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, ,$.EFFECTS OF CHAIN LENGTH AND
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LENGTH MISMATCH ON ORIENTATIONAL ORDER IN FLUID STATE LIPID BILAYERMEMBRANES
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-
It is ~ll.ygwat pleirsure to tllnnk all tbom wBo Ihnvc r r , ~ ~ l , r i l ~ ~ ~ ~ c r l
I,,
1.1tir ~ l i s ~ ~ r ~ i ~ ~ i ~ ~ a o . I am gralcrod t o my mlpervianr. Dr. Y i r b w lR.
Morn,w, lor lhir xnpps~l a w l gtridil~~vl.over tbe wl~alo stngc or m y .csrarcL work and 111t~is writing.
I wid, t o tllank Drs. I. P. WhifeLt~ad, CLris W, bl. <:rant i ~ t n < l Ih.v Singlt lot Il~.il.
mllal,aration ou my rescnrrlt projerla. I lnnvr Icnvtbc.<l n lot. lr<,ltl !III,III. 1 ; ~ X O SY~XII 10 thank Profwxor M. B l w m u l d Clnrp Morriru~b rnr ~ p ~ ~ ~ v i d i ~ ~ g 1) co1>y 01 111~. 811..l~ill~illg progmm.
I expressnny appreciation t o Drr.
N.
H. Ricll nlld .I. IN. dr Hruytb hnr tlm<~ir~~il~.t.i<.il~iolitn~~i n my Supervisor's Committmmcl lor lllclr connnlrotx n~,cl rnrrrul nmrlitng rnl tlmir I.l~nix. I would also wish to thauk Dr. Ran Benvis, wlm nhu b~~r.rvcd eta tIw S ~ p ~ ~ r v i ~ , ~ ' ~ (bn8s8itlt.t..
I would like to thank M n . J. Bwmn and Ma. D. Coil>rlt BI. tlwir tvllic.ic~ttt ;tutl kind se,vice.
I gmtcrlllly ack.ow~odga tllc financial naxiatalln l l ~ v i c ~ r c ~ hy LIDV S,.I,C,UI
or
(:n,i~,,r~.,.Studies nnd Departlnent o l Plnysiu* i n the lorn) or Gractlmlr lil~ltowsltil, a ~ j ~ l li,nrllirlg Assistantships. I also gratefully acknowledgr tlw Wonlcn's An*ocixlIon e l Mctr!ori;nl Ilui- wrsity br their awarding rnc a Cradunlc Stltdortt Scl~olanbitr for I!t!M.
I k . ~ ~ t c . r i a ~ ~ NMII hpcrtmscol,y w n ~ !used tostudy l l ~ ~ ~ ( r p c 1 ~ 0 f d ~ a i ~ n l ~ o g t h and r h d n hr16rll ~ ~ ~orimlt;bt~olla~ i ~ ~ ORIO~ ~ .i. lfitlid stnk, ~ ~lil,icl ~hilayer m o c ~ r ~ nll.n,~,mllpa.
Sa~tnplw likc tliu:yl ~plm~*ipl~oli~~id*. glyralil~ilis, lbinary rnintuaes of pho.iplraliplds, binary rm>ixtuna of glyrolii~iQs wilh pl~o~~~l>olil,ids, and tonnary rnixturcs c o t ~ l n i t ~ i t ~ g cl~olr.qteml wcw tuu.rl. Spcrinl nttrrltion war paid t o exnrnlniug lhow the line rlmpe of the o r i o o l - tionnl orclor pnmtnclcr lpmfilc and t,he tetnpcraturc depenclencr of firat mo~neal auar tLc at~l/lI.tirl ( p l b ~ r l?i~l!aititnl WPIC clelrrtninrrl Ihy n linlitcrl h r l of ;&aors.
'PIII, sltnpc af tls. srnoollnal orclrr pamnlctrr pmfilr has h a n buncl l o be drlrrlninecl Iare:ly 14 lhv rnvan order p a r n u ~ w l < ~ for thc cliit~yl plna~pholil,icl hilayers i f pasitiotb nlotxg Il,v rlli~irt is tmmmliz<.d. Evnl in, lhc rivr of biuary mixtures, tlmr observed rllnpes of I.l>c, x8lncrolla.d onlc.r pnmaurt8.r pmliles will, tlle same rnrnn order pnratn~ter r e r e largely il>clc~pc.~l<lnnl or I lac. rotmtilctet~t's conrentration w i l h i ? ~ the rnend,ra>e. These observnlionr
~ u g g d . tI1;1t illp lllrntl OXIP~ I,aralnctcr is of a few paratneters WIL~CI, det.m,isr tllp shapv o f xlsootla~cl u r l n ~ t n t l ~ # ~ n l order paran~etcr pmfilrs. I t was alao obsrrvcd t l ~ d with dvrrr;ui8~g rlbniu I n ~ g l h , llte annplitlldo of the cliscor~tii~uily i n Mj decreases and t h r rlsl,#. of M I vrrvtts
T
i~trrca.ru for the diacyl pl,oapltolipid bilayers at tlac trnnsil,ion Irtt8pvrnlar<~. I t was found that l l ~ c depcnclcncc of MI 013T
could be accounlrd for I,y a ILa18tInll tltmry and t l n ~ t thc observed I,rbaviour was sensitive t o t l ~ e chain len@l><lcr8c.n1<lc,rtl ~~ITPICIIC~S bclween lhe spinodnl lempernlttre and the tmnritian temperat~cre.
I!, ~.li~i!b.lrtngtl~ n ~ i a s m t r l ~ c ~ l Lilnyrr*. the arientntional onler paralnetcr lor
~ v r y Itmg rhnilla wrrr fmnscl to Lave, n aecond platetau near the methyl end of the chain.
'l'br ~ l i r t l . i l c c ~ ~ l l e h n srcolld plateau ill tlle order lrnranletcr profile suggests thal llle
mismatcl~cd part of l l w long rllninr aznl llir ~ n r l l ~ y l n>elr ol l l w rlwrl rlt;linlr 1t7~111 1111.
opposite lnorlolnycrr arc tniaglc~~l witlt c.ia.lj crlbcr. fortnit~g i b W Y V lluicl ~r.r#l,ii#l I;t).rr ill IIIV lnicldlr o f tlw bilnyer. This fluid r r ~ l l r n l I v r r ,nay lltnk l l w tn, xi$c~ of tint, Ihihtyc.l. il l lltt.
biological rncnnhmlles. T l l r onirtcsrc or rl8olntrml i n 8 t l ~ w rl8ni11 ~ a i r ~ ~ t i ~ l r l ~ r ~ l xy8t~.r~~r la,@
innuence
orr~er pnrunrtrr ,,,OI~ICW itl c.~lihil,x I,IIL I,;,s;,
I~I~I,.influen~e on the second platc%!l fo? t l ~ v c ~ y b s g c l t i % i ~ l ill 1/81. Inilayt).l.~ ~~ni'il~tr,..
TI," pllhw c~iagrms for hiy hlll ~ ~ ~wit11 i,.~I.II,!~ ~clllllllO1l,.lll. t ~ ~,I~.~~I,.~;~~.<I ~ . ~ IS,.
clillcrabt. I t was loand Lllat 111,. %-NMII rpc-tra r l ~ i c l ! rc.lman>l clill~tt.!~t I;!l,c.lt.cl VOIII- polleulr a t tllr same l ~ t l l p e r n l ~ t r r s i t n ~ ~ l l r ~ t m l l s l y rcq,icnll tlr. rlHl<r 1,f 1111. I.wc, I.IIIIII)II- nenls b n given mirlurc, wllewns lhis ia not tltr C;LW for I.lt(. prolll~s s ~ l ~ ( . l ~ l t u Ih%vq. 1,111.
same plateall value. This discovcry~nay br l~clphll for it~lrrl~rrl.i~~gxll.NMI1 r r l ~ ~ ~ r i ~ u e , ~ ~ t ~ l I rrsults for 1hinnr.y lipid bilayor mixturn.
Acknowledgements I Abstract
Abbreviations List of Tables
List of Figures xviii
1 I n t r o d u c t i o n 1
1.1 Structum oi Lipid Bilayers
. . .
I 1.2 = H - N M R Study on BilnycrSl>ttclorc,. . .
:I 1.9 Asalysis o i 2 H - N M R SI>PC~I.L.. . .
7 I.:l.l Order Vnmiect<~r Prolilr. . .
X 1.:4.2 Sl,cdrai Pirxl Molt>rlll nucl P L w l'nmxiliot~r. . .
!I 1.3.3 Technirluc~ U r d to Bxlract Onlcr i'nn~t~etsr IPn~liitli. . .
I1 1.4 Aboul This Work. . .
I:%2 Review of2H-NMR Theory, T h e W i d e Line Experiment, and Materials I n 2.1 Harniltosrians ancl Qunrlru~~olo Splittitng b r Spit, I Sysl~.sl
. . .
IR 2.2 Quzdrupnic Ecllo. . .
2:l 2.3 Parameters lor Qtrndntl,oie Echo I'aiac Sccltwncn.. . .
2!1 2.4 The Speelmmeter. . .
:Ill3 Information Obtainable f m m M o d e l Membrane A w l Chain Spectra 35 .$.I Slllrul.l~rd Onlcr Pi~mu8nal.cr Profilc~
. . .
:I5.1.2 Gr!!figl!rntiol!al Slatislica ol Acyl Ol~niu Sqlnunt*
. . .
102 I I x i
. . .
I0 .1.2.2 lil>t!!rlting of 11)s Clmitl. . .
IS .i.
.I $1, vctral Mmosrcstr. . .
4.1. . .
.$.I Iii!~;~ry I'ltnar Dingmms.
'Il-NMR Sllertml S a l ~ t n c l i o ~ ~ 15 4 Experimental Results and Discussion (1): Single Diacyl Phospholipids 48 4.1 lelmdactio~~. . .
194.2 C!lmniu-hngtlt Scnlit8g ol Orirtvtntioual Order Parameter Pmfiln
. . .
604.1 Smling Property and Mean! Molecular Pield Tbeoiy
. . .
634.4 P l t w Trntailion Rcl~nvior lor tlle Diaryl PC Rmily
. . .
59.I. I.1 M o d r l i s ~ ul tlw Tra~mailion
. . .
O l 4.4.2 Al>nlysis 01 Dnln. . .
GG .I ..I..! salllmilry. . .
OX 6 Experimental Resulti and Discussion (2): Chain Mismatched Systems 70 5.1 I n t r o d ~ s t i o ~ ~. . .
705. 2 OnlCor awl OalCcr/SOPC Mixtures
. . .
71. . .
5.2.1 N-lig~~orcroylgnlnctoaylcera~~~ide (24:O OdCer) 73
5.2.2 Mixtuwa of <:lyvoxl,bingulipiclr (US!.) 1''.1:1I (:;d('cr. IR:ll 1:;1l(\.rl rvitl, SOP(!
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . --
r , 5.3 Mirlsre. of UMPC/DSP('. . . . . . . . . . . . .
. !I116,:l.l Selection of Sperlrn for (!etrl,nrinn, of Uhl19(' r t t c l IlSI'(' i l k 1111.
Mixtlnrc
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
111 5.3.2 Chnill Ordering is DMI'(:/DSPC Ililzxyt,rr. . . . . . . . .
!Ili5.3.3 (:hain Exlensiott of IIMPC at14 DSP(! ill W i r l l ~ r r r
. . . . . . . .
11111 6.4 Ternmy System of Cl~olrslrrnl ill Glyrolipic!/SOI'('. . . . . . . . . . . .
111:l5.5 The Arrangemolll of tlw Ernva Chain in 8ilnyer Mixlun.
. . . . . . . . .
lllli6 Summary and Concluding Remarks I l l 8
6.1 The Chain-Longtl Scaling Pmperly olOnlcr Pam~rnel,rr Prulilc~r
. . .
Ill86.2 Rmt Moment Versos Tce~prmlure Ncnr T11c C l l i ~ i ! ~ Mc4lit1g Trir!t~iliutt
.
10!1 6.3 Cl~nin Misnlalcln E f f e l r it, Lipid Hilayer Syslntlr.
.. . . .
. .. .
. 1111Bibliography 112
L i s t of Figures
I .I A schen~ntic th t r r cli~nc,>sbsnl ricw o l a r;n,nll rrrlicxa or Ihiclh,pil.al IIIVI~I- b r n e .
. . .
2 1.2 The !>arts of t l w ~phmpl>ulilrid ~nolerztlr pbun~~l~ati~lylrhc,lit~~~ n.prc.sc.slnlit, lormulir(A) and as R sytnbol (R1.
. . .
:I 1.3 Lipid hydmcnrbon chain nt~d ro~tfoinratin~>x al,oul ;r xinglc, (:-C bolal. TIM.t b ~ e s t g b r e d conlormalions (ahown iht right colatns) an, virwrcl ;doup the C-C bond (see left roh~mn) nlld are n.lalcd I,y 120' r n l x l i u ~ ~ ~ i~ltcml the bond axis. Stclic interncliatix lhrlwn,!b tln. tsvcr chain xq!,#rn,~mlr. (f'IIz).
nnrl (C&),, csusr llnp two ~ Z L U C ~ L P <~t>brnt>ill.iou~ t u Bv t ~ l Ihiphvr PIII.RY tllall the 1rana conlormdioa.
. . .
.I 1.4 Powder symtrum lor DMPC[dsn] a1 41 O C .. . .
li1.6 The de-Paked spectrunn lor DMPC d 4.1 Of! ( $ e r o ~ ~ v o l a l ~ ~ $ ln,u~ Ci8. 1.4).
The double1 with llxe srnollrst nplittitrg corr<~spunclr l o tlto ~ m ~ ~ l l ~ y l X ~ M ~ I >
ia tlne acyl chins. The next doabld corrcsl,aalr to lla. ~ ~ ~ c ~ l . l ~ y l c ~ ~ ~ c ~ g x q n next to the ",ethyl grnnq~. The ix,mniuit~g ~lo~tblsts ,may 11,. axiptt..l
I.,,
1.11t.other ~retbylenegmups (seeChaptm 3 lor details).
. . .
12 1.6 Chemical forn~ulalor lipid t n o l n u l c ~ ocsrrl i t , lllis work: DSI'C (a), SOP(!(b). Gnlaelosyl Ccmrnidc (c), ancl cl~alestoral (cl).
. . .
I41.7 1.ilrids !mod i t , l h i r w ~ r k anr rcq>rrreuted ~cl~ematicdly. Their claen,ical h~ro>~ulnr i ~ r r rhr~ws it, Pig. 1.6. Riiaycrs (a) to (d) are single molecltle Ihilnyca. They r l i k ullly i a chniu Icnglh of the lipid cornpasent. Biinyer (I:) ix ib1.w ;l~inmglc% an>olrasir Lilnycr but its two moieties d i k r in length Iby six ravl~wts (see Pig. I.G(c)). Ril;~yc:ra
(0
l o (It) are binary lipid miutsn~s.'PI#<.y s ~ a y vnry c.illvor ill rolilpoaa~lt drniu lesglik (I) or hear1 group (g), or Ihcatlb (11). Bilnycr (i) is thr nnixulrrnf bilnyrr (g) a t ~ l cl~olrpteml. Bililyrr (j) is llle tnnixluw of hilayor (13) and cl~olateml.
. . .
2.1 E k e 1 or Zee~nno and Zecmnu plus quadrupole interactions on llno enorgy
. . .
icveis of n rlculeron i n an external magnetic field.
2.2 Mcnthrnnc in an external magnetic field with all lipid chains cleuterated it1 n si,ecific sits. Local orientntiou ol the bilnyer ~narnbal [a); ~pecifimtion or vnrious nuglw in, chnmclerieiug the motion of a c h i l l (b); and the.
<l!ma<ln,~,"ic al,litting (c).
. . .
2.3 Qa~ttdmul,olr pulse squcncr.
. . .
2.41 Rlock diagram of n NMR %]~edmsleter.
. . .
:$.I Mail of the dcPnkerl spectrum for DLPC at 7 'C. The area or peak C
. . .
proviclrs a rrlerpnrr i n the peak resolving ~pracesa.
:1.2 'Tlw ~ p o s s i l ~ i ~ seg~nent conlorn~alio~~r and the relaled order parameters. 6 is l h r angle belweon thc. Lilayer normal and the normal to the plane $panned by the two C-D bonds. The segmenl order parameter Sco =
E;, She
= ( u - ~ ~ - v ~ ) / 2 .. . .
S.3 A ~clncmalic ~plmae diagram for n binary system forming a regular solution.
Rvsiotl I corresponlds to tllc fluid pbare. Region 2 is tile region ~ r g e l / f l ~ i d two ~plmas~ raerislcnee. Region 3 corresponds to the gel phase.
. . .
4.1 2H-NMR spectra set 2 01 tabC I.1. (A) I)SI'[:[dm] nl lil O('
.
(11) DPPCldeel at 62 'C. (C) DhIPCCL] nl .la O f ' . (11) 111.1'('[d4~] al 2;'C. Tllesr apertra display similnr ~ t > a g ~ i t > ~ ~ h ~ 01 II~P B P ~ C I p a r a 1 1 1 ~ 1 ~ ~ irl the plateau redot) of thr a p c r t ~ w r .
. . .
524.2 De-Pnked spectra (lelt) ntmrl tllrir sor~ontl,<~l orinalntioanl crnler ~p;.nm>rtc.r profiles (right) lor set 2 of table 1.1. (A) DSP(![dl.] st 62 Of: (0); (1%) DPPCld.,] at 52'6 (0): (C) DMPC[du] nl41'C ( 0 ) ; njnl (I)) DI.P(![<ln;) st 27 'C ( A ) .
. . .
5:l4.3 Smootlled orcler p a r a m e l ~ r ~ ~ m f i l e s lo! sots of*prrtm rh<*u.u LU Imim~rir~~il;tr rnagniludea of the order parnnnrlsr i n 1111. plntval~ n,gias. (!llsin ~ x n i t i ~ s x are ~rom>alized. Order Imrsmcter. lor an- I u ~ l at&-2 r l ~ d t > clrulmn>s (rr- cept at the opoaitios) nremrngwl. (a) Spectra Lelotngiug tc) sc.1 I ~Il.;,l~lt.
4.1. (b) Spectra belonging t o sel 2 i n tnhlc 4.1. (c) Spc~.Lm B~~l~,sging hr w t 3 of table4.1. For each set olpralilrs, tlbc sy#~nl>olr i~ldirntr, ( 0 ) IlSI'(!, (0) DPPC,
(0)
DMPC, and ( A ) DLPC.. . .
64 4.4 Snnooll>rd order ~parnmeler profile8 for n>ixtt8ro of spcrl.ra r1nurn.n tcl 1 ~ ; s ~similar nmgnitudrr a1 first nnutnent MI (m: to lahlr 4:'). (;I) SIMT~~;!
belonging t o the minture.of DMPC/DSPC[dm] with I)SI'C r o ~ ~ c t v ~ t r r l . i s ~ ~ x 0125.2 mol% ( 0 ) . 50 I"oI% ( 0 ) . u~cl 74.8 nlolX ( A ) . Onlor ~pihr;~!~s.tc.rh for . ? - I and an-2 chain deateru~xr arc avrragrd. (I,) S l r r l . ~ ; ~ Ibclc~~bpi!~p t o the nlixturrr a1 l8:O OalCw/SOPC will) IX:O C:nl(L.r c.ur~n~t~l.ral.iol~x 01 10 mol%
(0).
20 IIBO~% (O), 29 nrolX (A), ancl :1!1.1 !mol'%(v).
( I , ) Spectra belonging to tlio mixtureaol24:O OalCcr/SOI'(: will, 24:O (:nl(:t.r eoneentmtions 01 10.1 mol% (O), 2S.Y nnul% (0). :34.1 rnel%, (A), 10111 6:l mo%(o). . . . . . .
684.5 liir.1, rnc~rncnl MI vcrnur T for (A) DLPC[dra],
(0)
DMPC[dsr], ( 0 ). . .
DPi'C[dm], ( 0 ) DSl'C[d,]. 60
4.0 in~vcrn: cllnir~ c.xtet~sio~n (I)-' vc:rsus T. (I)-' is obtained rrotxl MI using I.Ite rc.l&tioxrLip givvs iir Bq. 1,1.1:1). (A) DLPC[d4s].
( 0 )
DMP(:[dnl, (0) I)i'P<![rlr.ll, ( 0 ) DSI'C:[d$. Tllr upcn ryn~bolaareobtainecl fmsn lltedsln ptcac.~~lucl i n Pig. 1.5. TInr rulirl ~ y ~ n l n l s nr? nd<litionnl dn1.n ~ r l s collrctrd l r n n tl~csn~ncaa~nplos or anlnples 1pmpare.d i n the satno way from the salno. . .
stack nlatcrinl i n order to lldrer localizc thc tramition. 62 4.1 A ndnc~nntic represonlatian of I.he freo encrgy versus ordec parameter r e
I ~ t i ~ ~ r s l l i p given by Eq. (4.17) for (a) T
< Ln,
(b)T
= T,, and (c) T>
T,. 63 4.8 A ~ ~ i , ~ , , , ~ t i ~ i~~,,~t~~ti,,,.r
order l,arnmeter temperatllre R.Iby Eq. (1.14). The points (T*,5&) are spinadals. The caexialence curve r r m w r = 0 nt the critical temperalure T,. The transition occurs s t tile cnoiialcnce lar,perature ?:. (tmlnbcled) wl>iclt is indicated by tile solid vcrtical linr belwwn T+ and
T . . . . .
654.31 Plnls of T vrrjua :3[(r-a+/a+]z+[(r-a+)/a+]3 i a the liquid crystal plr;uc.
br (n) DMPC[dnll otaing (I);'= 1.092
2.'.
(I,) DPPC[dm] using (I);' = 1.123 ;I-'. and (c) DSPC[dml uaiog(1);' = i.141k'.
The interceptgiwa tLc: spil~odal tcmporaturoTI
and the slope gives (T., - T+)/2. Valuer of .st = ((I);'-
(I);') /(I);' were adjusted l o obtain eonsirtent values of T+ Imt!~ lllc slope and tLc: inlercept. Sixelra which contained any gci rn~~~ponentl we- onnilted rmnn this analysis.. . .
674.10 Inverse dmin extausiuti (I)-' vcrstls
T.
(I)-' is o I > t ~ i w t I INIII dl, ~usiltg the nlationehip givcml in) Eq. (4.13). ( A ) DLI'(![<I*,I], ( 0 ) I)MPO[<lw], (0) DPPC[da2], (0) DSl'C[d:a]. D i E w n t mwples 01 n given lipicl imw tlvt distiuguislml. Spectra in wltirlt go1 and liqttid crystal n,tnl~,~nz.xllr st.n.found t o coexist have bmn omitted lor 111,. parpww of c~1itrit.v w a r Ila
~h~ lirles obtsillrl~ llsillb l,nr;lmc.trrs r',llltd W~IJ, ~II..
pmeedure illustrated i n Pig. 4.9 and lixtrd i n I b b l r *I.1. Solid s l a m ~u!ill.k tllo spiuodal pointa obtained i n thia may.
. . .
li!l 5.1 Temperature dependence of 'H-NMR 8p.rtrn for N - l i g ~ o c . ~ ~ w ~ y l [ d u ] (Id-Cer i n hydrated bilnyer fonn. Vertical nrrowa itn<lirnlc.
+
I 7 kll. ell 1Imvfrequency axis. The curved w m w indicnlr t l ~ r lw1ta.c. clue to 1.Iar !;at several segments itncluding t l l r 1me1Lyl group.
. . .
74 5.2 Observed (A) and do.Pak& (6) N M R $pod.m lor 1pl6rc. hdly I!y<lr;~tv,l24:0[drr] OnlCer a1 l 'C.
. . .
75. . .
5.8 Smoothed order parameter pmfilw for 21:O C:nlCar at ffi ' C . 7B 5.4 Temperature dependence of the firs1 spcetrd !rmtnc.#$l, M I . lor N-((?A4
GnlCer) i n SOPC (right) at mnle lractiommr .r = 0.ffl ( 0 ) . s = 0.:IA (0).
E = 0.24 (A), z = 0.10 ( v ) , a t ~ d z = u.05 (0); &tb,I fop N-((:In C:rl(:?r) i t $ SOPC (left) at mnle Ira-tioaa r = 0.40
(O),
r = 0.2!J (O), .r = 0211 (A).=
= 0.10 (o),at~d z = 0.05 (0).. . .
77 5.5 Concentration dependeneeofaH-NMRsl,ectnbfor N - l i ~ ~ o c : r r ~ ~ l ~ l ~ ~ ] ~ d i u . -losyleeramide (21:O[d4r] GaIC'er) i n SOPC a1 tcmpcralam# of I Y:, I f i
"(:,
and 70
'C. . . .
?!I6.6 Sprrlm rr,rnpari~on of ~nmplca mntainiog 24:0[dr] CalCer (lower) (i.e., spcx.llirally lahc1c.d on tbv t.crminal mell~yl gmup and l h c two adjacent
~~~c~Lltylcscgn,ul~r i e tllc rcyl chain), witin corresponding sanlplm i n whirl^
thc lot~bcl>ain ratty acid was pordeuternlc!d (i.e., 2kO[drr] GalCer, a t low tnol% ill SOPC)(~rppcr). Spectra. shown b r 24:0[dr] GalCer contain 8 mg of dct!leratcrl glycolipid. C:alCer coaccntration was 10 md%.
. . . . . .
80 9.7 Concmtmtion clapendence of %NMR aprclre for N-stexroyl[dal galnr-tosylncramide (Il:O[dp. OalCer) i n SOPU at temperatures of I 'C, 16 'G, iual 70 ' C . Spectra are erranged i u vertical goups wit11 glycolipi<l lnolo frnrtion snd 1emporat.ttre indicated. Curved al.rows for the I 'C (gel plbew) 70 'C (fluid p~lsse) 0.05 frartion indicate fea~.cln.
aaxnrinlcd w,itl! tile lacarbon fatty ncid terminal nlelhyl.
. . . . . . . .
82 6.8 Spvrtra 01 (;alC!e~[d~~] in SOPC at 13 ' O . 8 denotes tbc mole frwtiono i OnlCrrlcl,,] in SOPC b~. a mrrejponding spnlrum. Spectra A, B, E, mtd
P
are obscrvcd npectra. C, D, G, end H are end point spwt*.obtnincd fmm spectral aablraction. C = A - 0.4SB.
D
= B-
O.BA, G= E
-
0.18F. and H = I-
0.15E. Spaclra C and D an? assumed t o be rl~nraeleristic o l l l l e proposed G2 aud GI plaapes, mpeclively. The qllality of lllr sul~tmetlos for obtaining C is not rufieient to distinguish bdweea G I and C L bul the ealeulated endpoint composition fails i n the GI ran*cletrnnit~rd by the suLtracl1on shown i n tbr left ploltings.
. . . . . . . .
84 5.11 Exal>qrlc of spectral subtraction for N-slcnroyl[d~~j galaetosyleeramide(I~:O[~I,S] GalCrr) i n SOPC at temperatures of 31 'C. Spectra A nnd I
3are ubxrved spectra. Slmctrum C is A
-
(0.35)B. giving an endpoint nt I , = 0.16 (Raidus point); rpeclrun>D
is B - (0.20)A, givin&im endpoint wl .r,=
0.52 (slidus poinl).. . . . . . . . . . . . . . . . . . . .
855.10 Proposed phase dingranls lor (lell) N-stman~ylgalartnsylwra~~~i~lc. (1X:ll GalCer) and (right) W-lignoceroylgalncto~ylc~rnt1~idrfrf(2~1:0 (:nl('c.r) ill SOI'('.
Vertical error bars wpiescn~t eitilnnlcd rango o l t u ~ t c ~ ~ t i l i n l y it) b(>tl!t(li~~
nossings determind by inspmlion of sprrlrn nucl n,nairlrmtiun~ of dl,.
Horizotltal Ilam indicate tho range olruperioat,atrl valucr olslni,>t~l I U S ~ U ~ spectral subtraction ted~nique. will, vanoar slrertral crerxnl>it>atiu~~*.
. . .
nC5.11 S p e r t l ~ and their ~nloolhed ordt.r Imnrntrl.cr ~prolilcr lor N - n t ~ ~ n , y l [ # l . ~ l OalCr,r (a, and
0 )
and N-ligaoaroyl[<lrr] <:nlCsr (I), nud 0). clirl,c~t.nvl In SOPC at I 0 mol% at ?P "C. . .
885.12 (a) 'H-NWR speetrrm o l DWP(:[d*] i s oxcear waloi at 57 '0. (I,) 'If- N M R spectrlmm of DSPC[d7~] in excess water at 57 ' 4 . (r) "I-NMII speclnm of 4.4 nml% DSPC[dio] i n DMPC at. 12 ' C . (rl) SmooIJ~ccl cxi- entational o d e ? paranletmpmfile$ cor~xapoodi~&g to tls, r l ~ * : l n ~ it, i t (01, b
(0).
and c (A).. . .
!12 6.11 ltI-NMR spectra (Icll) and lhalf oi thc corroslro18rling de-l'ihkc~l a ~ , ~ ~ l ~ . i \(right) for DMPCIDSPC mixt!wtsi,l. DSPC coara!~lndicr~~ of60 a > o l Z n~lcl T=60 O C
.
(a) IIMI'C with DSI'C[dm]. (I,) T)MP(:[cli41 will) DSP(:. (v) DMPC![da] witln DSPCIIm]. TIE dc.Pakcd spcclrun, rhuwrr nx a rolirl lilw rarrenponds lo thr oberved DMPCldsl] witli DSPC[d7.] pmvdcr ~p;dtc,rtt.The
de-Paked spcdrum shown ax adarlled lincia t l l r weighted X ~ I I I I o l t l r - Paked spcctrunl lor DMPU will, DSPC[dm] and I)MP(:[du] wit11 I)SI'(!. 945.14 211-NMR spectra (loft) and half of tho corresponding dhPaked speclrn (right) far DMPCIDSPC mixtures i t DSPC concentration of 50 mal%
Temperaturn were selected to ~ i e l d powder patterns with t h e aame max- imum apiilting. (a) DMPC with DSPC[dm] at T=60 'C. (b) DMPC[<b*J wit11 DSPC a t T=53 'C. (e) DMPC[dsrl with DSPCIdrnl a t T=56 'C.
Tlte de-Paked spectnnrn shown a. n aolid line corresponds la the ohservcd DMPC[dul with DSPC[dm] powder pattern. The dc-Paked spectnzm
~Ilown as n daslncd line is the weighted sum ol depaked spectrum loi
. . .
DMPC with DSPC[dml and DMPC[du] with DSPC. 95
5.15 Smoothed orientat,iannl o d o r parameter profiles a t 60'C. Profiles for both nMPC/DSPC[d,.] ( O ) , and DMPC[ds,]/DSPC ( 0 ) with DSPC percent- agv mols ronwntrslion of 25, 50, and 76 nre shown nt Idt, middle and right plottings r~spectlvely. Profiles for DSPC[dm] (A) and DMPC[ds4]
. . .
(v)
are also shown in tlie three plottings. 975.16 Change oloderparameteralong tl~echains in the aystemrof DSPCIDMPC at OO'Cin~lrioa~constitutional coneentralioos. ASOO =Sc~(DMPC[d14]
1x1 DSPC)
-
Sco(DMPC[du]) shown in the ielt g a p h in which mixtures have DSPO mucenlralionr 01 25 m o l l ( O ) , 50 mol% (D), and 75 n ~ d %(v).
ASoo =Sco(DSPC[dio] in DMPC)-
Soo(DSPCldm]) ahown in tlre right grrph in which mixtures have DSPC[dm] concentrations of 4.4 mol%. . .
( O ) , 25 moI% (Dl, 50 mol% (A), and 76 mal% (0). 99 6.17 Representative2RNMRpowder spectrs(left) and dePaked spectra (right)
for Is:O[&] GdCer in SOPC (s) aud in SOPC/chaleateml (b); and for OI:O[d<r] GaICer in SOPC (c) sod in SOPC/cholwteml (d). All spectrs rlln on, nlultilanlellar vesicles a t 40 ' C .
. . .
1045.18 Smootl~ed order parameter pmliles k,r 18:O[dZsl GnlCer (a), nltd 24:0[dr;]
GalCer (b), st 40 'C in bilnyer of SOPC
(O),
and SOP(!/ri~oiotrml ( 0 ) . I05C h a p t e r 1
I n t r o d u c t i o n
I ~ i n t ~ ~ o ~ n l ~ m a t ~ c r are curnplicaled systems. To understmld their pl,ysiologiral mles ssc, ~ r ~ ~ r l , us$crslattrl lhoir slra~rtclrr nttd physical propcrlie*. Technical ihlnovationa i n tlr. Iaboratcrry lhave Id to Lhe accumulation of a great deal 01 knowledge. A nnunlber of ~ , n c . r l l n ~ t bookr clanlin~g with tile properties 01 n~ernbmtics and bilny~rs have recently Ircxln ~p~hlialted [I-6)
.
In Lhis Clmptor, the membrane structure mtd research nrarll~ods relnlc~l 1.0 rrty PI1.D. projmt will be described briefly and my project will !be oatlincd.1.1 S t r u c t u r e of L i p i d Bilayers
All biologirnl mnnbranea am amembliea of v a r i e t i ~ j 01 lipid and protein moleculei Iht.ItI r s ~ ~ l l n r r Iby t ~ o ~ ~ c o w i l s t ~ t istermctioau. A 9cllemalic view of a small section o l cell
~ t w ~ t ~ b r n ~ > c ia rllow~> i n Pig. 1.1. As can be seen in llnis figure, lipids i n the membmne are i b ~ r Ihili~yer conSguration. The lipicl bilnyer provides the bade structure o f a rnemb,nne.
Vntiotnx prolc,in tnuioruloanrc embeddcd i n the lipirl bilayer and n~ediate~ome functions U c . t~>en>bratle.
In c.c.11 ~~naml,rn!ws llhrrr are lhm. lnlajor t y p a oi lipids, namely plnaapbaliplds (the trtwl nl,ut#dnut), cltolrslcrul, atxi glycalipids. Thwc lipids ~ n ~ p h i p h i l i r ~ n o l e r u l e s wit18 our o a l lnyclmpl~ilir (polar) and the other end hydropl~abie (uonpolar). Fig. 1.2 shows a typical phorpholipicl mnoleeule wllich hao a palm headgoup and two hydrophobic tails.
'rlw Laila mny vary i n l m g l l l and clegiee 01 saturallon. Differences i n chain length and
pmtein molecule
/
\I
bililyer lipidmolecule
saturation influence m e m l ~ r a r ~ r ~ d ~ y s i r ~ l lpropertira, littrh na Iltliclily, wltic.lm clc~lc~nni~w 1.h~.
functioning of membranes.
Two-chain i i p i d molcculs generally fol.m bilayrr v w i c l ~ s sl,urtla~a.c~aaly wl,c.u ~ l i x - per& i c ~ water. This is due to Lhrir nrrzpltipl~ilic nnlen,. Otlr of tint. vcvy i#r,lu,t.l.i~,tl.
features of iipid bilayen is their t l ~ e m ~ a l r n p i r ~pltnac, Idmvior. Ihtrpcrrtntt p l ~ o u p l r ~ l i p i ~ l phase* observed, i n order of increasitng te#epcmt~nro, inrluclr 1111: crynlnlli,#<. 1,lnn~~. (I,,), gel p l m e (Lo), an intermediate ripple phase il)ll), awl the Illrid or licluid rrystdlirr!
phase (L.). The gel to liquid crystal ttansitian a t tcznperatum 7:. is cnllc~l tltv nrni~in lransition and is identified as a chdt?-malting tranmition. II Inas l r r n ~ l c ~ s e t m l r r l a l l l ~ ~ f . the bellavior of an artificial lipid bilayor (model monlbrat~s) is ni~niiar te l l m l of 1 . l ~ lil,icl
IVigtnn 1.2: 'Phe p a t s o f tltr phospholipid ~noleculc pbaapl~atidylehaline represontml iis
runrllln
( A ) and R sytnbul(B).
1.2 *H-NMR Study on Bilayek, Structure
'nw
1 3 ~ ~ ~ s i b l r motion orlnoieet~lc. it! a, membrane includediffusion and isomerization.I1 Itna Lnrt widvly arcrpte~l that the hcadgmups of lipid ~nolecules and water fornl at, itnlt~rwt,nlung whirl> oneend o f ~rtolecule m o w
[Z]
and that l l ~ e mtation about the C.C hottda 01 the l i p i d Ihydrucarbon chains contributes t o the bilayer flaidily and determine ntnny o f l l t r ~physirnl pmpcrlics of the l i p i d bilayerPI.
The rotation of eacll methylene W $ I I C ~ ~ al>ot~t a C C bond creates n different conformation. There are thrcr alablcronformaliaz~s for a segmenl i n n lipid aryl rb3n. tu~tn~.ly gntrclrr+ (!I+). Inrnr (I), i u ~ l gauche- ( 9 - ) as shown ia Fig. 1.1. Tlnc coufor~~~.rliat~ clnitngra w i l l ~ I I i u > ~ ~ l z , r i ~ r l i ~ t rate of abont iOg s-' at mom l ~ r n l l c i n l u r ~ 181.
Figure 1.3: Lipid ltydmearbon cllhin and ronfarn~ntio~ts aI,o#ll, n ~isglc (!.I: llcr~vl. 1'111, three stwered eonformntions (sl~own in right columl~) am vieweti along Liw (!-(! l>e11,1 (see left column) and are relaled by 120. mtaliottr allout line bond itxi-. Stvri~. iutvr.
mtions between the two clnain aqnneals, (CH?), R ~ C I (CI12),, ralbe 1111. two giut1.11~.
mnfom~alions to be of higher etleigy thnll tBc trans eonfom~af,ios.
The cllnio molion can be partially clxarncterizcd lhy a81 sric.nl.al,io~ml orc1c.r prnattc.1~1.
[2][9]. 111 the liquid erystnllitxe stale, an average, 1 1 ~ con*lilsetal lipid trwlcr.ttlcw law.
tnotio~w d,arncterizpd by cylinclriral ~yrnmetry will! tllc I,ilayvr orrnlal ;u Lltc. ;uis twf
motio~~nl averaging. For &givencarbon doulori!rn> lboncl on &lipid ~.l~i~in, I . I ~ ~ ~ ~ ~ t i t ~ r t l ~ I . i o ~ ~ i ~ /
.r,l,.r I,.m,,r?lc?r ir clafine,l as [ti, 9. 101:
wlnvn Of:, is tltc nnglr hetwcofb the C-D bond and the bilayer nor~nnl and the average
ix tilkell ovc.r ~ . ~ ~ ,~ ~ ! , ~ c d r ~o. ~the tilne ~ ~ t i ~the experirnellt. ~ ~ ~ R ~th,. c ~ ~ ~ ~
~Iai~ir! is ch~rnii~att.d Ihy mr~brnrnlions b r wlricll O m = 90°', Sco ir gnwrnlly ncgnlivc [!I].
I b r n ('-1) I~,scl ~ l t n b ~ g o i n g irulropir r#,o.orin>tntiotn, ( m s 2 0 C ~ ) = and SCD=~. TIIIIS a I;L~#<. r~l.o~l,lr. vit~,lc.
.r
1.1,~. ordrr pnmleptc.r ilrl,lic* -arllln~~ RI,,~,I~I.~,~~ rmric.lltalioll tllc.*,.g,3,c.,,l,.
lic~r.it~,l;r tlw tensor inlernctions a( tbe sl,in systarn are !lot lully averaged by >molcrulnr nrlI.icnm ill llnc lhiiny~r, 211-NMR, rrs nl,plicd lo hilayer membranes, is refcrmd to ua rolicl- rl.idr NMH.7lr. 'TI-NMR q,cctnan a l e dnltem~, on n lipid ncyl chain is n Pnke d o l ~ h l r l iht tltt, l i < ~ u i < l cvy6lalli1w ~plnm. I1 mst1lh lmtm t l x s!k~~erpositio~> or d o u l ~ l ~ ~ l ~ ~ arising ln,,~~ r;#8brlv!?~ly cric!!!lccl r l o m ~ i # # r and is a150 relcrrecl l o as a pasdpr paltcnl. Sltnrp c~1g.r c.fi,rwxpt,rldiag t o ~nulw*.l!lni mvrinltit~g ahaul axes perpendicular to llle a!~plierl ant;sttc,l.ic f i ~ l d nrc sl,nralrcl by tine qundrupoir splittiag, Avo 191. The orienlntiomnal unlrr 1pamtmr1c.r c.nn he rncwlnrrd via lhr nurlcnr q o d r u p o l r splitting through
Awe = ?*p 'I
,,
' "D' (1.2)w11t.n.
$*
cz 12ikllz. Sro d r c l s t ltime averaged angular aro.plitude ~ of motion ol llsr rl!nin xrgnlnnl on tltr 2H-NMR l i t n r scale of 1 0 - 9 0 10."- and is tllus se~~sitive I*, tla. avenng n w i m t ~ m n l t ~n~nl,letl e. mulecttles clilluse tllmugh tlm bilayer. Pig. 1.1~ I ~ n v s 2% lypirnl 'H-NMR sprutratn lor a perdeuterntcd (i.e. w i l l all hydrogen atoms on nn avyl rlmniu rrpinr<rl by deeulrriatns) sanlplc in, tile liquid crystalline pLar;e. I t consisls sl xstl,c.rl,nrilionx of Pnkr ~ l o ~ r b l n s nriaing from deulero#x along tlnr chain with a muge of sric.utiliu,al 0rdc.r pnm~n~ckra.
Arter the pioneering ZH-NMR work dnllr os soil18 IOYI~XIIC~ by Oldlirlcl c.t ;XI, (I!lil) [II], tllc2H-NMRrnethod ans.mon npplirrl luclinryl lipid bilityvr snmi~ntnn.. 1'hn>o~glt ;a series or studies. Seelig and co-workan [9. 12-19] ltnvr a$drrawrl vwiotir lhnrir i s s ~ ~ c ~ s . rttrlo as : (I ) hydrocarbon dlnin orientation at varionr pmitioss ia lbc. Ibilnyt,r. (2) tnoliums cd the &=in segments, (3) tile delemmi~l;llion 01 chniu rxlc.!mioe ( l l w cll;*ia lhmgtlt ~ p ~ d ~ ~ . l ~ . d on lilp bilayer normal) or bilnyer thickness i n t c r n ~ ~ o l l l t c ~ ~nera!tn.d rrgmnatnl o n l c ~ 18%
ranelern, (4) rnapetic orderins of Ipl~ml~l~olipid nloln11rnnc.s [IX], m ~ d ( 5 ) n~s$nllidioa:~l changes of the headgmuj> due t o me~nl,m~~e~lol~yclrntint~ [Is].
150 kHz
Figure 1.4: P o w d o spectruln lor IIMI'C[dn] a1 44 ' G
'Ib list all ronlrib~ators in this ficld ir dificult b ~ a l ~ s c o f llle diversity of metnbnnes irwl l,I~c.ir 1rLy8icrl pmpcrlin. Hcrc I will sl>ecifically mention two nloregmupr, no1 o!lly ih<r,wlnr limy Ihavg? c o n l r i b ~ ~ t ~ ~ l s i g ~ ~ i f i c ~ n l l y ill this field, but also because the teclnniques clcvc:lol,~~~l Iby t l t r ~ n lhavc hccn llcnvily used is this project. B l m m and ec-workers [20-'251 1t;rvc. nvn<ls i~ n p ~ r t n n t mntrihutiona to tho understanding or the pllysical iefomatiotl con- laiscrl is 'll-NMR spoclra One of tltcir contributions is spectral 'de-Pakelng' [21]P2], wllicln in r. pmcdure for obtaining tile spectrum of MI oriented ryrtern from tlnnt of the
~powclc,r rpt.ctnm lor a ~pcnleutrratted systrm (see Fig. 1.5. Thew the total width of tbp alwcc~~~on (I50 kHz) il ihdicalrd Iby the hatlorn line. This practice will be followed i n llbix tltai..). This procednrm improve. tlie definition between the peaks i n a spectrum nntl is wicloly !used n l present i n the analysis of spectra. D w i s and m-workers [G, ZRSI]
lhnve nlsu made many contributions l o the field of membranertudiea by use oi2H-NMR, il~cltlding lecllniques to con~tnnct binary phase diagrams by spectral subtraction. Otlber i s ~ p e r t u > l rontribations related to tmy project will Ibc eiled i n the later chs],ters b this Ll,<rii".
1.3 Analysis of W N M R Spectra
Itnfu,~nation about acyl chain ordering, obtained from 'H-NMR, can be variously rxprmru.d ns nu orienlational order parameter profile, a mean order parameler, and a sp"lra1 firat tnometlt. The rigttificmlce of thee properties in the description or bilayer stnlclan, nncl bilayer p l m e behaviour is briefly discussed i n this section. Thc teclnnique br r r t r w t i n g tbc oriontational order parameter profile fmm the N M R apeelrum is also B~ECIIS~YI. The theory of 'H-NMR ns applied to bilayer systems is reviewed i n the next cllnplcr.
1.8.1 Order Parameter P r o f i l e
The orientationnl order parameter pmRIe 01 n lipid nryl rlkni~t is oi~tnlnnl by lplotlinlg order parameter versus carl>on aan~l~cr. Ilsadly. vnll~va of 111r on1t.r ~par.nm,<tvn L a the upper half chain, near the benrlgmup, cl~nngr slowly w i l l lraitiotn nloug tlr. rlmiu.
Along tire lower half of t l ~ r chain, the order lrilratnctcrn 1x1 t ~ r a g t ~ i t ~ i d r dt.rrc.ilsc~ ~mon.
or lmr o~~,aneotially toward lbe ~netllyl cad. Tllc rcgion \vlnerr the vnittw of IItr o n h ~ parametez dl-inge slowly is eallsd llte ~plntrnu.
The orientational order paratoeter reflect. tho tilno-nvcragml o r i r ~ ~ t r l i o ~ ~ .,I a trlnnis segment. I t is not d i w t l y related to thr rat" oft.11~. xcg~nct~tirl snoticno, w l ~ i r l l is I,c~l.tc~r s t u d i d by relaxation time rxlrerimeats. Howrvei, i~ smaller vnl?~u uf t l t r 1rn1c.r ~ p i s i ~ ~ ~ ~ ~ ~ l c ~ v geltera~~y mea.a a larger s.gu~ar anlp~itla~r lllot,ioll 01 th.. c.~lnirl rrsl.c.st. 'I'I,~,~ t.ltc.
shape of the order parameter profile ihldiculer that %,gtg.>cnts is tllc ~ , l ; ~ t ~ ~ i u ~ arc.;, o f ;L chain* sre mare ordercd than the rest of bite chain and thal the ordrriug ol r<xtta.r8tx it8 a chain decreases along the lower lhalf or tlac r h d e rrsolting ia n !more lluicl 4,1111. ill tho hilayer middle region.
The term flux is sometinres used to deurril,~ the extnnrion of t L . ellainn p;ruring 1p1.r unit area toward tine bilnyer middle region. Tile sl~q,c or lhe orcicr tpars!!rkr tpn$ilt? 111573
~ ~tliat the t s dlaill
nux
cnrrcapondillg lu LI,~ l,~aisml rogioll ir iL and tbat the Bun docrezses ,now or less rxponcntially lowanlr lhc? mrl.l>yl grr>t#pPSI.
Theoretical consideration o f experimentally deterrnitlsl order tmramcrtcr pmfilrs IISj[:l:l]
ha. suggested that the molecular chains l i e bmically lparallrl lo the, 1bil;g.r sunm~i,l. 'I'Im?.
pmbability or l l ~ e acyl ehaiu segments foldiug hack rnny br scgligil,lr i n 111~ lple.t.n1 iuf,r ancl increase along the lower half ellait> l o R !t~arinluttl v a l ~ ~ ~ ~ ili)o~$t 0.14 hrr Lhc. 1m~~tl8yl i n a chain with 14 carbons P4].
Knowing the order psrameter profile, one c a ? ~ a l i n ~ n t c mean e l ~ a i ! ~ sxtesriun [16jl:16].
I f d # l i t i o t ~ n l ~ ~ ~ t t n l p t i o n s an? madc, ih~rornlation ahout the arca per eltnin for the hilayer is thc I l l l i c l state <a18 Ibe obtdncd rmm the mom order parameter,
(so")
=a,
( N - 1 ) (1.3)
wbcw N ir t l l r l n l d cnrbu!, tutl!nbciul the. chnie. TIE area prr cl~nin then l h r . n simple
#:rrll>iric&l rc.lnliosrllig wit11 ( S O D ) , aa d e e ~ a ~ t r a t c d Ihy Bodem et al. b6].
Tlltrn lltc ordcr pmatnrtcr and its profile prwidc strueturd information about cltain wg!nc:nl pai it ion, orientalial~, and eonlorn~ntion i n n lipid bilaycr, fmnl which 1,llysical qtli~ntiti* liko t lhilayer tltiekness, tlte a m per liPd molecule, atad the caefficier~t ~ o l lltertnnl ~~xl,m%ion or tl-e u y l chain Icngtl~ ran be obtained.
1.3.2 Spectral F i r s t M o m e n t and Phase l t a n s i t i o n a 'I'bc first momom~t of tltc lhalfspeetruna io gives by
,,
- FI(.~)wdw%f(w)dur
'
(1.4)wlicrr f(u) is 1110 srectrum. Tlle relationship between Ma and the meat, orientstiot~d un1t.r ~,nrnmotcr o l n pcrdnmtcratrd chain (SO") is given by [GI
llae ~ p b n n 11.ansitiotl bdtavior o f a hilayer is reflected i n the dependence of
M I
on ten).pomdare T. For a single component hilnycr.
K
changes drmatieally s t the temperature of tltr ennilt pllnme tmnsitb~t. Using tlte nod el 01 Scl~indler and S ~ e l i g 1151 the mean cx- lot*ion in,A
per mqnent ofthe acyl cltain in a hilayer can be related to the Rrst moment ic~ k l l r Llrot$gI> [6, 18. 15. I T ] ,I1 th e bilayer volunle is treated as being eonstant, l l n r nrrr p r r lipid 111ay tI~..u 1,s. takt.~, to be appmximalely proportional lo (I)-' 137). This qnt~ntily also r l m n p r grmlb. .luring t l ~ e phasc tranaitiou.
We
thus aec lhnt MI is c l o d y nclntcd to t h r xtnnc%t8rid parisac,lrrx of the bilayer.Some featurn of the bilayer p h w ~ transition C R I ~ be mocldnl by quxiug n I ~ I ~ C ~ I I ~ ~ ~ ~ N ~ I ~ ~ - lobical Landau tlleory 1381, hl tllir model, lhc f m o n r r g y /(a) is c.rlmtaclc.cl nlr n 1pc8tvc.r series i n an order pnranneter r aro!ttbd r = 0. Wlnctl
I(*)
is n gl<,l,nl tninim~tm J,,,(.e,,,) at e,., then &(sin) is equal to the Gibbs lm enrcgy ul tllr *ysk,ot. Thc. L a l ~ ~ l r u ort1a.1.paratncler is defined a. a sesiar order parnmctor [SO], s r t i s l y i n ~
r # O , TtT,.
where T. is critical tempcratum lor the ayalem. The Landntn f r t r rtwrgy g<wc.r;tlly lhilx lhe brm:
f ( n ) = " o + " , d + ! " 2 8 2 + 1 " 3 1 1 3 + l , 1 , d ~ +
...,
2 3 4 (1.1;)
rrl~ere
oo
is a constmt, and ot,al,...
are lulnetio~la or to~nperntntreT,
bt Clnnl,tw I 1111.determination of s thermodynamic Landau orclor pnrnmsler from l h c nryl rhaitt ~mt.nrt orientationsl order parameter for ndiacyl pha~~,lmlipid fnlnily will
Lt.
.lisnrrxcvl.The phase behavior of a two.con~pouent lipid lbilnyer is grr~<.rally ,won. c~crtt!lllil.dvll.
As temperaturn is i n c r d , the system usually gom fro!!: l h r p5I phnw, via 8 , n.giet> ef two-phase mxistence, to liquid eryslalline p1~a.o. The rornapoxmdiug lir*L rawma.nl ~BI.S not cllsnge as abruptly as i s single component hilayer. I s pscml, the sl~nlrr e l tht. tww phase region i n the binary phase diagram will depend as wllicll eos~l,ots:~~t ix <lc.st<,mlorl [40][41]. In some cases, acyl chain 2H-NMR speclra lor a binary mixt-tn: car, 13,: ~ u r . t l to constr~tet the phase diagram. Phane boundaries call bc dstcrmiurrl by lfrup<rtios ell lhc
xp,:~.trx cnml,ised with tho IIX o f spectral .uhlrnctiol~ [4i-43)
.
This appraacit is umd i n Cltn1,lc.r 5.1.3.3 Techniques Used t o Extract Order P a r a m e t e r Profiles
'I'Iw flnt orclclr lpertlrrhatiou l l a m i l t o ~ ~ i n n (are nprt chapter for detail) d w r i b i s g axially xytnrtnrtric m n d - m n l : tenwr interactions is sealed by sn arientdiallal factor, I),(cn.d) = (:icosad-l)/2, whorr 4 is t l ~ c angle between theextornally applied ntqnetic flclld nnrl tlmc motional symmetry nxis (biinycr narnml i n lipid membranes) [91[24] (see Pig. 2.2). i n t l l r c w of eryrlailinw powders contniniog n large number of mndomly o r i n ~ t c ~ r l clomnina, this scaling w!~lln i n n rharncterislic powder line shape ("powder palkna") clnu t o lllr auprrp~ilioll of rantrihutions fmm each euci~ domain. I n a spin I system, Litc powdcr patten, has n characteristic linc alnnpe damiuated by a pair of peaks ir~u,ci;~tecl witit
4
= n/2, tlnc most ~,robnl>le value of4.
This line shape is called n "Pake~lo~~l,lvt," niter C:. E. Pnkp who wna the first Lo stljdy such systems i n detail [44][45].
Wvll n,wlval i~owdor ,raltcrss call be obtnined fmtn samples with n few s i l o rpeciF irnlly dnllerakd. i n t l w e rases, tile rorr~spuncliag order parmnetrrs can) b e lneasurpd I l g y .Ilowrver, ill !nore complex eyatem, with a large aatnber of deutrrntion sitex pcr n>olceule ihtvoived, i t is diflieult t o get accurate order psrametcrs d i r n t i y fmnl lrowtlrr rirrrtra. Bloom nnrl enworkers ['ZI][B] have demonstrated t i n t the powder t pat- tc.ni tflwlaml by n polycryatnliine sample can be deconvoluted to a. "oriented spctrum"
wlbirit would arise lwsn a single crystal with an orientation parallel to the external mag- netic fic.l<l (i.c,. 4=0°). For n pcrdetnterated lipid membrane, the oriented spectrunl can be 18~1,rl 1s c>btiin R m>ootLed orcler parameter pmfilc, whicb reflccts the pl~ysicnl illforma- tiou rmuired t o ellarmterizc tllc anisotropic order of membranes, by assuming ti>& the onlcr Ivarawetcr decmasm n>onotonrically along the chain f m m the interface towards the Irilnyer ttlidcllc re& 1461. Pig. 1.5 allows the depnked oriented spectnlm of tho powder
r.;-lt?um shon, i n Fig. 1.4 for DMPC at '14 ' C . Tlnc s r l l t o d of iprak naript,xnrnl k llr.
chain segments in DMPC will be discusac<l it, Clmplrr :I. 11, this so1.k. *ntcx,tiu~l ~,nle.r lparamrter profiles obtained from sueln oric~nt<vl sperlnt rwa~ IIRCYI l a oblnis x ~ . r , ~ r l ~ r n l and ti>ern>odynnmic infornlntiou for lipid biinyrr systnns.
Figure 1.5 The dePaked ai,eclruls lor DMPC a t 44 ' C (deconvolulc~l rnlrtt Pip. 1.4).
The doublet with the ~ m a l i r s t nplilting e o r ~ ~ r n ~ ~ d s In 111. n w l l ~ y l g r n ~ p it, I.lmr iwyl ebains. The next doublet corro~pa~~tla M t l l r nreti>ylet>c,&rntq' n w t to 1111. IIIC.I,IIYI gmn~ln.
The remaining doublets may ibc n3aignnl to tho o l l ~ ! r e>atl~ylalc. gnnulrx (ur (!lm;q~lc~ :I for details).
1.4 A b o u t Thb W o r k
'I'Itt: orienlrtiotnd onlcr parnmsler profile ~ t l d the mean orientational order are im-
parta~tt lm,pcrties of a biiayer aystcnn. TI,. goal of this work is t o examine the extent to wlnicl, rllesc pralwrtics arc rlctrrnlinpd by a limited set of faclors i s a series of model s r ~ ~ ~ i > r n t w s with isrrmwing dcgrcra of complexity. Among t l ~ c iss~xrs d d m e d are : I ] 1,111 r e l i ~ l i o r ~ x l ~ i l ~ ibetwcen oricntatia~>d order psranleter profiler; far hilayer lipids with a givcw i ~ ~ . ~ d g m u p and d i k r e n t chain ieagtl~s;
2) thc rlepenclet~cc of tlle mean cltnin o r d n parameter on temperature near the rlnain 111~.1ti#lg tral~silion;
:I) crnlcr ~punnnctcr pmliio Ibci~nvior it) mixed lipid bilnyeraystemr with rnisnintrhal d a i n i+.,,gths; *,,cI
*I) t h r rc~lnticrlmbip I ~ c ~ l w ~ ~ r n binary nnixtnrrr rrtiseibility nncl tile eiauirl length clifference b<.t~<.l.ll c"llllm11~~111~.
Fnrton w l ~ l e l ~ ltlflo~e#lrc chnlu ordrr were sxnmind in a systematic way i n sorn~ re- ic.rled I~ilnyrrwyatems. Tlnreeciwses of lipid which are important i n biologieai membranes wcrr 8nwrl. TI>- arc. pl~oel,holipids, glycospl~i~~golipid.,and cholesteml. Their structures nrr rlrown i!~ Pig. 1.6. The kinds of biiaycr examined were (1) single componeut ~pi~os-
~pl~oiil,icl bilnyrra with the name Itend group but witit chain lengths of 12, 14. 16, and IN r.lrI>o~~s (DI.PC, DMPC, DPPC, and DSPC respectively)'; (2) b i n w y mixtures of pitcmpholil,ids with tho same head group but different &ail, lengths (DMPC/DSPC); (9) tlcv rit!glc.giyrolipid 24:O CslCer '; (4) binary mixturesofa giycaphinplipid and phw- p l d i p i < l with smnil chain length anismatch (18:O GalCer/SOPC) and with significant rlbai8~ length nnist~rnlrl~ (2(:0 (:dCcr/SOPC); ( 6 ) ternary systems calltaining cl~oiealrrol
-
'IlI.1'1' l ~ l . ~ ~ ~ m ~ l p l ~ a ~ l ~ ~ ~ ~ ~ . y I ~ h o l . l . r . DMPC. d ~ ~ n ~ ~ ~ m o ~ l n l ~ a p h n I d y I ~ L a b n e . DPI'I' <l.n%l 0 8 .! n y l ~ ~ t ~ ~ m ~ ~ l ~ Y ~ ~ l y I ~ I ~ o I ~ ~ ~ USI'I' d alnrqvltlhapl aIodylcnol~lor 'H U ( i d ( Z r S.lynunroyl&nl~rln)l crnm#dr
.I* tl(:al,kr V.8t-arol 8ala<tm>l <ernna.d? SOI'C l ~ ~ ~ a r o ~ l ~ 2 ~ ~ l ~ ~ l p l . ~ p l ~ ~ ~ ~ d ~ l c l ~ o l ~ ~ ~ ~
and either 18:O GnlCerjSOPC or 21:O CnlCcr/SOPC. Tlwsr nystrsw ;are repn.wc.ulnl schematically in Fig. 1.7. All samples wcre prc.pnlr.d nr sntltilnmc4lar vrsirlo ~lirpnri~,r,s i n order to avoid the effecls of vrairle tntnhling nnd highly rf~rvrcl bilityvr *~l~.fac,cx.
pigure 1.6:
cllernical rornlula
lor lipid lno~ecll~n USYI it, tllia I)sI'(: I;,), SOI'(:(b), Gnlactosyl Ceramkie (e), and d,olesterol (d).
Glycasphingolipids were trsocl as cxnn~plc. of a loog eltitir~ ~sc.tsbrn#w ,r,mpvsv>I ill this work. An important reasou lor usr of thr glycuspl~ingoligilIn ill thi* nwmrc.ln ir l.hal, glyeolipids have sonno rereplor function i s n ~ o n ~ h r n ~ ~ c ~ nt~cl that this n.cc.ptol. hlt~clioo~ is known to dependon aeyl chain length [47]. 1.glymapi~isgolil>idn, t l t ~ : r p l ~ i t ~ ~ r i s c . p o r t i ~ l ~ ~ of the eeramide backbone does ,not gcncrally vary. Thc lalty arid, wlticll ~rntnmnonly ~ i ~ # ~ p i ( lrom 18 to 26 carbon atoms, may dctc.minc rocoptor Rmclian. I t ltm lh~!c.vm rotultl tlliut glycoiipid lhtty acid chain lenlth has an erect 028 antlhody hindilrg to galacturylrsn~~~~i.Ic.
i n phosphatidylcl~oiine lipasomes [471[48j. I t has beclt 111ggc~te11 Lbd 1111. I ~ R > I I R P ~ imrn~nttt.
n:?posn. wil,ln lotbgr ctlairt ~ p c c i a is clue to relativ~.ly greater carbohydrate llrnrlgroul~
~pt<,lromxicr~~ l r o ~ n tlw n~cmlrrarnui, w.alting from ~x~ironalcl~ or Lhc long fatty acid cltnirl witla thv h o ~ t nnmt~ix 1471. Chulcsteml war tlnrcl i n acme sllxdirs to e x s t ~ ~ i n e the effect of
Pigtcrr 1.7: Lipids used i n this work are represented schematically. Their chemical for- t r ~ t ~ l n r arc shown i n Pig. 1.0. Biiayem ( a ) to (d) are single !nolecuie bilayers. They d i L r ouly it, chain lengtln or the lipid component. Bilayer (el in also a single molecule biiaycr Inn1 its Lwo tnoietiw dill'er in lm@h by six carbons (me Plg. 1.6(c)). Bilayen (1) to (it) arc binary lipid mixtures. Tltoy may vary eitlne~ i n component chain lengtb (f) or head gmq, (61, or hotln (In). Biinyer (i) is tI,e mixture of bilayer (g) and d>oiesteml. Bilayer (j) is t l l r m i x t t l r ~ 01 bilayer (It) and cholesterol.
rtrril. rnnvtrni#lt o t ~ glyrospl~iugolipid fatty acid arrangement in hilayers. Samples of 23 lx~ol% rbolstcml will, 10 n d % 21:O CalCer i n SOPC and with 10 malW 18:O GalCer in SOPC wcr<.uuar*l. Allsnn~plncut~laini~~gglycolipids weremadeby Dr. Ci~ris1V.M. Grant and
MI.
Drv Singb of the Rioeb~tnistry Departmenl, Univenity of Western Ontario.Chapter I. Inlroductioa 11;
A rommon theme in this work is Lbr way i n wl~irlm t C rlmlrr s l l h r u s m , l l ~ ~ ~ ~ l uric.s- tationsl order parameter pmfile chntlgrs ~s tlac contplrxily 01 thr aystou inc.n.nserc fn,~,, a bilayer with n single type of elmin nud Lmdgmap. tlsoagb bilnyt,rs sill,
;,
siuglr Ihtecl- gmup but two chain lengths. ta hilayers conlnil~ing dillcvc.!tt vlnsn-r oflipicl~ ail11 ~lilfvrrtxl.chain lengths. Oue goal is l o sllldy bo$v tlw oriex~lalionnl unlrr pnmu~!rtc~. l,n,lilr ilmbll 111,.
tnnperature dqcndenre of the ,neat, order ~ramstrl.c~r rlt.#mp rill, vbnis ic~n~c11 sillti#t a fanlily of single component phoapllolipirl bilayem. A8totltur p n l is le Ia,;m~ Ihos tint.
pmfile reflects changes in cl~ain packing i n n r u e s of r l ~ n i ~ t - l c ~ ~ g l l ~ ~nli~maldj.
For the single mnkponalt uliacyl pllaspholipid Ibilnyrra, tlar clk.rt a1 rllain lc.t>gl1> UIB tlto orienlationnl order pnranlelrr pmfile (OOPP) wnr r.xamintc$. I t wn* btxnmcl Ll~id, 1111.
OOPP for ll~losp~lo~ipida having difirent CI,~~,, I ~is dcc.nllila.,~ ~ I,Y ~tilc I,I'LII.ILU ~ V~,I~,(. ~ I ~ ~ o l the orientational order parameter il poailiou nloug tlr, rltniu is aralari [I!!]. 'I'l~c. I~,IBI-
perature dependenceof the mem order parameter for a e h ~ i l l ~ncnv t l ~ r 1>>c,lli81g ttnlxil.iu,m and the jump in meat) order parameter at the lrntlsiliun werr n l ~ t r i ~ ~ ~ u l br p l ~ c a ~ ~ l n l i l , i ~ l ~ having direrent chain lengths. Thae oh9ervationr m e fittctl using n l,nucln~l IIICICII.I 611.
free eneru 1371.
For thscl~sin mismatrl~edsyste~~a, i~tcluding~ringbcon~l,usr~~t tnlixarl-cl>ainryrtrta>.
a numl~eraf binary syatem., and a ternary system, tlte cflnt u l rbain lrl~ptim ~mias~idrlt cw the order parameter profile w e examiner1 in somcdotnil [fiO-S.IJ
.
I1 way lirst fe,tat~d thrl.tbe orientntional order parameter prolile for R very loag cilnitl in rrlni~iu ~ t ~ i s r t ~ i l t ~ l ~ c ~ ~ l liltid hilayer hu asecond plateau near the metlnyl gmup enxl oftlluclnai#~ whirll rermrpar~,lx 1.0 the hilayer middle region 151-541
.
The same may dso be trwr for lhinary lil,itl Idlety<,~i sf DMPC/DSPC containing small co~lrcntrntinns of DSPG. Cl~olestoml lhw lil,llc i~~1lcrc.11~~on the appearance of the second platcau ill llne PC-glycolipid xyntvsl ntadiu,d [:I:$]. l'llc.
experimental m u l l s aumest that when a second plateau nppuara ih at! arlcr~tslis~~;~l arql<!r parameter profile, the tails of the long dnain from the oppo~itc sno~~dayc.rs e l 1111. lipitl
Lilnyer arc mmtiy mingled with each other, forttiibgavery Ruid central layer i n the center
or
tlla I,~I~YC~.'I'hc? ollect of cltein mismatch on a binary plrare diagram ws. also examined. Gel p b w immireibility was found inn a lipid bilayer with chains significantly mismatched
(%:a
(;alar/SOPC), hut not i n n related lipid bilayer with chains effectively matdted (i8:O OaiCcr/SOPC) [60][51].i n tlrc i,innry system DMPC/DSPC, ph- diagrams constmeted from the spectra
lor uric or the other component deuteraterl differ slightly [40]. However, it is usehi to
n~akc 1110 comparison between spectra (or OOPPa) lor the lwo components. I t is thus smvrary to determine an appropriate way t o select a pair of corresponding spectra for c28lr or tltc other rnmpolvent dolteraled, whidt ran represent the stnlrs o f the two rumlatmrnts i n a givon mixture simaitnncoualy. Work i n Chapter 5 will demoustrte that n pair of orirntationnl order parameter profiles which represent one or the o t i ~ c r ro~ni,usrnl deuterated, at the same temperature, simultsneouriy repwent the stales of 1110 two components i n a given mixture. This is not the cede for a pair or profiles, for the two In1,eled components, selected to have tho same area p m lipid. This result mnfirnls as fsriier supp~stion that the area p m lipid cannot h assumed to he Yiorked.in" i n a blx~nry lipid bilaycr [40].
Tltr rest of this t h ~ l i s is arranged ed follows: Chapter 2 include. the review of 2H- NMR tlaeory and the wide linelH-NMR experiment; Chapter 3 discusses the entrnction or illforlnntion Imm model membrane scyl chain spectra; Chapter 4 presents the exper.
iznnltnl resuits and diseuuians for single component lipid bilsyers: Chapter 5 holds the cxtrrrinlental results and disc"-ions lor binary mixtures. The experimental r u u l t s for the sit,glc mixrd-rl~niz~ lipid mentbralle 2 4 0 GalCer and on the eKects of choleslerd on the OniCer ehnin arrangement i n SOPC are also included i n the Chapter 5. The last chnplcr, Citapter 6, is n summary and some concluding remarks.
Chapter
a
R e v i e w of lH-NMR Theory, The W i d e L i n e Experiment, and Materinls
NMRtheory nlaled t o this project and rumr details of tine w i d c ~ l i ~ ~ ~ . a l i - N M I I B W ; I X U ~ - menta performed i n lhis project are reviewed i n this clmptei. Tlrr throry dinc.ntwt.tl 1nc.n.
i r basically a quantum mnhanieal descripliau of deaterias~ NMR, itltllcrtc~l~ ~ l n v s i ~ t d (pic tures far N M R are included for clarification. Tile firat section d i s r u ~ r m the I I ~ ~ t i l t ~ ~ t t i i ~ ~ ~ i n a spin I system and intmducw quadrupole splittiag~. The srrnnd m~.tien c i c ~ r i l ~ r the formation of the qundrupole echo by using tile apiu dcnxily opc?raU,r font>nlixm. 1'Bv third section presents the parameters for tho qudrupoie who pulw s ~ l ~ a w c . r . Thr h,urtl!
sectiou describes the spectrometer.
2.1 Harniltonians and Quadrupole S p l i t t i n g for Spin 1 System
Following Grimmer and Biumich [55], tile energy of n d.:uLcritsnn tntncluun ill a Ihigb external magnetic field ( B o ) is composal of tile Zeeman energy
(Z),
cllldn~puiv ~.~tc.rgy(9).
dipolar intersstion energy (D), stld cltemieal shirt roergy (D). Tilc totill I l a ~ ~ i i t r , ~ ~ i i sN
may be written as the s u m of the Hamiltaninna for cacin intiividtml ihnl,v,mtist~:The order of magnitude (in the frequency ?,nits, rsd/s) of tllr individual it~krnrticnr~s a n I@. IOU, 5x10" 22x10' for N Z , N Q , X D . and NC, r q r ~ t i v e l y [fi5]. Thus i n RIB 'II.NMII experiment, dipolar and chemical shift i~~tornctions may bc segicclr~d, clnatrriu~n nnay III.
treated as an isolated spin I nuclells, and the quadn8l,0l~ ihtc.r~rtios nnny Ir. tm.id#.ci n*
f!l,nl,lrr 0. 1lcvk.w of 'H-NMIL Theory, The Wide Line Experiment, and Malerials 19
n lir.;l-onler ~p#:rto~rhaticn~ on tllc Zwman ihtomdion P0][55].
'I'Lt. lln~r~iltu~tinrm for ti,.: Zevntnn interaction is 1561
w b r ~ ~ b =
lrpr
rlunotn Plnnck's conslant, -1 andi
are the gyromagnetic ratio and na~c:lc~is apir~ upemlor for titr $cutcron, wo = 2nv = -yBo is the Larmor frequency, and tlmc, ~liw~rlient of 1It1: Z-axis 01 tlnr lnbovalnry coordiante syslem(X. Y.Z)
is defined by~IIc. rnagnmrtir fi~lcl L%. T l ~ r eign!vai~res of the Zeemnn Hanliltanian (see Fig. 2.1) are
'l'lnc. l l a t ~ ~ i l t c ~ u i n ~ ~ lor tlbr quadnq,oic interaction a r i s e fmm the interaction ibetworn
&In. z~~~vlear c(nmrlnnpolc nlonnent of the dcutemn nvcl the electric fidd gradieut
(EFG)
at let. pcwitio~> of tltc, rleatamn. Following Slicliter 1571, i t has tile formw l s n r ia l l ~ c ~ ~ l e ~ ~ ~ e n t n r y clniirge, cQ is llre electric quadrupole moment of the deutemn, liWj iii tlle rlcclrir l i d d giuiient operator, u t d n and
6
stand lor any three orthogonal xxvs. Ti>. g!~ndnlgule internclian can be regarded as a scalar product of two irreducibleI.,.,,~,,~
olrrn,tonor
r.lk tsvO [s6][sa1.?P
=ce
I-I)~T:~IV~~."=-2
(2.4) wl8m 1:r' ir ,>antally delinrd is 111" Inborntory mordinnte system
Cftapter 2 Review af'SNMR Tl~eoly, The Wide Line Experinnent, and Mnlerinb 211
l a and It = I x t i l v am dentemu spin operators. The electric field gmntlinll (131T:) tensor har its sinlpleat expressior~ in the priuripnl %xis IYSCIU (I,, y',:'), I n I.bis ~y~lb.>n, the irreducible EFG tensor elenneuts
vi.2
are ggicn by 191:\Q =
v,.;.
= c,,vj.2,
= 0. (2.5)vg2
= +(v zI.I -V"'#)=l,,Iq.J O
'whew V,w, and K,,. (or eq) are eleclrie field gradienlr n l w g tlne tlrtr. cxxrlc~la~
axes. 7 ia called the asymmetry parameter and deli~necl Vdd
-
V V ~2, = -
v,,:, ,
(l.li)where i t is assumed that V,.,. 2
Kt,.
2 V,.,.. Recause tbe spin t r t l n r olr:l.nlrrr l'(21 is expressed i n the laboratory frame, tbo ~ l e c l r i c field g r d i e a t le!~sor inn &I. (11). V,p.must be exprerred i n the laboratory system as well. TLis E R ~ be w l l i ~ v < * I tllnmgll the transformatian.
v:'~
=9
D:!~V,!!;,, (2.7)*1=-2
wl~em D:!" are the Wigner rotation matrixe. 191 wlnicll tranmaform t l x e l n t r i c lirld ~ n ~ l i - en1 tensor fmm the principal cmrdinate system (v,) :.!; t o tlte laboralnry ryrtcw (K?)).
To first order apprmimation, among the Tia) ill Eq. (2.4), ultly
T?'
91rc?d1 10 11,.considered [58]. Therefom only
@'
i n Eq. (2.7) m e d s t o b~. consideml. 13q. (5.11) tltcv bemmes@ =
C
~I11,,111 P o a l= - ,;~:,)(sl?
-
1 ( 1+
1));[(3m.20-
1 ) + ~ " i 0 ' 8 ~ ~ ~ 2 * ] , (2.8) where*
and 0 are the two Eule"an angles fur l l ~ c first two racozsivc mlnliu~w i n bringing the major to laboratoryz
axis WII~~, i~ ttlu c~in?ctio."r
DO. TII,,~f:l,a,>lr~ 2. Ilevicw d X H - N M R Tlmry. Tlre Wide Line Expen'menl, and Malerials 21
tlzc g~ancln~pole inlcraction rlmifls Zeonmn energy levels (Fig. 2.1), to first order, by the a,,,o,r,,t:
~@~,=&(3rn'- I ( ! + 1 ) ) 1 [ ( 3 m 2 0 - l ) + v s i n a O c ~ 2 V 1 . (2.9)
Piburr 2.1: Eflrct of Zrrmsn and Zeemau plus quadrupole interactions on the energy I r w l s 01 n cleutemn in an cxtennal magnetic field.
'PIN. aclection rule A n t = tl makw possible two transitions among the three s h i b d Zrrlnnn energy levels for the deutemn. Tile resulting spectrum is a doublet will, a r p l i l l i t ~ g AuQ(%. 8) 191:
whcrc = 1tilktIa is the quadrupole coupling constant for the deuterium i n a C-D bot~d. 11, the rnxp of C-D bonds on a fatty acid cbsin i n a lipid bilayer, q is a very snnall
~xwnbrr (11 5 0.05), SO the term containing the aymmetry parameter i n Eg. (2.10) is usn!nlly acglccted [91. This leave*
(2.11,
Cixapter 2. Review o12H-NMR Tlreo~y, Tlre Wide Line Expeperi#,8onl, and Mntrrialx 52
"I=,-m;O
qxoo
n*O-w,I=-
(c)
Figure 2.2: Membrsne i n an oxlernal u>agnetlc Pcld with all lipid cl>hinr tlc~a~lc.ral.~~l at i~
specific sile. Local arientatiar~ or the Ihilnyer nonnsl (a); r p r r i l i r ~ t i o n or variotma ;tugLvi i u draraclerizitng the motion of a rltain (1)); aud 111- qcmi~lrtnl>olo xl,liLl.intg (c.).
It is orten convenient t o clistinguirh tnotionr which sw fast or slow or> tBc NMIl tilta.
scale. Conrider r ~ t reorientation about n slowly varying axis or *ytnmatry. 'rhe xuglr Q, varying slowly on the 'H-NMR time scale, is define4 lo be tho nnglc lh<:l,wtr~! thr extmusl magnetic fidd
