + 1)] - 2 / ( 2 / - 1) = 47(2731) (A-10) Q2±2 = VëeQIl 4 / ( 2 / - 1) where Q is a constant called the quadrupole moment determined by requir ing (for instance) that eQ =< iV^|Q2o|-^ > = < N\A2o\N > for some nuclear state \N >. For the deuteron Q = 2 . 8 7 5 x 1 0 - " cm2 (Re id and V a i d a , 1972). S imi lar ly , by wr i t ing B2m i n terms of i ts cartesian coordinates and defiiung the traceless, symmetr ic 2^ *^^  rank electric field gradient ( E F G ) tensor operator, V , j , where V(x,y,z) is the operator describing the electrostatic potent ia l produced at the point T{x,y,z) such that Vij =< Vij > , the W E theorem allows the relationship between the m a t r i x elements B^rn and Vij to be determined: B20 = 1 / V 6 F , , =^20 B2±i = l/V6{V,,±iVy,) = V2±i (A.12) 52±2 = l/2V6{V:,.-Vyy±2iV:,y) = V2±2. In this equat ion , due to the general absence of degeneracy for the electronic o rb i ta l quantum number i n bulk m a t t e r , the E F G at the nucleus may be treated classically and , therefore, expectat ion values over a wave funct ion representing the single nondegenerate electronic state have been used i n E q n A . 1 2 . A l s o , i t is useful to move f rom the arb i t rary reference frame used so far into the p r i n c i p a l axis frame of the E F G tensor; then Vfj = 0 for i ^ j. Further , we choose the axes i n this frame such that |V^y| < {V^xl ^ and define the field gradient eq = V^z, and the asymmetry parameter rj = {V^^ - VYY)IVZZ (0 < < 1), so that the E F G tensor i n i t s p r inc ipa l axis system is Kjo = ^9 /2 , ^2±i = 0, and V^^2 — eg7?/2's/6. Us ing this notat ion the quadrupolar H a m i l t o n i a n may now be w r i t t e n : m = - 2 = 4 / ( 2 / - 1) - -^(^ + 1) + ^^ (4 + (A.13) T h e E F G p r i n c i p a l axis frame is typ ica l ly known i n the molecule centred coordinate sys-tem and must be ro tated into the laboratory- f ixed reference frame i n which the spin opera-tors {Iz,I±) are k n o w n . Th i s is done using the W i g n e r ro tat ion m a t r i x for tensors of rank 2 / > ^ , „ ( a , / 3 , 7 ) ( U . Haeber len, 1976; A . R . E d m u n d s , 1957): W ^ ' = E V2'm'Di'mi'^,P,l), (A.14) m ' = -2 where a , / ? , 7 are the Eu le r angles (e.g. B r i n k and Satchler , 1968) describing the required rotat ion (see F igure A . l ) . Us ing this expression i n E q n A . 1 3 we obta in = E Q2m E Vi^,Di,^{a,p,j). (A.15) m = - 2 m '= -2 z,w f i rs t rotat ion (x.y.z) : about z - o x i s : ' (u,v,w) second rotat ion about v - a x i s : (u.v.w) ^ (x',y',z') F i g u r e A . l : E u l e r A n g l e D e f i n i t i o n s . T h e E u l e r angles a,f3 are defined i n this drawing for right-handed ro-tat ions. T h e angle a describes a r ig id rotat ion of the xyz-coordinate system about the z-axis into the new uvw-coordinate system; /3 de-scribes the rotat ion angle about the v-axis for rotat ion of the uvw-coordinate system into the x 'y 'z ' - coordinate system. T h e Euler angle 7 has been taken to be zero as discussed i n the text . To first order we only keep the terms Q20 (Speiss, 1978). N o t i n g that £)^,o(a,y9,7) is i n -dependent of 7, we take 7 = 0,o; = $ ,and/? = 0 , supposing that this corresponds to ro-ta t ing the E F G principle axis frame into the laboratory frame. U s i n g tabu la ted values for •^m ' o ( " = = 0,7 = 0) , and t a k i n g the magnet ic field H to be paral le l to the laboratory frame z- axis ( H || ziâb) then ^ « = 4 / ( 2 / - 1)^^^' " + m^cos'Q -1) + -vsin-'Qcos2^]. (A.16) The selection ride A m = ± 1 for single q u a n t u m transitions between these levels impl ies that , for each value o f $ , 0 there w i l l be two N M R lines w i t h a quadrupolar splitting between the lines given by A.= l^i^^Sq^ + l,sin^ecos,i). (A.17) T h u s , non- interact ing spin 1 deuter ium nuclei homogeneously experiencing E F G ' s of fixed o r i -entation relative to the external magnetic field w i l l spl it each Zeeman level into three, result ing i n a doublet spec trum. Mo le cu lar mot ion which occurs fast on the N M R timescale ( ( A i / ) " ^ « lO""* — 10-^s) mod -ulates the or ientat ion of the E F G tensor and ensures that the observed quadrupolar sp l i t t ing is actual ly an average over the molecular reorientations occurr ing i n this t ime interva l : Se^qQ Zcos^e-1 1 . 3 ^ „ ^ , . A i / = < 2 :^Vstn^®cos2^ > . (A.18) E v a l u a t i n g t ime averages of tensor interactions as i n E q n A . 1 8 , necessary when there are molec-ular mot ions , is a recurr ing theme i n the study of l i q u i d crystals i n general , and of phophol ip id systems i n par t i cu lar , whi ch we w i l l now discuss. A . 1.2 O r d e r P a r a m e t e r s T h e packing constraints on rod- l ike molecules i n the l iquid-crysta l l ine phase, as discussed i n Chapter 1, do not restrict rotations about the symmetry axis and angular frequencies about this axis may commonly be i n the range of 10'^ - 10^° cps (Seelig, 1977). For samples i n the l i q u i d crystall ine phase we expect the loca l symmetry axis to be the bilayer normal , n . F i x i n g a l o ca l or thonormal coordinate system, w i t h uni t vectors x , y , z , to the molecule (here considered to be rigid) and t a k i n g a bilayer-fixed coordinate system hav ing unit or thonormal vectors x ' , y ' , z ' ( n II z ' ) , a commonly used measure of the fluctuations is the so-called order parameter tensor Stf = ^ < ZcosCiaCosCjp - 6ij6ap > , (A .19 ) where a,P — x',y',z' and i,j = x,y,z (De Gennes, 1974.) ^ We consider the average i n E q n A . 1 9 to be over molecular reorientations w i t h i n the timescale of an N M R measurement; also, cosQa and cosQ^ are direct ion cosines for the or ientat ion of the molecular reference frame axes relative to the bilayer-f ixed reference frame axes, and the Sij,êa,/3 are delta-functions. B y explo i t ing the symmetr ic nature of S"f for a w i t h respect to f3 and for i w i t h respect to j , for the case of greater than 4-fold ax ia l symmetry and a r i g i d molecule; tak ing z ' || n; and supposing the bilayer leaflets to be ident i ca l ; then the order parameter tensor may be considered to be a symmetr ic 2"°^ rank tensor, Sij, hav ing at most five non - zero terms (De Gennes, 1974; D a v i s , 1983). T h e diagonal terms of Sij may be wr i t ten : Sii = ^< 3cos% - 1 > , i = x,y,z (A .20) where the average is over the angular fluctuations of the i " * coordinate axis about the bi layer normal z ' w i t h i n some characteristic t ime for the measurement being made. T h e Sii are the commonly used measure of the order i n systems of l iquid-crystals and are called the order parameters: S^x, Syy,Szz, satisfying Su G [-|, 1]. T h e orthogonality of cosines, YlfCos^d = l , i = x,y,z, ensures that only two of these are independent. ( A x i a l symmetry of the E F G tensor may further require Sxx = Syy i n which case Sxx = Syy = -^Szz)- T h e direct ion cosines i n E q n A . 1 9 , A . 2 0 may be wr i t t en : cos(^x = X • z ' = sinBcos(j> 'The a and 0 used in this expression are dummy indices with no relationship to the Euler angles a and P used above. cosQy = y • z' = sin9sin<f> (A.21) cos(^z = z • z' = cos9 where are ident ical ly the Euler angles a = <f>,fi = S,and7 = 0> defined i n F igure A . l , now describing the rotat ion of the molecule-fixed coordinate frame i n t o the bilayer-f ixed coordinate system. We have now identif ied three " n a t u r a l " reference frames of use: the laboratory frame i n which the tensors Q a m are wel l -known, the pr inc ipa l axis (molecular) frame i n w h i c h the (static) E F G tensor is known, and the frame which includes the ro ta t i ona l symmetry axis n as a coordinate axis (see Figure 2.1). T h e effect of r a p i d f luctuations about the director n here is to average the stat ic E F G tensor over the t ime of the N M R measurement resul t ing i n a n effective E F G tensor which is ax ia l ly symmetr ic about the director ax is . The re lat ion between the order parameters Su and the quadrupolar sp l i t t ing Av ( E q n A . 1 8 ) may be determined i n a straight- forward manner by decomposing the necessary ro tat ion of the E F G tensor f rom its molecule-fixed pr inc ipa l axis frame into the laboratory frame (see E q n A .14 ) into two rotations: a first rotat ion through Eu ler angles a , /Î , 7 f rom the molecule-fixed p r i n c i p a l axis frame into the bilayer-f ixed frame containing A as a coordinate axis ; and a second rotat ion through Eu ler angles a',/?',7' f r om the bilayer-f ixed frame in to the laboratory frame containing H o as a coordinate axis . If we do this the quadrupolar H a m i l t o n i a n then becomes: W = E E E V,^^,Dl,^,.ia,(3,j)Dl„^ia',l3',Y). (A.22) m = - 2 m " = - 2 m ' = - 2 A s previously, to first order, we keep only terras i n Q20 and , for rotat ional motions about n which are fast on the N M R t ime scale, terms containing 7 are averaged to zero. Therefore, assuming no mot ion (or slow motion) of the director n relative to H o , 3 e^qQ ^Scos^P'-l^, 3cos^0-l 1 . „ ^ = 447(273T)( ^)[<—^>+^V<s^n^/3cos2a>] [ 3 / ^ - / ( 7 + 1 ) ] (A.23) a n d , m a k i n g the identi f ication a = (f> and 0 = 9 in Eqns A . 2 3 and A.22, the order parameters Sii may be rewr i t ten i n terms of 6 and (/> so that the quadrupo lar spl i t t ing due to 7{Q becomes where /3' is the angle between the magnetic field Ho and the local bilayer director n ; also, Szz = § < Scos'^O — 1 > where 0{t) is the instantaneous angle between n and the E F G tensor, and the average is over t ime; and {S^x — Syy) = | < sin^0cos2<f) >. Since i t is k n o w n that T) < 0.05 for C - D bonds (Hoy land , 1968; Derbyshire et a l , 1969; Barnes and B l o o m , 1973) we may neglect rj. T h u s , for l ip ids i n a domain where the director n is at angle /?' to the magnet ic field H , the quadrupo lar sp l i t t ing A i / becomes = 2 ~ T ~ ^ ^ ^ 2 '^ ^ ^ ^ where SCD = Szz- A summary of the reference frames used i n this derivation is presented i n cartoon f o rm i n F igure A . 2 . A . 1 . 3 D i s t r i b u t i o n o f S p e c t r a l I n t e n s i t y : T h e P a k e D o u b l e t . T h e samples used i n our experiments typica l ly consist of a large number of randomly oriented l i p i d domains. E a c h domain w i t h bilayer normal n at angle relative to H contributes a doublet to the N M R spectrum, as shown above. T h e observed superposit ion of a l l such doublets is called a powder spectrum. T a k i n g 77 = 0 for C D bonds then E q n A . 2 5 again applies; then, defining X = Avj^ScDVQ where vq = 3e^qQ/Ah, a symmetr ic powder pat tern lineshape function /(|a;|) may be determined (Seelig, 1977; Dav i s , 1983): , ( , , , ) J ( 3 H ^ W - V ^ + ( 3 - 6 N ) - ^ ^ i f O < N < | ^^^^^ [ (3 + 6H)-i/2 i f | < | x | < l . T h i s funct ion has l ogar i thmic singularities at x = ± 1 / 2 (/?' = 90°), ind i ca t ing the relatively large number of spins i n a powder sample which have loca l director orientations at P' = 90° (called the "edges") compared to , say, /?' = 0° (called the "shoulders" ) . T h e frequency sp l i t t ing between the P' = 90° edges {Ai')poujder ~ SCD^Q , i n the case of smal l l ine broadening, is F i g u r e A . 2 : U s e o f W i g n e r R o t a t i o n M a t r i c e s . T h i s cartoon shows a carbon-deuterium ( C D ) bond w i t h i n a l i p i d bilayer membrane seen at an instant of t ime f rom the perspective of three different coordinate systems: molecular-f ixed system (x,y,z) , bilayer-fixed (x ' ,y ' ,z ' ) , and laboratory-f ixed (x/aj, Yiabi z/oi)- T h e intantaneous axia l ly symmetr ic electric field gradient ( E F G ) tensor (not shown) is paral le l to the C D bond direct ion . Wigner rotat ion matrices are depicted as accomplishing two successive rotations of the E F G tensor: f rom the molecule-fixed to the bilayer-fixed system, which allows the quadrupolar spl i t t ing Au i n E q n A . 2 4 to be wr i t ten i n terms of the order parameters Su] and a second rotat ion from the bilayer-fixed frame into the laboratory frame, which accounts for the /?' term i n E q n A . 2 4 . of pract ical importance since i t means the static quadrupo lar coupl ing constant e^qQ/h may be determined f rom a powder sample. W e can simulate inherent l ine-broadening (usually due to magnetic interactions between neighboring nuclei ) , b y convolut ing a broadening funct ion w i t h /(|a;|). The spec trum that results from choosing a Gauss ian broadening funct ion is shown i n Figure A . 3 . T h e characteristic powder pat tern shown i n F igure A . 3 was first observed F igure A . 3 : P a k e D o u b l e t S p e c t r u m W i t h G a u s s i a n B r o a d e n i n g . T h i s figure represents the tota l absorption signal I(x) when each resonance centred at x' i n the Pake doublet has a Gauss ian lineshape described by a broadening parameter a so that I{x) = (27ra2)-^/2 r |/(a:)|e-[(---')V2-']da:', J—CO where |/(a;)| is defined by E q n A . 2 6 i n the text . T h e l inewidth A at one-half m a x i m u m is then given by A = \/8/n2 w 2.4<T. The lower spectrum is for a = 0.02 while the upper series of spectra shows «7 = 0 .02 ,0 .03 ,0 .04 , . . . , 0 . 1 . for dipolar-coupled pairs of sp in 1/2 particles (Pake, 1948) and is called a " P a k e doublet" spectrum. T h e spectral features w i l l be altered for non-zero asymmetry parameters as wel l as for differences i n the type of broadening funct ion chosen ( c f . Dav i s , 1983; Seelig, 1977). It is common to use the Gauss ian function for theoretical spectra of dipolar-broadened solids and a Lorentz ian function for model ing mot ional ly narrowed isotropic fluids. In pract ice , for l iquid -crysta l l ine systems, neither funct ion is quanti tat ive ly correct and other methods - such as the use of moments - are often necessary for quantitat ive comparison of spectra. A . 1.4 D e n s i t y M a t r i x T h e quantum mechanical analologue of L iouv i l l e ' s theorem for the density operator cr of a system of nuclear spins evolv ing under the H a m i l t o n i a n hH is ^ = -i[H,cT]. (A .27) T h i s equation is especially useful when an or thonormal basis set {pi|i = 1 , 2 , . . . , n ' } is k n o w n to span the L i o u v i l l e space of operators. T h e n a may be wr i t ten as a l inear combinat ion of the P . : n' n <^=J2 <^iPi = 1 + Z)<^'P" (A-28) i=l 1=1 where n = n' — 1 and , for convenience, we have chosen p „ / equal to the unit operator 1, and taken , for a fixed number of spins i n the sample but wi thout other loss of generality, c„/ = Co = 1. C o m b i n i n g E q n s A . 2 7 and A . 2 8 (and not ing that T r { [ A , B ] C } = T r { B [ C , A ] } ) we obta in a set of n coupled differential equations for the c,'s: ^ = - E ^ « i ^ i . (A-29) i where TZij = -iTr{pi[pj,n]} = -Tlji. (A.30) T h e details of the dynamics for a part icular system are determined by the commutators [p j , H]. Since 7i may also he expanded i n terms of the basis set of operators, the dynamica l equations for the Cj ' s depend upon the commutators [ p „ P j ] . For the systems considered here the necessary commutators have already been tabulated (see below). Therefore, i n pr inc ip le , i t is always possible to construct the density m a t r i x from which , as is well known, expectat ion values for any operator A may be determined: <A>= Tr{Aa}, (A.31) (which is the real usefullness of this approach). A.1 .5 P u l s e Sequences T h e expectat ion values of an appropriate basis set of operators {p,} w i l l be phys ica l observables. For a t y p i c a l spin system at equi l ibr ium i n a magnetic field H i t is i n pr inc ip le possible to transform the equi l ibr ium nuclear Zeeman polar izat ion into a po lar izat ion of any of the other observables (Vega and Pines , 1977; B l o o m et a l , 1980). A variety of "pulse sequences" have been developed for Fourier - transform N M R i n order to accomplish such transformations. We now briefly review a general approach to interpretat ion of pulse sequences and go on to discuss the pulse sequences used i n this work. Precession Diagrams . In the fo l lowing discussion we w i l l work w i t h the or thonormal basis operators {p,} ( B l o o m , 1987): p<, = l , p i = 2 - i / % , p2 = 2 - ^ / % , (A.32) P3 = 2 - i / 2 j ^ , p4 = 6 - i / 2 ( 3 J 2 - 2 ) p, = 2 - ' / \ i a . + W P6 = 2-^/\lyIz + Izly) p r = 2 - l / 2 ( j 2 _ J 2 ) ^ 2-^l\lxIy ^ Xyl,) for which the commutators [ p i , P j ] are known ( M . B l o o m , as tabulated by Ster iun , 1988) and have been reproduced i n Table 2.1^. For a given H a m i l t o n i a n , knowledge of the commutators for the P i , p j ' s allows determinat ion of solutions for the c,(f)'s i n the set of coupled diff"erential ^This table appeared in (Bloom and Legros, 1986), subsequently in (Bloom, 1987) and, with minor corrections, in (Sternin, 1988). i J P i P2 P3 P4 P5 P6 P7 P s P i 0 P s -P2 -\/3p6 -P8 >/3p4+P7 -P6 Ps P2 - P 3 0 P i V ^ P 5 - V ^ P 4 + P 7 P8 - P s P6 P3 P2 - P i 0 0 P6 - P s 2P8 -2p7 P4 \/3p6 - V S p s 0 0 \/3p2 - V 3 p i 0 0 Ps P8 \/3p4-p7 -P6 - V 3 P 2 0 P3 P2 - P i P6 - V ^ P 4 - P 7 -P8 P5 \/3pi - P 3 0 P i P2 P7 P6 P5 -2p8 0 -P2 - P i 0 2P3 P8 - P s P6 2P7 0 P i -P2 2P3 0 Table A . l : C o m m u t a t i o n relations for orthogonal spin-1 basis opera-tors . The entries i n this table represent —iy/2[pi,pj] for the p,-defined by E q n A . 3 3 . equations above ( E q n A . 2 9 ) . For the pulse sequences we are interested i n i t is sufficient to consider a H a m i l t o n i a n hH such that n = n, + nQ{+'H.,ny) (A .33) where = -cjolz = - V 2 w o P 3 (A.34) is the Zeeman t e r m corresponding to the magnetic field H appl ied along the z-axis; and , from E q n A . 1 3 w i t h T) = Q, UQ = ^ ( 3 J | - 2) = y|a;,p4 (A.35) is the quadrupo lar H a m i l t o n i a n for a spin-1 partic le w i t h = Ze^qQ/AU] the terms i n brackets i n E q n A . 3 3 are associated w i t h a radio-frequency (rf) magnetic field generated transversely to H i n order to manipulate the spin polar izat ion for short periods of t ime ( typical ly a few microseconds): Hx = - - ^ i P i (A.36) Hy = -\/2uiP2- (A.37) The solutions that result f rom straight-forward appl i cat ion of the L o u i v i l l e formal ism to the i n d i v i d u a l terms of H tend to couple some of the p^'s whi le leaving others as invariants of the m o t i o n . We w i l l f ind i t most useful to represent these couplings i n terms of presession diagrams ( B l o o m , 1987). Consider ing the Zeeman term Hz f i rst . Table A . l immediate ly shows that p 3 and p 4 com-mute w i t h Hz (proport ional to ps ) so that dcs/dt = dc^/dt = 0 i n E q n A . 2 9 a n d , therefore, pa and p4 are invariants "of the m o t i o n " . So lv ing E q n A . 2 9 for the other coefficients yields cou-plings between ( p i , P 2 ) , (PsjPe)» and (p r jPs ) which , i n precession diagram form, are represented as i n F igure A . 4 a ( B l o o m , 1987). P2 1 a Ps \ Pa/ Hz = - 2 CJ^PJ / _ , Invariants: • ' P i ' Ps ' P? b Pi Ho = (2 /3 )^ / ' a ; ,p , Invariants: ^ ' * P 2 c P4,7' / Invariants: A 2 " l t Pl,P7.-4 " P2 ' PB Pe P i , d Pa; 1 Ps / Invariants: ' P 3 P6 ' Pt.-7 F i g u r e A . 4 : P r e c e s s i o n D i a g r a m s . T h i s figure i l lustrates the precession diagram representation for the couplings between different elements p,- of the density m a t r i x a as this evolves i n response to the different Hami l tonians described i n the text : Hz,HQ,Hx,and Hy. T h e invariants of the mot ion are l isted at the r ight for each H a m i l t o n i a n . T h e operators p4_7, P 4 , _ 7 , P7,4, and P 7 , - 4 are defined: p 4 , ± 7 = ^ P 4 ± | P 7 , and p 7 , ± 4 = i p 4 ± ^ p 7 . T h e couplings between p i and pa i l lustrated i n F igure A . 4 a show that a magnetic f ield appl ied a long the z-axis is effectively equivalent to ro ta t ing the coordinate system at angular frequency CJQ about the " z -ax i s " (pa) of the subspace spanned by p i , p a , Pa- T h i s is because Pi» P25 P 3 t ransform under rotations as spherical harmonics of order 1: Yi^mi^,^)- It is worth not ing that p 4 transforms under rotations as Y2fi(0,(p), and (ps.pe) and (p2 ,P5) as symmetr i c and ant i - symmetr ic combinations of y2 ,± i (^)^) and 1^2,±2(^)^) respectively. In a s imi lar way for HQ we may easily show t h a t p a , p 4 , pr, and pg are invariants of the mot ion and that the couplings, shown i n F igure A . 4 b , are now between (p i jPe ) and (p2 ,P5) . F igure A . 4 c, d give the corresponding result, w h i c h w i l l be used shortly, for the 7ix and Tiy terms of the H a m i l t o n i a n . E x c l u d i n g re laxat ion for the moment, then these diagrams are sufficient to describe the evolution of the magnet izat ion terms p i , p2, and p a , and of the higher order terms (p4 - pg) - wh i ch have no classical analogue - for the pulse sequences used i n this thesis. These are the quadrupolar echo pulse sequence ( Q E P S , 90j^ — r — 90^ — t ) , useful for obtaining spectra and for measuring spin-spin {T2) re laxat ion by vary ing r (see below); and the inversion recovery pulse sequence ( I R P S , 180j, - r i - (90j^ — T2 — 90x — t), useful for measuring spin- latt ice (T i ) re laxat ion by vary ing r i (below). T h e significance of this notat ion w i l l appear shortly. Ti and T2 i n the simplest case specify characteristic t imes for the irreversible disappearance of the magnet izat ion l ong i tud ina l ly or transversely to the stat ic field H . (Re laxat ion is discussed below.) Before discussing these pulse sequences i n detai l , we consider a simple single-pulse experiment. S i n g l e P u l s e E x p e r i m e n t . Suppose that a system of spin-1 nuclei are i n thermal equl ibr ium w i t h po lar i zat ion along the z-axis such that < >— I'g = —2hiJo/kT, i n the usual high temperature approximation for the B o l t z m a n n d i s t r ibut ion . In the L iouv i l l e formal ism this equ i l i b r ium may be described by saying that the i n i t i a l po lar izat ion is entirely along the pa-axis and , since ca is invariant under Tiz, then ca = I'ol^ ^— and c,- = 0 for i > 1 ^. If we now apply, for a period of t ime Ty, a r f *We exclude from this discussion, and will to continue to exclude, the identity operator po =1. magnetic field of magnitude H j directed along (say) the y-axis of the reference frame r o t a t i n g at angular frequency Uo, the density m a t r i x described by the c .p i ' s evolves i n t ime f r o m i ts equ i l ibr ium configuration a = a{t = o) according to the H a m i l t o n i a n Hy = —v/2aJip2. T h i s procedure transfers magnetization f rom the Zeeman ordered state described by Oo in to other parts of the density m a t r i x . U s i n g the precession diagrams of F igure A . 4 this s i tuat ion may be considered further. F igure A . 4 shows that Hy couples ( p i , p 3 ) , (pe, P s ) , and (p4_7,p5). Since only cz{t = 0) = is i n i t i a l l y non-zero, then the t ime evolution of the c,(i) due to Hy dur ing the t ime Ty for w h i c h the r f pulse is appl ied is C3(0) = / o C3(rj,) = hcosuxTy (A .38) c i (0 ) = 0 Cx{Ty) = losinuiTy (A .39) w i t h aU the other c,- = 0. Th i s first pulse of r f is normal ly used to prepare the system i n a Aînown non-equ i l ibr ium state. For instance , i f TJ, is chosen such that uiTy = 90° then, at the end of the preparat ion per i od , the magnet izat ion may be described as h a v i n g been prepared along the X-axis ( p i ) , by ro tat ing the i n i t i a l magnet izat ion about the y -ax i s , and we would ca l l this a "90j,-pulse". T h u s the order i n i t i a l l y i n the project ion of a onto the ps axis would have been transferred i n t o order (polarization) along the p i axis . Subsequent evolution of the spin system due to HQ , dur ing the t ime / after the rf-pulse is turned off, is described i n F igure A . 4 b ; by inspect ion there, Cl{Ty) = loSinUlTy ^ Cl(Ty + t) = losinuiTyCOsUgt (A .40) ^eiTy) = 0 ^ ceiTy + t) = IgSinujiTysinUgt (A .41) C3(TJ/) = loCOSUiTy ^ C3{Ty •{-t) = loCOSUJxTy (A .42) where a l l other c,- = 0. We must inc lude re laxat ion i f there is ever to be a re turn to equ i l i b r ium. Special izing to the case of a 90j, preparat ion pulse (WITJ, = 90°) , and w r i t i n g the c,'s i n vector form, relaxation may be inc luded for now i n an ad hoc way: c = {l,IaCosujgte-*/'^\0,0,0,0,Iosimjgte-^^'^^ ,0,0) where the t ime constant T^ must i n general be more precisely defined than we have done so far (see below). In the spectroscopy we consider here only magnet izat ion i n the xy -p lane is detectable. T h e resultant N M R signal observed after the first preparat ion pulse for a macro-scopic sample of such (non-interacting) deuterons, called the free induction decay ( F I D ) , is the ensemble average of ci{t) over the spectrum of w, 's and is the Fourier transform of this spec trum. E x p e r i m e n t a l constraints aside, one could obtain the N M R spectrum of a;,'s f rom such a one-pulse experiment by determining the Fourier transform of the F I D start ing f rom t ime t = 0; i n pract ice , this is not possible. In order to detect the quadrupolar splittings of deuterons on hydrocarbon chains over the necessary range of about 250 k H z the detection device, i n c l u d i n g a tuned c ircuit w i t h a h igh-Q co i l , must use wide-band low-noise preamplif iers, a wideband receiver, h igh t ransmit ted power - H i « 10"^ T at ~ 45 M H z over a volume of about 1 m l - and fast d ig i t i zat ion . T h e l i m i t i n g factor i n such a device is typ i ca l ly the receiver deadtime d u r i n g which r ing ing i n the detection c i rcu i t , subsequent to appl i cat ion of the r f pulse, obscures the N M R signal for several microseconds. The resulting F I D is unusable for detection of weak signals w i t h large quadrupolar splitt ings since this information is contained i n the i n i t i a l part of the F I D . It is for this reason that the Q E P S (Davis et a l , 1976) is so commonly used i n deuteriated l i p i d systems. Q u a d r u p o l a r E c h o and Inversion Recovery Pulse Sequences. T h e Q E P S consists of two r f pulses which are 90° out of phase and separated by a t ime r between the pulses. A s mentioned, at the end of the first pulse the spin system has a component of magnet izat ion perpendicular to H . A t this t ime, the presence i n the sample of a d is tr ibut ion of spectral frequencies causes the prepared phase-coherence of the perpendicular component of the magnet izat ion to decrease as i t evolves under Tig i n the r o t a t i n g frame. The t ime constant for this dephasing is called T2 . A c c o r d i n g to F igure A . 4 b the quadrupolar H a m i l t o n i a n mixes the polar izat ion i n p i (mag-netization) into Ps (double quantum coherence) while leav ing pa (magnetization) invar iant . I n general, a second r f pulse further mixes this po lar izat ion i n t o other elements of the density m a t r i x cr. For two pulses exactly 90° out of phase as i n the Q E P S then , at a t ime / = r after the second pulse, po lar i zat ion w i l l be refocussed into observable magnetizat ion i n the x y plane (maximized for 90° pulse-lengths). Therefore, the Q E P S results i n an "echo" signal which , for long enough r , can be made to occur outside the deadtime of the receiver. Fourier analysis is then performed s tart ing f rom the peak of the echo ®. T h e i m p o r t a n t criterion of prov id ing an exact 90° phase shift between the two pidses is seldom satisfied. Th i s has been corrected for i n this work by a l ternat ing the phases of the two pulses according to wel l described methods (Hoult and R i chards , 1975; Ranee and B y r d , 1983). T h e refocussing of the magnerization by the second pulse is i n pr inc iple perfect when irreversible effects due to static magnetic d ipolar interactions w i t h other nuclei (Boden and Lev ine , 1978) and fluctuating quadrupolar and d ip lar interactions may be neglected ( B l o o m et a l , 1980). However, irreversible effects result i n the loss of the quadrupolar po lar izat ion over t ime . B y lengthening r the ampl i tude of the peak of the echo is observed to decrease w i t h t ime constant T2e. T h e re laxat ion of the Zeeman po lar i zat ion (pa) may be observed using the I R P S defined above. T h e first pulse of this sequence s imply inverts the equ i l i b r ium magnet izat ion, which is then left to evolve under Tiq for t ime TI. Since pa is invar iant w i t h respect to HQ, the Zeeman magnet izat ion dur ing TI is only effected by re laxat ion processes act ing to return pa to its equ i l i b r ium value. Subsequent appl icat ion of the Q E P S hav ing an interpulse delay r chosen so that r < Ti and r «C Tae allows observation of the non-equ i l ibr ium value of the Zeeman magnet izat ion <P3 > after i t has relaxed for t ime w r i . B y vary ing r i and leaving r fixed the *In the experiments to be reported here the digitization process often results in there being no datum for the peak of the echo. This is handled by a five-point interpolation of the data (Davis, 1983) to ensure a digitized point occurs at the peak. t ime constant T i ^ describing the decay of the Zeeman polar izat ion m a y be easily determined. A p p e n d i x B M o d e l M y e l i n M e m b r a n e s This A p p e n d i x consists of two sections: a concise description of some experiments we have proposed to study a "model mye l in membrane" ; and , following th i s , a par t i cu lar ly detailed version of the procedure for extract ing basic proteins f rom b r a i n mye l in , f ract ionat ing this into i ts charge isomers, and then characterizing these isomers using alkaline gel electrophoresis. T h e first section is meant only to out l ine a k i n d of s imple guide for N M R studies of M B P i n an unusual ly complex l i p i d system. It should be understood t h a t , given the current state of knowledge i n th is f ie ld, the idea is to perform the experiments i n a "quick and d i r t y " fashion and look for large effects. T h e second section has been included as a physicists guide to obtaining M B P from mye l in (i.e. lots of s imple instruct ions) . B . l P r o p o s e d N M R studies in M M M ' s T h e under ly ing goal of the experiments that w i l l be suggested here is to explore whether current knowledge of model membrane systems, l i p i d - l i p i d and l ip id -prote in interact ions, is sufficient to obta in in format ion f rom a more complex, medica l ly impor tant , l i p i d system. Specifically, we wiU investigate a system w i t h potent ia l relevence to the pathology found i n M u l t i p l e Sclerosis. In the pathologic case of demyel ination, an insult to the external wrap of bilayer would expose the in terna l "dense l i n e " port ion of the bilayer to extracel lular mi l eu . Exposure of M B P may contribute to further myel in destabi l izat ion, promot ing increased tissue destruction, irrespective of the details of the immune processes occuring^. Such a destabi l izat ion of the mye l in u l t r a structure would be expected to aggravate insult due to these processes. ^MS is usually considered to have an auto-immune component. We suggest, as have others, that M B P b ind ing at the p lasma membrane performs a s ta -b i l i z ing funct ion i n myel in (Fraser et a l , 1989). Therefore, i t is expected t h a t further charac-ter izat ion of this b ind ing would be useful i n t r y i n g to understand M S pathology. We believe the t ime is r ipe to address the problems associated w i t h M B P b ind ing t o l ip ids us ing tech-niques to be described shortly. A series of experiments w i l l be proposed invo lv ing a re lat ively complicated system of l i p ids , buffer salts, and the two most impor tant proteins specific t o the myel in -produc ing cell of the C N S (the ol igodendricyte) : M B P and P L P . T h i s system w i l l be refered to as a M o d e l M y e l i n Membrane ( M M M . ) It should be emphasized that b ind ing of M B P to a bi layer may be cr i t i ca l ly affected by buffer p H , l i p i d compos i t ion , and presence of other proteins (eg. P L P ) . T h e M M M studies seek i n a sense to to look for empir i ca l connections between N M R spectroscopic features and M B P b ind ing to M M M . Therefore, the experi -ments are designed to proceed w i t h the most complex system, i f this is indeed stable, and to then vary the important parameters i n a physiologically meaningful way. For instance, whi le the exper imental variations on the buffer are " i n f i n i t e " , the physiologically relèvent change to study is that between the intrace l lu lar versus the extracellular domains. L i p i d s are included i n the model membrane only i f they are components of central nervous system ( C N S ) myel in . Fur ther , they are combined i n the appropriate relative concentrations as defined by (Rumsby, 1978). L i p i d s inc luded i n the M M M are cholesterol, galactocerebro-side, sulfatide, l -Pa lmi toy l -2 -Oleoy l -Phosphat idy l cho l ine ( P O P C ) , l - P a l m i t o y l - 2 - O l e o y l - Phos -phat idylser ine ( P O P S ) , and l -Pa lmi toy l -2 -Oleoy l -Phosphat idy le thano lamine ( P O P E ) . A l s o , deuter-ated versions of P 0 P E , P 0 P C , or P O P S w i l l be used i n the ^ H - N M R experiments. It is known that the type of buffer influences thermotropic behavior of sphingo l ip id /phospho l ip id mixtures ( R i n t o u l and W e l t i , 1989). Therefore, the buffer for the resul t ing M M M w i l l contain physio-logical concentrations of the ions Na+ , K + , 0 1 " , HCO3 " ,and Ca^+ ,at the intracel lular levels, and at a p H of 7.4. M o d e l membranes w i l l be reconstituted us ing s tandard techniques. M B P w i l l be introduced into the membrane by the method out l ined by (Boggs et a l , 1980) and the result ing M M M then repetit ively frozen and thawed to ensure a dispersed d is tr ibut ion of M B P . W i t h this model system the exper imental program then involves: • a b ind ing study to determine the fraction of M B P (or l ipophi l in ) bound to M M M as a funct ion of the M B P ( l ipophi l in ) concentration. • determinat ion of a temperature range for the N M R experiments w i t h i n which the model system is i n a l i q u i d crystal ine phase. T h i s w i l l involve Differential Scanning C a l o r i m e t r y ( D S C ) , 3 i p - N M R , and possibly N M R difference spectroscopy (Huschi l t et a l , 1984; V i s t and Dav is , 1990). • the use of D e u t e r i u m Nuclear M a g n e t i c Resonance ( ^ H - N M R ) to study the influence of the interactions between l i p i d and prote in molecules on the acyl chain and polar headgroup conformations. B . 1 .1 ^ H - N M R E x p e r i m e n t s The ^ H N M R spectrum is sensitive to the deuteron environment and the mot iona l characteristics of the deuterated l i p i d . In par t i cu lar , the quadrupolar spl i t t ings of the deuterons y ie ld valuable information on the loca l or or ientat ional order of the molecules i n the v i c in i ty of the deuterons. B y p lac ing deuterons on the polar headgroups of those l i p i d molecules whose conformations may be expected to be influenced by the highly charged M B P we obta in an exquisite probe of the p r o x i m i t y of charged regions of M B P to the deuterated l i p i d . Deuterons on the acyl chains also provide, i n pr inc ip le , in format ion on the penetrat ion of M B P into the hydrophobic interior of the bi layer. T h e experiments which follow vary m a i n l y i n the type of deuterated probe l i p i d being used i n the M M M . S i n g l e - C h a i n D e u t e r a t e d P O P C i n P O P S a n d C h o l e s t e r o l ^ . T h i s experiment ex-amines the quadrupo lar spl i t t ings of acy l chain deuterons as a funct ion of M B P concentration i n systems of P O P C / P O P S and P O P C / P O P S / C h o l e s t e r o l , where the P O P C has been perdeuter-ated on a single chain . T h e work follows-up that done by (S ix l et a l , 1984) who studied ^This part of the experimental program has already been carried out. deuterated headgroup interactions w i t h M B P i n a s imi lar l i p i d system (no cholesterol) a n d w i l l provide a baseline for the inflence of M B P b ind ing on membrane fluidity i n the presence of cholesterol, but wi thout other v i t a l components of myel in . S i n g l e - C h a i n Deuterated P O P C in M M M . In th is experiment the influence o f bi layer penetrat ion of M B P on the ^ H - N M R spectrum w i l l be measured. Spectra w i l l also be s tud ied as the salt concentrations are varied to "extracel lular" levels . Freeze-fracture electron microscopy w i l l be used to assess whether p r o t e i n / bi layer agrégation of l ip ids is t ak ing place (as i s char-acteristic i n true myel in formation) . T h i s experiment could give information on whether the short non-hydrophi l i c amino ac id sequences found i n M B P actual ly penetrate the b i layer . T h i s experiment is also (potential ly) sensitive to changes i n the thickness of " m y e l i n " membranes induced by the b ind ing of M B P . T h o u g h thickness changes due to M B P are not necessarily expected i n the absence of proteol ip id prote in ( P L P ) , the add i t i on of P L P might alter th i s . H e a d g r o u p - D e u t e r a t e d L ip ids in M M M . W e seek here to examine the interact ion of M B P w i t h the l i p i d headgroup region. It is expected that such interact ion w i l l be strongest w i t h the negatively charged l ip ids P O P S and Sulfat ide , since M B P has a large net posi t ive charge. W e propose to use headgroup deuterated P O P C , and P O P S . T h e p l a n is s imp ly to add a n increasing amount of M B P (up to 50 w t % ) to the differently deuterated versions of the M M M . A g a i n , at each M B P concentration the quadrupolar spl i tt ings of the probe deuterons w i l l be recorded. T h e salt concentrations w i l l be kept at intracel lular levels. Recent studies of the influence of membrane-bound charges on po lar headgroup ^ H - N M R spl itt ings ( R o u x et a l . , 1989; Seelig et a l , 1987), suggests that such experiments shoidd y ie ld in format ion of the locat ion of the pos i t ive ly charged moeities of the lysine residues of M B P w i t h i n the polar headgroup region of m y e l i n . L i p o p h i l i n i n M M M . It would be useful to repeat the above experiments w i t h l i p o p h i l i n , b o t h w i t h and without M B P included i n the M M M . In this way i t is possible to determine the effect of l i p o p h i l i n on M B P b ind ing at the bi layer and whether this prote in plays a cooperative ro l l i n the format ion of m u l t i l a m i n a r regions. (It should be reiterated here that we are looking for b ig effects.) C o m p a r i s o n W i t h H u m a n M y e l i n . The next step i n this program is to introduce deuterated probe l ip ids directly into the myel in f ract ion . T h e procedures for this step are less well characterized but are presently being considered. If one is able to introduce a suitable amount o f deuterated l i p i d into myel in i n this way, i t is then desirable to repeat some of the above experiments as a measure of how closely the M M M approximates real myel in . (The difficulty here is that one is per turb ing the myel in i n these experiments i n a different way: by addi t ion of the deuterated probe. However, by use of a su i tab ly large sample, the per turb ing effect can be m i n i m i z e d w i t h i n the l imi ts of signal to noise necessary for N M R spectroscopy.) B.2 M B P : Isolation and Separation into Charge Isomers. M B P was harvested from two sources: A u t o p s y number B 595-88 according to the classification of M . Moscarel lo (Toronto H o s p i t a l For Sick C h i l d r e n ) ; and f rom Vancouver General H o s p i t a l autopsy number A892431 . T h e first donor had Alzheimers disease while the lat ter , an obese 60 year o ld female, was diagnosed as having overdosed on ethanol . In the last case a per iod of less than one hour passed post m o r t e m before the cadaver was removed to await autopsy at lowered temperature . M y e l i n was harvested f rom the major tracts w i t h i n about 15 hours post mortem. T h e procedure for preparing M B P from the aquired myel in w i l l be described here i n three parts : separation of basic proteins from the white matter ; fract ionation of the basic proteins into their various charge isomers by cation-exchange chromatography; and characterization of the charge isomers by alkaline gel electrophoresis. The possible importance of charge micro -heterogeneity of basic proteins i n the formation of mult i lamel lar structures is wel l recognized (see e.g. Moscarel lo et a l , 1986). B.2.1 Isolation o f Basic Proteins from B r a i n W h i t e M a t t e r . R e q u i r e d Solutions. 51. chloroform:methanol (2:1, V : V ) : 450 m l @ 4 °C; 52. 0.2 N H2SO4: 1000 m l ; 53. 10-2 M P h e n y l M e t h y l Sul fory l F lour ide ( P M S F ) i n ethanol ( E t O H ) [0.435 g/250 ml ] ; • Note : P M S F is a protective agent which inactivates proteases. It is an extremely toxic acetylchohne inh ib i t o r and gloves/mask should be worn when using i t tn the fumehood. 54. cold acetone: 150 m l . P r o c e d u r e . T h e fo l lowing procedure uses white matter from the major tracts of the bra in which has been previously separated and frozen. Care must be taken to use ordy a very fresh ba in and to m a x i m a l l y exclude grey matter f rom the harvest. D a y 1. T h a w 35 g of b r a i n white matter ; use a tissue grinder to homogenize smal l amounts of this i n 5-10 m l of so lut ion S I . D o this w i t h three strokes at a speed of 8000 r p m . Transfer t o a beaker on ice. Repeat for a l l the tissue. T h e t o ta l vo lume should now be ~250 m l . S t i r overnight @ 4°C using a fast s t i r r ing speed. D a y 2. F i l t e r through 32 cm size #1 W h a t m a n filter paper into 750 m l flask. W a s h the residue first w i t h 130 m l (cold) solut ion S i , then w i t h 150 m l (cold) acetone, both into the 750 m l flask. L a b e l the flask: "proteo l ip id prote in -f- myel in l i p i d s " , cap this and store at room temperature . A l l o w most of the acetone to evaporate f rom the residue but , before i t is a l l gone, gently scrape the residue into the centre of the filter paper . (Note that the residue contains M B P and that the filtering procedure may be slow, requir ing about 3-4 hours.) Remove the residue from the fi lter paper and, agai i i us ing smal l amounts, homogenize i t w i t h the tissue grinder us ing at he following solut ion: 130 m l S2 mixed w i t h 130 fA S3 . Save the homogenate i n a beaker and st ir overnight (fast) @ 4 °C. D a y 3. U s i n g ~ 6 30ml Corex centrifuge tubes, centrifuge the homogenate @9000 r p m for 30 minutes @ 4°C. (The supernatent contains the M B P . ) Decant the supernatent (solut ion S5) and save this i n a 500 m l flask. M a k e up the fol lowing so lut ion: 52 m l S2 + 52 ^1 S3 ; using a spatu la i n the fumehood wash the pellet w i t h this solution. Centrifuge @ 9000 r p m for 30 m i n @ 4 " C . Decant the supernatent and save this i n the solution S5. T h e to ta l volume of S5 should now be ~ 182 m l . A d d equal amount ice cold absolute E t O H (high p u r i t y ) and let stand at -20 °C overnight. M a k e up 500 m l of 90% E t O H and let stand @ -20tomorro. Save the pellets i n the Corex tubes for l i poph i l l in extract ion : cover and store at 4°C. These should be washed w i t h double d ist i l led water a n d spun down (several times.) T h e pellets may then be lyophi l i zed i n preparat ion for l i p o p h i l l i n extract ion. D a y 4. Transfer the M B P - c o n t a i n i n g solut ion into 14 30 m l Corex tubes quickly, careful to keep everything co ld . Centrifuge for 60 m i n at 9000 r p m and -10 "C . Remove the supernatent by suct ion . W o r k i n g quick ly and efficiently, w i t h emphasis upon r a p i d removal of solids more t h a n upon t o ta l vo lume added, make three washes w i t h 90 % E t O H (-20 ° C ) : at each wash centrifuge (9000 r p m at -10°C for 30 m i n ) . A f ter each wash the tota l number of sample tubes w i l l be reduced: 14-^6-» -3^1 . A l l tubes (and E t O H ) must be kept upon ice as m u c h of the t ime as possible. B.2.2 Fract ionation of M B P Into Charge Isomers. R e q u i r e d Solutions . S l a . Weigh 180 g (6 moles) U r e a plus 3 g (.08 moles) glycine into a 500 m l beaker. A d d about 450 m l double dist i l led H 2 O and stir u n t i l dissolved. A d d 10 N N a O H -drop by drop-u n t a reaching a p H of 10.5. In a graduated cyl inder add H 2 O up to 500 m l and then m i x . F i l t e r b y suct ion through an aqueous mi l l ipore membrane (Type H A 0.45 /xm) into a 750 m l flask us ing a stainless steel funnel . S i b . Doub le the recipe for solut ion S l a and br ing to a p H of 9.5 (i.e. make 1000 ml ) . (Note that these solutions w i l l be used for dialysis and fract ionation of M B P components; the filtration removes unwanted crud f rom the urea.) S 2 . W e i g h 60 g (2 moles) urea plus 3 g (.08 moles) glycine into a 500 m l beaker. A d d about 450 m l double d is t i l l ed H 2 O and adjust the p H to 10.5; b r ing the volume to 500 m l w i t h H 2 O and m i x . F i l t e r as for S l a and S i b . D i v i d e the result ing so lut ion two 250 m l volumes. T o one add 2.92 g (0.2 moles) N a C l and labe l . (Note that this so lut ion is for the gel co lumn salt gradient. ) P r o c e d u r e . D a y 1: preparat ion of co lumn for cation exchange chromatography. Prepare solutions S l a and S i b , p u t t i n g aside a few m l of S i b for (future) opt i ca l density measurements. We igh 15 g C M - 5 2 cellidose into a 250 n d beaker. A d d 100 m l S l a and st i r gently (by hand) w i t h a sloshing mot i on . A l l o w this to settle for 2 hours. P o u r off" the supernatent ( into s ink ) ; the gel w i l l r emain at the bo t tom of the beaker. Set up a .9 cm x 30 cm co lumn so i t is upr ight w i t h its resevoir screwed on top and the b o t t o m tub ing connected. A d d S l a to the co lumn u n t i l i t is about one-third f u l l . B leed the b o t t o m l ine by p lac ing a syringe i n i t and sucking ou the fluid unt i l there is about 2 c m of fluid i n the co lumn and no air bubbles i n the l ine . (Note , that a co lumn is always i n i t i a l l y loaded i n this way w i t h enough buffer that the membrane is protected f rom clogging when the gel is poured in. ) Resuspend the gel by adding about 25 m l of S l a and gently sloshing it about (to stir . ) Immediate ly pour gel into the resevoir of the co lumn; rinse the beaker w i t h 10 m l of S l a and add this to the co lumn. A l l o w the gel to settle under gravity for 2 hours u n t i l the gel level is near the b o t t o m of the resevoir. O p e n the flow control valve on the b o t t o m of the co lumn and remove the resevoir f rom the co lumn. Place the plastic tube attached to the per ista l t i c p u m p "feed" side into the flask containing S l a . T u r n the pump on a n d , when the fluid begins to exit the cap to the co lumn, remove the bleed screw on the cap and screw the cap onto the co lumn. W h e n the a i r bubble trapped i n the cap has escaped through the bleed hole screw hole then replace the screw. (Note : the flow control valve must be open.) Cont inue the w a s h / p a c k i n g of the co lumn by running the per istal t ic pump at 3 m l / 1 5 m i n overnight. D a y 1 (cont): P r e p a r a t i o n of M B P for C o l u m n : Dialysis If cont inuing f rom M B P preparat ion ( "Day 4") then remove the supernatant from the final C o r e x tube containing the pellet. W i t h N2, evaporate any excess E t O H then add 10 m l of buflFer S i b to dissolve the proteins. If using lyophi l ized basic proteins, weigh out 100-150 m g and dissolve this i n 10 m l of S i b . Dia l ize overnight i n 500 m l of S i b : 1. Preparation of the dialysis tape. C u t the tape to the desired length and b o i l this i n H 2 O ( w i t h a p inch of E D T A added) for about 1 m i n . Rinse w i t h dist i l led water several t imes. (Note : the tape may be stored i n a dark container at this point @ ~ 4°C for one week, or for about 1 m o n t h i f a drop of CHCI3 is added.) 2. Dialysis. T i e the dialysis tube w i t h a tight knot at one end. Check the tube for leaks by adding dist i l led H 2 O . E m p t y and draw tube through a paper towell to dry. Pour i n the 10 m l of buffered basic proteins using a funnel . C l i p the top closed w i t h a dialysis bag cl ip s l ightly above the fluid level (~ 1 cm) to allow for possible expansion dur ing dialysis . K n o t the loose end and place the bag into a beaker containing about 500 m l of so lut ion S i b . S t i r moderately overnight. D a y 2. • Finish Dialysis. Change the dialysis so lut ion , replacing i t w i t h the rest of so lut ion S i b , and let st ir for 30 m i n . T h e n cut the dialysis bag at the upper knot , remove the cl ip and pour the so lut ion into an appropriate tube for centri fugation. Sp in i t at 9000 r p m for 30 m i n at 4-20 " C . Transfer the supernatant to a smal l graduated cyl inder f rom which i t w i l l be pumped onto the gel . Measure the opt i ca l density at 280 n m (OD280) by t a k i n g 50 / i l of sample and adding this to 950 fA of the S i b solution which was saved for this purpose; comparison is to an OD28O reading for H 2 O . (Note : best yields are usually obtained when OD280 € [80,90].) • Fractionation of Sample. T h e fract ionation requires the synchronization of two set-t ings: the rate of ro tat ion of the turntable containing 100 smal l test-tubes; and the rate of p u m p i n g of the peristalt ic pump . T h e fract ionat ion is then done i n three steps: 1. P u m p the M B P containing solut ion onto the co lumn at a rate of 3 m l / 3 0 m i n into the first four tubes. 2. Collect the elutant of non-binding proteins i n the next 15 tubes at the rate of 3 m l / 1 5 m i n by p u m p i n g solution S l a onto i t . 3. Collect the rest of the solution (tubes 20-100) w i t h an increasing salt gradient (for cat ion exchange), as described w i t h reference to F igure B . l . In F igure B . l note the fol lowing: so lut ion S2 (without N a C l ) i s added to the t ra i l ing chamber first; remove a l l a ir bubbles w i t h a syringe and tub ing w i t h the valve a open then close valve a and replace the leaked fluid into the t ra i l ing chamber; add solution S2 without N a C l to the leading chamber and remove a l l a ir bubbles; bleed the outflow l ine from the pump and c lamp this l ine ; set the s t i rr ing rod to sp in moderately (not fast) i n the leading chamber; adjust the level of the two chambers to equal before beginning col lection. Co l lec t ion requires about 20 hours. Figure B . l : C a t i o n - E x c h a n g e C h r o m a t o g r a p h y . T h i s figure depicts a simple set-up necessary for r u n n i n g a gel co lumn to separate the charge isomers of M B P . • Optical density measurements. T h e OD280 must be measured for a l l 100 fractions collected a n d then OD280 is to be p lot ted against the f ract ion number. If things have gone we l l , this plot w i l l typ ica l ly show a number of peaks, labelled C i , C 2 , C 3 , C 4 , and Cg corresponding to unmodif ied basic prote in ( B P ) , and B P hav ing a net gain of 1,2,3,4, or 7 negative charges, respectively. T h a t i s , there are six charge isomers for M B P which may commonly be detected b y fract ionation and measurement of OD28o's. F igure B.2 shows a plot of OD28O versus fraction for basic proteins obtained f rom h u m a n white matter . Superimposed on th is plot is the conductance, measured F r a c t i o n , n Figure B . 2 : A b s o r b a n c e a t 280 n m v s F r a c t i o n . P l o t a represents the opt ical absorbance at 280 n m plotted against the fraction number (see text) and demonstrates the separation of four charge isomers (labelled peaks) each hav ing a net gain of n negative charges: n=7 (cs), n=:4 ( C 4 ) , n = 3 (cs), n=2 ( C 2 ) , or n = l ( c i ) . P l o t b shows the conductance of each fract ion , the l inearity ind i cat ing that the salt gradient was mainta ined as expected. ( M . Moscarel lo , autopsy number# B595-88; A lzh iemers ) . i n m S , for tubes 20-100. T h e straight l ine indicates that the salt gradient was mainta ined as expected. • Dialysis of components. W h e n the fractions containing the various components have been identif ied, the tubes containing a par t i cu lar component are placed i n a dialysis bag and d ia lyzed over the next couple of days i n disti l led H 2 0 . T h e water i n a four l i t re container should be changed at least 5 t imes . • L y o p h i l i z a t i o n of components. W h e n dialysis is completed the different components are transfered (washing w i t h double dist i l led H 2 O into culture tubes and label led. These are then frozen i n an acetone/dry ice m i x t u r e w i t h a ro l l ing mot ion to layer the sol idif ication. (Note : the culture tubes are sealed w i t h paraf i lm which has had holes made i n i t , before evacuation of the l yoph i l i za t i on chamber. B . 3 A l k a l i n e G e l E l e c t r o p h o r e s i s . T h e fo l lowing procedure is used to characterize the charge isomers separated from basic proteins according to the above methods. It is useful for subsequent screening of basic proteins. T h e p r i m a r y reference is to Diebler (Diebler , 1972). • R E A G E N T S R E Q U I R E D . A : 30 g acrylamide plus 1 g N , N ' - b i s acry lamide plus 123 m l H 2 O (store at 4 ° C ) . B : pure tetraethylenediamine ( T E M E D ) (store at room temperature. C : 3 g % (0.4 M ) N a G l y c i n a t e i n H 2 O at p H 10.6. D : 0.56 g % a m m o n i u m pensulfate in H 2 0 (make fresh: 25 m g +5 m l H 2 O . E : for the running buffer, 7.5 g glycine -1-1900 m l double dist i l led H 2 O adjusted to p H 10.5. A d d double d is t i l l ed H 2 0 t o 2000 m l . N o t e : A c r y l a m i d e is extremely toxic and is absorbed through the s k i n . A l s o , T E M E D is extremely flammable and should be stored at 4 " C . • G e l T u b e s . T h e dimensions of the tubes used are 5 m m (inner diameter) b y 7 m m (outer diameter) by > 11 cm. T h e clean tubes must be prepared by treat ing t h e m w i t h K O D A K P H O T O - F L O 200 solut ion, as per instructions on the bott le , and then dried i n a glassware oven. • P r e p a r a t i o n o f t h e G e l S o l u t i o n . The fol lowing procedure prepares 18 ge l / tubes . To begin, prepare enough glass tubes as above and stand these upright w i t h the b o t t o m end closed w i t h paraf i lm. D A Y 1. 1. A d d together the fol lowing i n a vacuum flask: 11.6 g u l trapure urea plus 6 m l reagent A plus 6ml reagent B plus 7.4 m l H 2 O . W a r m this i n a water bath to 37 " C u n t i l the urea is dissolved then add 1ml of reagent D and vortex briefly. Degas the result ing solution by p u m p i n g on the vacuun^ flask for a few minutes. 2. A d d 30 m l of reagent B to in i t iate po lymerizat ion (this occurs fast) . U s i n g a Pasteur pipette immediately transfer to the gel tubes, filling these to a height of 8.5-9 c m . Overlay the gel w i t h 80 fil double dist i l led H 2 0 i n order to keep the gel moist ; be sure do this very slowly and gently to avoid or otherwise per turb ing the gel surface. 3. Let s tand overnight at room temperature. D A Y 2. 1. Freshly prepare reagent E . 2. (Refer to figure A 3 , which shows the electrophoresis apparatus.) Remove the paraf i lm from the bottom of the gel-filled tubes and place these i n the rubber holders, labelled " a " i n figure A 3 . Ensure that the tubes hang straight down. P o u r 500 m l of reagent E into the bo t tom tank. W i t h the tubes upside-down i n their rubber holders (i.e. aimed at the ceiling) then , using a p ipette , place a drop of reagent E onto the bo t tom of each gel i n order to exclude air bubbles. Now place the upper tank i n its final posit ion (see figure A 3 ) . SIDE Figure B . 3 : A l k a l i n e G e l E l e c t r o p h o r e s i s . T h i s schematic (not to scale) depicts the simple apparatus used to perform alkaline gel electrophoresis to characterize the M B P charge isomers previously obtained f r o m cat ion exchange chromatography. (See text for the gel preparat ion procedure.) Electrophoresis was run for 3.5 hours at 3.75 m A . 3. A d d 500 n d of running buffer (reagent E ) to the top tank . Remove air bubbles above the gel using a micropipette . 4. Connect the electrodes to the power source as indicated i n figure A 3 . R u n the electrophoresis at 3.75 m A for one hour. 5. Sample Preparation. To a 1.5 m l eppendorf tube add ~ 500 fig of lyophi l i zed pro te in plus 250 / i l double dist i l led H2O. V o r t e x and then spin for 30 s i n a smal l centrifuge. (The supernatant contains the basic protein.) Into a new eppendorf tube add 10 fû supernatant plus 10 fil double dist i l led H20plus 20 / t l 8 M urea. V o r t e x . 6. Sample loading. Refresh the solution direct ly above the gel by removing i t w i t h a Pasteur pipette . W i t h a H a m i l t o n syringe l oad the gel: slowly add 40 / t l of the prepared sample so that the needle of the syringe is just above the gel surface. R u n the electrophoresis for 3.5 hours w i t h a 3.75 m A current. 7. Staining the gel. Prepare i n a 250 m l flask a so lut ion : 0.5 g amido black plus 93 m l H20plus 7 m l acetic ac id ; put paraf i lm over the top of the flask. T h e gel is extracted f rom the glass tube into a p a n containing double disti l led H20using the fol lowing method. The needle of a l ong syringe containing double dist i l led H2O, keeping the needle against the edge of the glass and paral lel to the long axis , and sq iur t ing water as i t is inserted to a depth of ~ 1 c m . Slide the needle around the entire perimeter of the glass-gel interface. T h e n , holding the tube sideways, repeat this procedure at the top of the gel ; be prepared to let i t fa l l gently into the pan of water as this is done. (Even better , catch it i n a wet hand and , being careful of or ientat ion, insert i t into the test-tube.) A d d to the test-tubes containing the gel enough of the prepared stain to com-pletely cover the gel. Let this sit for 10 m i n then , using rubber gloves, remove the gel onto a large curved spatula , pour ing the dye back into its flask. 8. Destain the Gel. P lace the stained gels into p last ic test tubes which have had smal l holes ( 0 ( m m ) ) dr i l l ed i n t h e m . P lace these test-tubes containing the gel into 2000 m l of 7 v o l % acetic ac id . W h e n the acetic ac id b a t h is fa ir ly dark, change the solution and repeat (i.e. use 2000 m l more of 7 v o l % acetic acid.) 

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