Dynamic imaging of lateral diffusion by electron spin resonance


 Hugh Shaw
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1 Dynmic imging of lterl diffusion by electron spin resonnce nd study of rottionl dynmics in model membrnes Effect of cholesterol Y.K. Shin nd Jck H. Freed Bker Lbortory of Chemistry, Cornell University, Ithc, New York ABSTRACT The effects of cholesterol on the dynmics nd the structurl properties of two different spin probes, the sterol type CSL nd the phospholipid type 16PC, in POPC/cholesterol oriented multilyer model membrnes were exmined. Our results re consistent with nonidel solution contining cholesterolrich clusters creted by the self ssocition of cholesterol in POPC model membrnes. The lterl diffusion coefficient D of the spin probes ws mesured over the temperture rnge of 15 to 6C nd over the concentrtion rnge of to 3 mol % of cholesterol in the model membrne by the electron spin resonnce (ESR) imging method. The rottionl diffusion coefficients (including R1) nd the order prmeter S were determined utilizing nonliner lest squre ESR spectrl simultion method. D, RL nd S of CSL devite considerbly from liner dependence on mole percent cholesterol. The D of CSL ws decresed by fctor of four t 15C nd fctor of two t 6C for concentrtions of cholesterol over 1 mol %, wheres those of 16PC were hrdly ffected. Cholesterol decresed R_ by fctor of 1 t 3 mol % of cholesterol, but it incresed slightly tht of 16 PC. A significnt increse of S for CSL due to the presence of cholesterol ws observed. It is shown how the difference in vrition of S for CSL vs. 16PC with composition my be interpreted in terms of their respective ctivity coefficients, nd how single universl liner reltion is obtined for the S of both probes in terms of scled temperture. Simple but generl correltions of D nd of RL with S were lso found, which id in the interprettion of these diffusion coefficients. INTRODUCTION The physicl properties of phosphtidylcholine model membrnes contining cholesterol hve been the subject of extensive studies involving rnge of techniques. The techniques tht hve been used to study the phse behvior re clorimetry (1, 2), spinlbeling electron spin resonnce (ESR) (36), fluorescence (7), freeze frcture electron microscopy (7, 8), xry nd electron diffrction (9), nd recently, Rmn spectroscopy (1), s well s neutron scttering long with freeze frcture electron microscopy (1 1). A conspicuous phse boundry in the temperturecomposition phse digrm ws found t 2 mol % of cholesterol in phosphtidylcholine model membrnes below the min chin melting temperture (Tm) (29), lthough it hd erlier been believed tht there ws phse boundry round 3 mol % (12). This phse boundry hs similr chrcteristics to the min chin melting phse trnsition: tht is, it is kind of geltoliquid crystlline phse boundry, implying tht it is considerbly disordered fluid stte bove 2 mol % of cholesterol. On the other hnd, it is gel phse below 2 mol %. There re two solid phses (tilted LO. nd nontilted Lp phses) which coexist in the region where cholesterol is <2 mol % nd t tempertures below the pretrnsition temperture (Tp) (7, 11), wheres cholesterolrich liquid crystline phse (P,B.) nd pure phospholipid gel phse (L,3.) coexist t tempertures between Tm nd Tp (with Tp Tm  1C) (4, 5, 8). But the xry nd electron diffrction studies did not confirm the coexistence of two phses in this region (9). Bsed on spectroscopic evidence, the cyl chin tilt begins to dispper with the presence of 58 mol % of cholesterol (9, 11). The phse behvior of model membrnes contining cholesterol in the L liquid crystlline stte (bove Tm) hs not been clerly estblished s yet. It ws pointed out previously (11) tht this might prtly be becuse of the experimentl difficulty of detecting fluidfluid immiscibility by the commonly used spectroscopic methods. There hve been few reports suggesting fluidfluid phse seprtion (5, 7, 13). A homogeneous single phse lso hs been suggested experimentlly (9, 1 1). In ddition to the phse behvior, the dynmicl properties nd ordering of the molecules in the bilyer hve their own physicl importnce. The rottionl dynmics nd ordering properties of lipid molecules or cholesterol nlogues in the binry mixture hve been investigted minly by mgnetic resonnce (14, 15) nd fluorescence techniques (16, 17). It hd been shown tht cholesterol decresed the fluidity of the ftty cyl chin in the liquid crystlline stte. It hs been possible to seprte severl spects of the rottionl dynmics rther thn to use the generl term fluidity. In the fluorescence study the rottionl motion ws nlyzed by model of wobbling motion confined within cone (16). In this model the Biophys. J. e Biophysicl Society Volume 55 Mrch /89/3/ /89/3/537/14 $2 $2. 537
2 viscosity within the cone remined constnt, but the cone ngle decresed with ddition of cholesterol. The nisotropic rottionl diffusion model defines prllel nd perpendiculr rottionl diffusion coefficients, s well s the ordering potentil. The ESR study bsed on spectrl simultion, utilized the model of nisotropic rottionl diffusion in n orienting potentil. It reveled incresed ordering, but only smll effect of cholesterol on the rottionl motion (15). Vrious studies hve greed tht the mjor effect of cholesterol is to reduce the ngulr rnge for rottionl motion without decresing mobility substntilly (14, 15, 16). On the other hnd, in the gel phse cholesterol induces locl disorder nd enhnces the rottionl motion. Generlly, fully hydrted bilyers hve been used so fr. But the creful study of low wter content DPPC smples by ESR showed effects of cholesterol on rottionl dynmics similr to tht in the liquid crystlline phse even in the gel phse (15). Another importnt dynmicl property of the bilyer contining cholesterol is the lterl diffusion of the constituent molecules. The effect of cholesterol on the diffusion of the phospholipid molecules hs drwn much ttention becuse it is directly relted to understnding the trnsport properties in biologicl membrnes. It hs been studied by fluorescence recovery fter photobleching (FRAP) (1821), pulsednmr spin echoes (PNSE) (22, 23), nd fluorescence correltion spectroscopy (24). Below Tm one or two orders of mgnitude increse of the lterl diffusion coefficients of the phospholipid nlogue bove 2 mol % of cholesterol hs been found, supporting the ide tht it is fluid phse even below Tm. Also, cholesterol decresed the lterl diffusion coefficient bout fctors of two t 2 mol % or greter, bove Tm (19, 24). In nother study, sterol type fluorescence probe ws found to behve in exctly the sme wy s phospholipid type probe (2, 21). However PNSE gve significntly different results for the self diffusion of phospholipid; the ddition of cholesterol ws observed to increse the diffusion rtes of DPPC up to 1 mol % bove Tm, nd then to decrese it bove 1 mol % (22). For the unsturted cyl chin phosphtidylcholines (POPC, DOPC) the lterl diffusion ws observed only to increse slightly with cholesterol concentrtion in the liquid crystlline stte (23). We hve developed n ESRimging method for mesuring the trnsltionl diffusion coefficients of ordered systems such s liquid crystls nd lipids (25, 26). We hve demonstrted tht our method is one of the useful spectroscopic techniques for studying lterl diffusion of model membrnes (26). We pointed out in our previous work (26) tht one could lso simultneously obtin the rottionl diffusion coefficients nd the order prmeters in the usul fshion (e.g., 15, 27) by nlyzing the mgnetic field grdientoff spectr which re just the norml ESR spectr. Such combined study cn be expected to provide better insight into the dynmic properties of membrnes. In this work we present n ppliction of the ESR imging method for lterl diffusion long with n improved spectrl simultion method for ordering nd rottionl diffusion bsed upon nonliner lest squre fitting (28), to oriented model membrnes of POPC contining cholesterol. The POPC molecule hs one sturted cyl chin nd one unsturted chin, s is chrcteristic of nturlly bundnt phosphtidylcholines in biologicl membrnes. Here we concentrte on the liquid crystlline stte for two resons: () Most rel biologicl membrnes exist in this stte (7), so n understnding of the dynmicl properties of both cholesterol nd phospholipid in n unsturted phospholipid model membrne such s POPC in this phse would be directly relevnt to the role of cholesterol in biologicl membrnes (7). (b) Our ESR imging method is well suited to mesure diffusion coefficients in the liquid crystlline stte of the membrnes which rnge from 19 cm2 s' to 17 cm2 S1 We used two types of spin probes, CSL nd 16PC (Fig. 1). CSL is good spin probe to revel the dynmicl fetures of cholesterol in model membrnes (6, 15). The other probe is 16PC, which is frequently used to study the properties of phosphtidylcholine model membrnes by ESR (27, 29). From comprison of the behvior of these two spin probes we could hope to better understnd the properties of model membrnes contining cholesterol in the liquid crystlline stte. FIGURE I CSL N 16PC Structure of cholestne (CSL) nd 16PC spin probes. 538 Biophysicl Journl Volume 55 Mrch Biophysicl Journl Volume 55 Mrch 1989
3 EXPERIMENTAL METHODS Mterils IPlmitoyl2oleoylsnglycerophosphtidylcholine (POPC) ws purchsed from Avnti Polr Lipid Inc., Birminghm, AL, nd ws used without further purifiction. Cholesterol ws obtined from ClbiochemBehring Corp., L Joll, CA, nd recrystllized in ethnol. The 3doxyl derivtive of cholestn3one (CSL) ws purchsed from Syv Co., Plo Alto, CA, nd lplmitoyl2(16doxyl steroyl)phosphtidylcholine (16PC) ws gift from Professor G. W. Feigenson, Deprtment of Biochemistry, Cornell University, who synthesized it ccording to stndrd methods (3). The purity of the 16PC ws tested by thin lyer chromtogrphy, nd it ws found to contin <2% impurity. Smple preprtion The two bsic smple requirements in our ESR imging experiment re () the spin probe distribution is loclized t the middle of the smple, (b) the smple is wellligned homeotropic monodomin of lipid multilyers. Becuse the experimentl time (At) required is proportionl to the squre of the initil width of the spin probe distribution (52) (26), the initil width hs to be s thin s possible to minimize At. To prepre smples stisfying such requirements, we followed the modified evportioncompression technique explined in our previous work (26). It is bsed on the hydrtionevportion technique (31) nd the compression lignment technique of Tnk nd Freed (27). For detils of the procedures nd chrcteriztion methods see references 26 nd 27. The spin probe concentrtion of the CSL ws.75 mol % nd tht of the 16PC ws.5 mol %. The ESR spectr of both smples did not show ny lineshpe brodening due to Heisenberg spin exchnge t those concentrtions. The wter content of the smple ws determined by weighing fter the ESR mesurement (26). The POPC/cholesterol smples were found to hve 152% wter by weight. Instrumentl nd dt collection A Vrin Assocites, Inc. (Plo Alto, CA) E12 spectrometer ws used for the experiments. The spectr were tken in the first derivtive mode with 1 khz field modultion, with microwve power of 5 mw, nd with modultion mplitude .8 G. Homemde figureeight grdient coils, which produced liner field grdient of 36 G/cm t 2. A current, were used (25, 26). A stndrd Bruker Instruments, Inc. (Billeric, MA) nitrogen flowing temperture control unit ws used to regulte the smple temperture. The temperture control nd vrition ws chieved by using n 1 mm OD single wll qurtz dewr nd by monitoring the temperture with thermocouple inserted inside the dewr from the bottom. The temperture ws controlled to ±.5C ccurcy. The temperture of the smple ws rised 1C between successive temperture runs. Dt were collected on model D PC (Leding Edge Inc., Cnton, MA) interfced to n HP3457 multimeter (HewlettPckrd Co., Lovelnd, CO). All spectr were digitized to 1,24 points, hd 1G sweep widths, nd 6s sweep times. Two grdienton spectr were recorded consecutively nd one grdientoff reference spectrum ws tken subsequently. About 2 grdienton spectr were recorded t fixed temperture, nd this took  1 h. Ech smple ws used for five different tempertures rnging from 15 to 6C. Dt nlysis Lterl diffusion by ESR imging. The mesurement of diffusion coefficients by ESR imging is n ppliction tht we refer to s "dynmic imging" (26). It involves two stges. A smple is prepred with n inhomogeneous distribution of spin probes long given direction. The ESR imging method is first utilized to obtin the (onedimensionl) concentrtion profiles t severl different times. The imging method is bsed on the use of mgnetic field grdient, such tht t ech sptil point there is different locl resonnt frequency. Typicl ESR spectr from imging concentrtion profiles re shown in references 25 nd 26; lso shown re the concentrtion profiles. With the pssge of time, this inhomogenous distribution will tend to homogeneous distribution vi trnsltionl diffusion. The second stge is to fit the timedependent concentrtion profiles to the diffusion eqution to obtin the diffusion coefficient. We hve shown (26) tht the nlysis is gretly improved by studying the sptil Fourier Trnsform of the concentrtion profiles. The onedimensionl diffusion eqution in Fourier trnsform or kspce is given by lnic(k, t1)i  InIC(k, to)i = 47r2 D k2 At, (1) where At  ti  t is the time difference between two mesurements nd D is the lterl diffusion coefficient in units of cm2s'. To obtin the concentrtion profile C(k, ti) t given time in kspce we deconvolute the grdienton spectrum with the grdientoff spectrum utilizing the convolution theorem in Fourier spce: I(k ti) Io(k) where I,(k) is the Fourier trnsformed grdienton spectrum nd I(k) is Fourier trnsformed grdientoff spectrum. The lterl diffusion coefficient D is determined by the method described in our previous pper (26). In summry, becuse we used smples tht re well pproximted by Gussin initil spin probe distribution, C(x) (2r)1/5 exp ( 252) The log of the concentrtion profile in kspce my be written s InIC(k, ti)l = (ti) k2, where (t;)  2r26i2 4r2D ti. Thus, by plotting IC(k, t;)i with respect to k2 one obtins the slope (t;). The (ti)s re relted to ech other by the diffusion eqution (Eq. 1): Thus plot (ti)s with respect to t, (2) (3) (4) (ti)  (tj) 4r2D(ti  tj). (5) yields D. We could estimte the hlf width t hlf mximum (HWHM) r of the Gussin concentrtion distribution by the reltion r(ti) = I N(t1)in 2, 7r t given time ti. The HWHM's of the Gussin profiles were bout.5 mm t the beginning of the mesurement. Severl exmples, illustrting how the C(k, ti) re nlyzed to obtin D, re given in reference 26. Nonliner lest squre spectrl simultion. During the course of ech experiment we collected the grdientoff spectr. They were nlyzed to obtin informtion on ordering nd rottionl dynmics utilizing ESR spectrl simultion methods (3234). The ESR simultions were performed utilizing nonliner lest squre fitting to obtin the optimum prmeters (28). For the spin probes we were using, we followed the xis system conventions described elsewhere (27, 35). The potentil V(Ql) determining the orienttionl distribution of the spin probe molecules round the ordering xis in the unixilly ordered (6) Shin nd Freed Dynmic Imging of Lterl Diffusion 539
4 lipid multilyers cn be expnded in series of Wigner rottion mtrix elements, e.g., V(Q)/kT = XD2 (Q) + p(d 2 () + Do2 ()) + * (7) where k is the Boltzmnn constnt nd Q is n Euler ngle specifying the reltive orienttion between the rottionl diffusion xis (it is ssumed to coincide with moleculr long xis) nd ordering xis. The vlues of the mgnetic tensor A used were Ae G nd A,.(A<) 5. G G for 16PC. Those of g for CSL, nd Ae 33. G nd Ae((Ay) were ge 2.89, gr  = 2.58, nd ge for both spin probes (27). One cn specify the ngle (I) between the ordering xis nd the pplied mgnetic field (H.). All spectr of CSL tht were simulted hd, wheres those of 16PC hd = 9. These vlues of hd been chosen to minimize the spectrl linewidths, thereby enhncing resolution in the imging experiments. The first step in the nonliner lest squre simultion ws to choose resonble strting vlues of the four prmeters, A, p, the perpendiculr rottionl diffusion coefficient (Rj), nd the prllel rottionl diffusion coefficient (Rl). They were chosen simply from previous results for the sme probes in DPPC multilyers (27). The fitting process ws iterted severl times by MrqurdLevenberg lgorithm until minimum in the lest squres ws chieved. To insure tht globl minimum ws chieved nd to gurd ginst spurious locl minim, the lgorithm ws restrted severl times with rnge of different seed vlues. Convergence to the sme finl set (to within the experimentl uncertinty) ws lwys chieved (except in few cses where no convergence ws obtined). The fits were very sensitive to A nd R, while less sensitive to p nd Rl. Once we obtined the potentil prmeters (A, p), we clculted the order prmeter defined by S <Doo() > =fdoo (Q) exp ( kvt) dq Jexp  kt) dl, (8) where D2 (Q) (1/2) (cos21). The spectrl simultions showed tht the vlues of A re bout n order of mgnitude bigger thn p for CSL. Thus, neglecting p nd higher order terms, we cn simplify the potentil expnsion to  kt XD) (), (9) for which the order prmeter S cn be written s S fd 2 () exp (XD 2 ()) dq * /fexp (XD 2 ()) dq. (1) This integrl ws clculted numericlly. An symptotic expression, vlid for lrge A, is given in the Appendix. RESULTS AND ANALYSIS Generl observtions Lterl diffusion Results were obtined for five different compositions of cholesterol in POPC multilyers,, 4, 1, 2, nd 3 mol % with CSL spin probe. Using 16PC probe, 1, nd 2 mol % were used. The temperture ws chosen to be t lest 1 bove the min chin melting temperture Tm of hydrted POPC. The lterl diffusion coefficients D of CSL in the different mixtures re listed in Tble 1. Those of 16PC re shown in Tble 2. One notes tht for mol %  cholesterol, DCSL/Dl&pc 1.6 consistent with the somewht smller size of CSL. Semilog plots of the temperture vrition of D re shown in Fig. 2, nd b, respectively. The ctivtion energy for lterl diffusion ws clculted for ech probe in ech mixture. It rnges from 6 to 9 kcl/mol depending on the concentrtion of cholesterol. There is noticeble increse of ctivtion energy of CSL (3 kcl/mol) between 4 nd 1 mol %. These vlues re given in Tble 1. Fig. 3 shows the vrition of D for ech probe t different cholesterol concentrtions. 1 mol % of cholesterol decresed the D of CSL by fctors of four t 15C, nd fctors of two t 6C. The further ddition of cholesterol over 1 mol % ws not so effective in reducing D of CSL s it ws below 1 mol %. On the other hnd, the D of 16PC t different compositions ws lmost unffected t high tempertures, lthough it decresed slightly t 15 nd 25C. Given tht the D of CSL or 16PC would not be much different from tht of cholesterol or phospholipid, respectively, the presence of cholesterol ppers to influence the cholesterol diffusion more thn tht of the phospholipid. Ordering nd rottionl diffusion Spectrl simultions were performed for spectr of CSL nd 16PC t ll concentrtions nd tempertures we hve studied. The best fitting rottionl diffusion coefficients nd order prmeters of CSL re given in Tble 1 nd those of 16PC in Tble 2. Some of the simulted spectr re compred with the experimentl ones in Fig. 4, nd b. The ctivtion energy for the R1 of CSL is given in Tble 1 for the different compositions. Fctors of two increse of the ctivtion energies t 1 mol % of cholesterol compred with tht t mol % were found. Fig. 5 shows the vrition of R1 of CSL with cholesterol. We plot the temperture vrition of order prmeter S of CSL t different composition in Fig. 6. The order prmeter S of both spin probes ppers to decrese linerly with temperture, nd to increse with incresing mol % cholesterol. We used = CSL spectr for ESR simultion. This mens tht we re observing the spectrum long the principl ordering xis. For this highly ordered probe the moleculr long xis is preferentilly long this principl ordering xis. Thus, in this configurtion, the spectrl shpe ws very sensitive to the vlue of R1, wheres it ws firly insensitive to RI (s confirmed by our nonliner lestsqure nlysis). Thus, we put less emphsis on in RI nlyzing the results of the spectrl simultions. For 54 Biophysicl Journl Volume 55 Mrch Biophysicl Journl Volume 55 Mrch 1989
5 TABLE 1 Dt for the CSL spin probe T D S P Rp RI OC 18cm2s' 17s'I 18s' mol % cholesterol E, = 6.3 kcl/mol E,Rl kcl/mol ± ± ± ± ± mol % cholesterol ED = 6.45 kcl/mol E.,R12.1 kcl/mol ± ± ± ± ± mol % cholesterol E.,tD kcl/mol E,R kcl/mol ± ± ± ± ± mol % cholesterol E,.D = 9.84 kcl/mol E.R, kcl/mol ± ± ± ± ± mol % cholesterol E.,,D = 9.94 kcl/mol E.R, kcl/mol ± ± ± ± ± TABLE 2 Dt for 16PC spin probe 16PC, the spectrl lineshpe ws found to be sensitive to R1 but lmost insensitive to the nisotropy rtio for X T D S P rottionl diffusion, RII/R (gin from nonliner lest "C 18cm2S' 18 squre nlysis). A model of isotropic Brownin rot mol % cholesterol  E..D 6.15 kcl/mol tionl reorienttion ws therefore employed to simulte ± PC spectr. The ctivtion energy for R1 of 16PC ± ws lso found to increse somewht with increse of ± mole percent cholesterol but less thn the cse for CSL ± However, over the temperture rnge studied, R1 of ± PC ctully incresed slightly with mole percent cho 1 mol % cholesterol E,8tD = 7.87 kcl/mol lesterol, wheres tht for CSL decresed very substntil ± ly. The order prmeter S, for 16PC ws observed to ± increse considerbly with mole percent cholesterol s ± ± ws the cse for CSL ± mol % cholesterol E,D kcl/mol Empiricl reltions nd ± Empreic e n ± correltions ± Order prmeter nd ctivity coefficients ± ± One is struck by very nerly prllel strightline fits of S for CSL vs. temperture (cf. Fig. 6 ). Tht is, the slope Shin nd Freed Dynmic Imging of Lterl Diffusion 541
6 rl(ok1) bki E 71 o FIGURE 4 () Comprison of experimentl spectr of CSL (), t 25 C, with simulted ones (*) t different concentrtions. The ngle *i is. There is noticeble decrese of hyperfine splitting with increse of cholesterol concentrtion. (b) Comprison of experimentl spectr () of 16PC, t 25 C, with simulted ones (*) r1 (OK1) FIGURE 2 () Semilog plots of DcSL vs. T'. Cholesterol concentrtions in POPC model membrne re (), 4 (), 1 (A), 2 (), nd 3 mol % (A). (b) Sme type of plots s except the spin probe is 16PC; (+), 1 (x), 2 () mol % of cholesterol in POPC model membrnes. (8S/oT)x does not depend on the composition (except for smll devition t 3 mol %). Let us rbitrrily define reference tempertures Ti (x) nd To (x), which re the extrpolted tempertures corresponding to S = 1 nd S = t given cholesterol mole frction, x. Obviously Tt (x) nd To (x) re different from composition to composition, but the difference To (x)  T* (x) must remin constnt for ll compositions, since the slope (OS/T)x is independent of composition. Thus, we my write the temperture dependence of S in the following 4 If" 2... A cholestrol mole frocon x FIGURE 3 mole frction x t different tempertures; for CSL, 15 (), 25 (), 35 (A), 48 (), nd 6 C (), nd for 16PC, 15 (+), 25 (x), 35 (), 48.4 Plots of the vrition of DCSL nd D,6pc with cholesterol (*), nd 6C (A). Dl&pc shows little chnge in the presence of cholesterol. Dt used were interpolted by Spline interpoltion from those in Tbles 1 nd cholesterol mole frction x.4 FIGURE 5 Plots of the vrition of R1 of CSL with cholesterol concentrtion t different tempertures; 15 (), 25 (), 35 (A), 48 (), nd 6 C (). The behvior of ech curve is quite similr to tht of DCSL (cf. Fig. 3). 542 B_phy JournlVolume55 Mrch1989 Biophysicl Journl Volume 55 Mrch 1989
7 s w. Cso p rv c on IC Tempermture(fC) 6 7 TABLE 3 Vlues of T, (x) nd T2 (x) x (cholesterol) T*"(x) To (x) CSL spin probe PC spin probe OC OC o. Compre with text nd with Eq zci S C c Cs tu.6 1. FIGURE 6 () Plots of temperture dependence of order prmeter S of CSL t different compositions; (OJ), 4 (), 1 (A), 2 (U), nd 3 mol % (). The slopes re ll the sme except t 3 mol % where it is slightly smller thn the others. (b) Plot of S(tU) vs. tu for CSL nd 16PC. Different symbols denote different compositions: for CSL, (), 4 (), 1 (A), 2 (A), nd 3 mol % (), nd for 16PC, (+), 1 (x), nd 2 () mol %. Fig. 7 is plot of S for CSL vs. cholesterol mole frction x. The chnge of order prmeter with cholesterol: S(x, T)  S(O, T) is found to vry with x but to be independent of T. The order prmeter S increses shrply up to 1 mol %, but S is not very sensitive to further ddition of cholesterol. We found tht "Lngmuir isotherm" type eqution fits the behvior of S(x, T)  S(, T) vs. x: S(x, T)  S(O, T) =, for Tconstnt, I + cx (13) with b = 6.28 nd c = 14.4 s shown in Fig. 7 b. Eq. 13 is consistent with sturtion of the ordering effect of cholesterol. Becuse S is proper thermodynmic vrible, we my combine Eqs. 11 nd 13 by stndrd thermodynmic methods [ds = (ds/dot). dt + (ds/ OX)T dx] to obtin: S(x, T) = form. 1[TTT(O)] + (14) S(x, T) = 1 [ T T (x)], for x constnt, ( 11) where = 1/[To (x)  T*(x)] = 2.77 ±.26 x 13K. The vlues of To(x) nd Tr(x) re given in Tble 3. If we define the scled temperture tu [T  T (x)]/ [To (x)  T (x)] (36), then S is simply S(tU) = 1 tu. (12) This scled eqution tells us tht the disorder prmeter 1  S(tU) is exctly the scled temperture tu, nd this behvior is universl for nerly ll compositions. Thus the ordering effect of cholesterol cn be thought of simply s equivlent to shift of the temperture scle. This universl behvior S(T) vs. tu is depicted in Fig. 6 b for ll our dt on CSL (s well s 16PC, see below). (A simple reltion between ordering potentil X of CSL nd temperture is suggested in the Appendix.) with T*(x)  I T*( ) = I 'bx I~~+ cx b (15) Eq. 14 expresses surprisingly simple universl dependence of S for CSL on x nd T with no crossterms in x nd T (except perhps smll correction t x =.3). We discuss Eq. 14 further in the next section. We now consider our results for 16PC. The temperture dependence of S16PC is lso found to be fit by the universl form expressed by Eq. 12 s shown in Fig. 6 b. We found n identicl scling constnt = [To(x) Tf(x)]l to tht for CSL within experimentl uncertinty. However, for 16PC, which is more wekly ordered, the Shin nd Freed Dynmic Imging of Lterl Diffusion Shin nd Freed Dynmic Imging of Lterl Diffusion 543
8 6... l I d P PO.CM x I O d I,, o e m x If *..**** &r.*.** *...U*** p.****.** ch mle frfction x chol.twol mole froctfon x I cho_bstrol mole froctfon x FIGURE 7 () Plots of S(x, T) for CSL vs. cholesterol mole frction x. Note the devition of S(x, T) from linerity in x; 15 (), 25 (), 35 (A), 48 (U), nd 6C (e). (b) Plots of S(x, T)  S(O, T) vs. x for CSL. A Lngmuir isotherm type eqution bx/(l + cx) fits the behvior of S(x, T)  S(O, T) with b = 6.28 nd c = (c) Sme type of plot s b for 16PC for five different tempertures: 15 (+), 25 (x), 35 (), 48 (*), nd 6 C (A). The line is drwn ccording to Eq. 17 with d.44. reference tempertures T* (x) nd To (x) re different from those for CSL (cf. Tble 3). In the cse of the x dependence of S16pc we obtin results nlogous to tht of Eq. 13 for SCSL in tht S16pc(x, T) Spc(O, T) hs  functionl form tht is (nerly) temperture independent. (cf. Fig. 7c), but this functionl form is distinctly different from tht for CSL, (compre Fig. 7, c with b). We now wish to consider point of view which incorportes the fct tht the ddition of cholesterol hs similr type of effect on the SCSL nd S16pc s suggested by their respective temperture dependences, nd yet there is mrkedly different dependence upon composition. This point of view, simply stted, is tht the mixtures of POPC nd cholesterol studied here form simple nonidel solution. Furthermore, becuse CSL is known to report on cholesterol in model membrnes (6, 15), nd 16PC reltes to the properties of phosphtidylcholines (27, 29), then we expect tht SCSL(X, T) nd Scho1(x, T) re comprble (or t lest the sme within constnt multiplictive fctor of order unity), nd lso S16pc(x, T) nd Spopc(x, T) re comprble (where SPOPC s used here would more precisely be relted to the ordering t the end of the cyl chin). Tht is, we my regrd CSL s merely lbeled cholesterol molecule nd 16PC s merely lbeled phospholipid molecule in our nlysis. Thus the fct tht SCSL(X, T) nd S,6pc(x, T) obey the sme temperture scling lw, Eq. 12 rises becuse one hs single simple solution. On the other hnd, the different functionl dependences of SCSL nd S16pc upon x could rise from the properties of nonidel solutions. If the POPC/cholesterol solution were idel, then we would expect its intensive thermodynmic properties (e.g. prtil pressure) to vry linerly with x. Since S,(x, T) for the ith component is n intensive thermodynmic property such s the prtil pressure (37), we expect S,(x, T)  Sj(O, T) to vry linerly with x in the idel solution limit (i.e. x  ). More specificlly, given the tendency of cholesterol to enhnce ordering, we would expect tht if idel mixing of lipid nd cholesterol were occurring, this enhncement to the ordering of both components would simply be proportionl to x. (Such idel solution type of behvior for S(x, T) hs been observed in isomeric mixtures of thermotropic liquid crystls [36]). The very nonliner dependence of SCSL upon x expressed by Eq. 13 would then imply nonidel solution (lthough s x  we recover the linerity in x expected for n idel solution). Such nonidelity would be the cse, if, for exmple, the cholesterol tends to ggregte nd not obey idel mixing s x increses. These rguments suggest tht the term in Eq. 13, 1/(1 + cx), which corresponds to the nonliner behvior should be relted to the ctivity coefficient ych., for cholesterol (with the ctivity chol ychol x). In fct, if = we simply set 1Yhd + cx (16) with c = 14.4 (corresponding to the solute convention tht Y,h.ol  1 s x  ), then the decresing ych.l with x is 544 Biophysicl Journl Volume 55 Mrch 1989
9 consistent with ggregtion of the cholesterol s x increses (38). Eq. 16 represents the simplest interprettion we cn mke of the effects of nonidelity on SCSL. It leds to the following form for Eq. 13: S(x, T)  S(, T) = bx7,1.. (16) More generlly we might expect higher order terms in 'Ychol or chol in Eq. 16, but significntly more rpid convergence thn just series expnsion in x. If, indeed, the nonidel dependences of Si(x, T) upon x re closely relted to the respective y, then the Si(x, T) for the two components of the solution cnnot vry independently. More precisely, the ctivity coefficients of the two components of solution re interrelted by the GibbsDuhem eqution (38b): x dinychol = (1 x)d lnypc. (17) (We re implicitly ssuming tht the region within the bilyer consists only of two components, with the third component, wter only t the hedgroup region nd between bilyers [39].) It is simple mtter to obtin n expression for ypc from tht for ychol (Eq. 16) by integrting Eq. 17 (utilizing s one set of limits of integrtion ypc = ychol = 1 when x = ). One obtins: epc= (1  x)c/(l+c)(1 + Cx) /(1+c). (17) We now need n expression for S16pc nlogous to Eq. 1 6 to compre with the experimentl dt of Fig. 7 c. We find tht form closely nlogous to Eq. 16: SI6Ppc(x, T) = S16_pc(, T) + dxypc t constnt T, (17b) with ypc given in Eq. 17, leds to good greement with the dt s illustrted in Fig. 7 c. In prticulr, we obtined tempertureindependent d =.44 within the experimentl sctter. It is found from Eq. 16 tht 'y1chol decreses by fctor of five on x incresing from to.3, wheres from Eq. 17 ypc increses only 13% upon x incresing from to.2. In other words, our simple nlysis shows tht the different functionl forms of SCSL nd S16 pc vs. x my well be consistent with their differing ctivity coefficients s required by the GibbsDuhem reltion for nonidel solutions. Lterl diffusion vs. order prmeters It is known tht in n idel solution the self diffusion rte should be liner with composition (4). The nonliner vritions of the selfdiffusion coefficients observed in this work for POPC/cholesterol solutions re chrcteristic of nonidel solution (443). It hs been suggested tht one use the excess selfdiffusion coefficient (4, 41) nlogous to excess thermodynmic functions, to mesure the extent of the devition from idelity. Simple rguments indicte tht such n excess coefficient is negtive (positive) for CSL (16PC) in nlogy to cyclohexne/ benzene (41) nd hexne/nitrobenzene (4) solutions. We shll tret the nonidel chrcteristics from nother perspective. We now consider whether the lterl diffusion coefficient D of CSL my be relted to the ordering S, which we hve shown provides direct mesure of solution nonidelity. We show in Fig. 8 tht t ech vlue of temperture, In D vries linerly with S2 (x, T). More precisely, we empiriclly find tht D(S, T) = D exp {[(T)S2(x, T) + i3]/rt}, (18) with DO = 9.18 x 16cm2s,1 = 133K * R nd tht (T) = ' + b'/t (18) with '= K * R nd b' = 1.33 x 16K2  R (nd R here is the universl gs constnt). The vlidity of Eq. 18 is illustrted in Fig. 8 b. The vlues of (T) shown in Fig. 8 c were obtined from the vrition of In D with S for ech T, s ws the vlue of DO(T) = DoeIRT. Fig. 8 b shows the universl liner curve obtined when In[D(x, T)/DO(T)] is plotted vs. (T)S2(x, T)/RT for ech vlue of x (i.e. constnt x behvior). We hve lso been ble to fit our results on D for 16PC to n eqution of the form of Eq. 18 s illustrted in Fig. 8 d. There is somewht more (rndom) sctter due in prt to the somewht greter error in our mesurements of D16pc vs. DCSL. Nevertheless, we find tht these results re lso wellfit by Eq. 18 with DO = 1.6 x 14cm2s1, = 2317K R with ' = 2.6 x 14K * R nd b'= 8.56 x 16K2 * R. Note tht for both probes (T) decreses monotoniclly with temperture over the rnge studied. This smller vlue of (T) t the higher tempertures implies weker dependence for DCSL nd D16PC on S t the higher tempertures. We hve tried vriety of different functionl forms of D vs. S, but only the form of Eq. 18 ws successful. This sttement must be qulified with the following observtion. We were lso successful in the cse of CSL (but not 16PC) with fitting our dt to liner dependence of In D vs. S(x, T), nd the x2 test ws comprble to tht for Eq. 18 (X2> 12). We point out in the Discussion section tht (T)S2 + in Eq. 18 is the ctivtion energy for the lterl diffusion. In the cse of the fit of In D vs. S(x, T) for CSL, however, the numericl fit leds to negtive ctivtion energy (nd very smll DO), which mkes no sense physiclly. We hve thus ruled out this ltter functionl form on physicl grounds for CSL nd sttisticl grounds s well for 16PC. Rottionl diffusion vs. order prmeters We found n interesting universl reltion between R1 of CSL nd its order prmeter S in the highly ordered Shin nd Freed Shin nd Freed Dynmic Imging of Lterl Diffusion 545
10 o o w S S T A P. *I ~ ~ ~ II. 8. _..2.4 S2(X.T) S2(T)(1/RT g d 8,i. s W. 3. I r C r,cl.k) S ' S2MT)(T)/RT FIGURE 8 () Semilog plot of DCSL vs. S2 t different tempertures: 15 (), 25 (), 35 (A), 48 (), nd 6C (). (b) Plots of [ln(d(x, T))  1n((DO(T))] vs. (T)S2(T)/RT for CSL t different compositions: (), 4 (), 1 (A), 2 (U), nd 3 () mol %. (c) Plot of (T)/R vs. T ssocited with b. (d) Sme type of plots s b for 16PC: (+), 1 (x), nd 2 mol % (). POPC model membrnes contining cholesterol: R1 = A(1  S)2, (19) with A = 9.15 x 1O' s'. The constnt A is independent of both composition nd temperture. This universl behvior is illustrted in Fig. 9 for ll our dt on CSL. On the other hnd the form of Eq. 18 or its vrints proved unsuccessful. In the cse of R1 for 16PC, we could not find ny simple correltion with S (including the forms of Eqs. 18 nd 19). In fct, from the dt of Tble 2 we find tht R1 increses with S s the ltter increses with mole percent cholesterol; on the other hnd R1 decreses s S is incresed by lowering the temperture. Thus, there is no simple reltion between R1 nd S for 16PC. This is perhps not surprising, since the motion of the 16PC nitroxide moiety locted t the end of the cyl chin (cf. Fig. '1) is known to depend gretly on the complex internl modes of the chin. The cse for the rigid CSL probe is most certinly much simpler. "IC Pi. N : d S x q I d (1S)2.3.4 FIGURE 9 Plot showing universl reltion between R1 nd (1 _ S)2 for CSL: 15 (), 25 (), 35 (A), 48 (U), nd 6C (). 546 Biophysicl Journl Volume 55 Mrch 1989
11 Comprison with other work: lterl diffusion The previous studies of lterl diffusion hve lmost ll focused upon phospholipid diffusion. Our results for D of 16PC do not exhibit significnt influence of cholesterol. The PNSE study of the sme system (23), lso showed little effect of the cholesterol on the selfdiffusion of the POPC molecules, but it showed smll increse compred with our observed smll decrese. Only in the FRAP studies of lterl diffusion in DMPC nd eggpc model membrnes contining cholesterol (2, 21) were both fluorescencelbeled sterol nd phospholipid studied. However, these studies gve significntly different results from ours in three respects. First, the diffusion rtes of the fluorescencelbeled sterol nd phospholipid probes were nerly the sme under ll conditions of cholesterol concentrtion nd temperture in the liquid crystlline stte. Second, the temperture dependence of selfdiffusion coefficient ws very mild in ll compositions. The ctivtion energies were bout 23 k cl/mol, which is lmost fctor of three less thn those of CSL. Third, selfdiffusion coefficients of both fluorescence probes were lmost constnt until the concentrtion of cholesterol reched 1 mol %, nd then they decresed by fctors of three t 2 mol %, but they did not chnge much in the rnge from 2 to 4 mol %. We believe tht the different result from the two experiments, including those with respect to the reltive behvior of those two probes, is due to the fct tht the photosensitive functionl group ttched to the prent molecules used in the FRAP experiments is very substntil in size so tht it could hve dominnt influence on the diffusionl process, which could result in identicl diffusion coefficients tht re different from tht of cholesterol nd phospholipid. It ws found previously tht the mjor effect of cholesterol is to increse the structurl ordering in the bilyer of phosphtidylcholine t low wter content (15). In the present work we find tht it not only increses the structurl ordering but it lso reduces the rottionl diffusion rte (R1) considerbly, (lthough it seems to enhnce rottion round moleculr long xis, i.e., RI for CSL). The difference my be due to the low vs. high wter content of the bilyer. DISCUSSION Our extensive results on order prmeter S, rottionl diffusion coefficient R1, nd lterl diffusion coefficient D, nd the simple correltions between them both s function of x (mole frction of cholesterol) nd of T in the liquid crystlline phse (bove Tm) re cler nd strong mnifesttions tht this is simple nonidel solution of POPC nd cholesterol. This is, of course, in greement with the observtion of Sckmnn nd coworkers (11) who found single phse for DMPC/cholesterol mixtures for x =.14 nd possibly s high s.45. The order prmeter of the CSL molecules which should relte closely to the properties of cholesterol molecules, nd of 16PC, which should relte to the properties of POPC, re simply interpreted in terms of nonidel solutions in the present work. This suggested n pproch whereby the ctivity coefficients re simply given by the devition of the respective order prmeters from liner behvior in x. The diffusion coefficients R1 nd D lso show rther simple nd monotonic vrition in x nd T in this phse. In fct, surprisingly simple correltions with S hve been found for them, nd hence with the ctivity coefficients obtined from them. It is perhps remrkble tht such consistent evidence could be obtined from results on these three quite different types of prmeters. In generl, we hve observed very substntil vritions of S, R1, nd D for CSL s x is incresed from zero, wheres only modest chnges were observed for 16PC. While this might nively seem to suggest some peculirity, we hve shown in the previous section tht it my simply be due to the GibbsDuhem eqution pplied to ychol nd ypopc. The observed ychol vrition with x is consistent with preferentil ssocition of cholesterol molecules with ech other in the POPC solvent. This leds to vlues of ychol < 1. It is therefore no surprise tht D nd R1 for CSL re modified significntly s x increses from the very dilute limit (i.e. less thn 1 mol % of CSL). This tendency to ggregtion of the cholesterol (including CSL) molecules mens tht the environment of CSL chnges significntly s function of x, from tht of flexible POPC molecules, to the more rigid cholesterol molecules. One might expect tht cholesterolrich region would be more dense nd compct thn the pure POPC bilyer providing less room vilble for the molecule to diffuse. As result, the self diffusion of CSL in such region should be slower thn in the pure POPC bilyer. The rottionl diffusion will be more restricted by the incresed ordering, but this feture hs lredy been included in our rottionl model tht distinguishes the Rtensor nd the restoring potentil from which S is clculted (cf. Eq. 8). The cholesterolrich regions must lso be more solidlike due to the dense pcking, thereby providing greter frictionl resistnce to rottionl motion, to explin the observed order of mgnitude decrese in R, for CSL with x. We do note substntil increse of ctivtion energy (cf. Tble 1) for both D nd R1. The tendency of cholesterol to ggregte mens tht Shin nd Freed Dynmic Imging of Lterl Diffusion 547
12 the POPCrich regions re less influenced by cholesterol molecules thn would otherwise be expected. This is consistent with the rther modest effect of cholesterol on the lterl diffusion of 16PC. We did observe smll increse in R1 for 16PC with the ddition of cholesterol. It might imply tht the increse in overll ordering results in slightly lower friction in the endchin region (somewht nlogous effects re known in other systems [44]). Self ssocition, creting lrger nd more cholesterolrich regions or clusters, possibly competes with the cretion of new clusters in the nonidel solution. The sturtion effect on ychol (hence on S, D, nd R1) for cx > 1 (cf. Eq ) suggests tht in the concentrtion rnge 2 1 mol % cholesterol, the ddition of more cholesterol merely increses the extent, but not the nture of the cholesterolrich clusters. This my be thought of s preprecipittion regime of the nonidel solution. When we consider () the temperture independence of ychol nd yypc, nd (b) the universl dependence of S for both CSL nd 16PC on the scled temperture tu (cf. Eq. 12), these re surprisingly simple results. Relted behvior hs indeed been seen recently for SCSL in mixtures of nerly identicl thermotropic liquid crystls (36), where the temperture ws scled reltive to the observed phsetrnsition temperture t which SCSL ws independent of composition. More unusul perhps is Eq. 19 expressing R1 for CSL simply s proportionl to the squre of the disorder prmeter, 1  S. This seems to suggest tht for the highly ordered CSL, the rottionl dynmics should be referred to the rigid crystlline stte of cholesterol, where the disorder prmeter would be expected to be zero, nd the pcking forces imply ner infinite frictionl resistnce to reorienttion. Tht is, the microviscosity my be expected to be monotonic function of (1  S)'. Thus, finding tht R1 is function of (1  S) my not be surprising, lthough the simplicity of the ctul functionl form tht is found is not, t present, esily explined. We now wish to consider the S dependence of the lterl diffusion coefficients s expressed by Eq. 18. We cn regrd (T)S2(x, T) +,B s the ctivtion energy, for the self diffusion s we hve lredy noted. It seems resonble to interpret this s n enhnced ctivtion brrier to self diffusion s membrne ordering is incresed by the ddition of cholesterol. In fct, in theoreticl nlysis of viscosities in thermotropic liquid crystls (45) n S2 dependence of the ctivtion energy ws predicted in the context of free volume model. In tht theory the relxtion time is proportionl to the probbility tht the molecule finds enough free volume to mke trnsltionl jumps between two equilibrium positions, nd this leds to n S2 dependent term in the ctivtion energy. There is lso, in tht theory, term liner in S in the ctivtion energy which comes from the contribution to the relxtion time rising from the probbility tht the molecule hs enough energy to overcome the potentil brrier due to the moleculr field creted by the other molecules. Diogo nd Mrtins (45) clim tht "in most prcticl cses" the S2 term is dominnt. Our results imply temperturedependent ctivtion energy such tht the effect of ordering is enhnced t lower T. This could be due to the higher pcking (i.e. incresed density) s T is reduced, which enhnces the role of ordering in providing resistnce to diffusion. All in ll, some remrkble empiricl reltions hve been found between R1, D, nd S in this study of POPC/cholesteroloriented model membrnes by ESR. It should be vluble to further test their universlity by similr experiments utilizing different phospholipids in conjunction with cholesterol, s well s phospholipids lbeled t other positions long the cyl chin. To gin the full power of ordering nd rottionldiffusion studies by ESR, these studies should be performed s function of orienttion of the multilyer in the mgnetic field (27), even though such studies would hve to be performed fter the ESR imging mesurements of lterl diffusion re completed (rther thn simultneously s in the present work). CONCLUSIONS () The ESRimging method is useful nd ccurte method for mesuring lterl diffusion coefficients of nitroxide spin lbels in oriented model membrnes. (b) POPC/cholesterol mixtures led to nonidel solution in the Lphse bove Tm s evidenced in the mesurements of the order prmeters, S, the lterl diffusion coefficients, D, nd the rottionl diffusion coefficients, R1, of the spin lbels. (c) The nture of the nonidelity is consistent with the tendency of the cholesterol molecules to ssocite. (d) A simple nlysis of the order prmeters of the spinlbeled components suggests they my be used to estimte ctivity coefficients of the cholesterol nd the phospholipid. (e) Surprisingly simple correltions of (i) S vs. x nd T, (ii) D vs. S, nd (iii) R1 (for CSL) vs. S hve been observed in this work which pper to offer insights into the dynmic moleculr structure of the model membrne. 548 Biophysicl Journl Volume 55 Mrch Biophysicl Journl Volume 55 Mrch 1989
13 APPENDIX Asymptotic behvior for lrge ordering potentils nd order prmeter The order prmeter in Eq. 1 is written in nother form, where p  s=3 d(ln fexp [pt2ldt) 2) 2 dp 2 3/2 X. The integrl is pproximted by Jexp[ptL d 2 3/2' (21) for resonbly lrge vlue of X. By substituting Eq. 21 into Eq. 2 we hve simple reltion between X nd S: X +2 or S (22) The pproximte eqution (Eq. 22) fits well to the vlues of the numericl integrtion when X is >2.32 (S >.5) s is seen in Fig. 1. Becuse the Xs re generlly >2.5 for CSL in POPC/cholesterol model membrnes (except for x  ), we use Eq. 22 to express the temperture dependence of the men field ordering potentil A. Fig. 6 illustrtes the temperture dependence of the order prmeter S, which is liner in T, nd the slope is independent of the composition. Thus we hve from Eq. 11: (T [TT) 2 or where T* is reference temperture t which S becomes 1, nd it depends on the composition. Co FIGURE 1 Plot of order prmeter S vs. ordering potentil A; () from numericl integrtion of Eq. 1 nd (.) from Eq. 22. We wish to thnk Professor G. Feigenson for his gift of the 16PC. We thnk Dr. D. Clery nd Dr. J. Moscicki for their helpful comments on the ESRimging methods used here, nd Dr. R. Crepeu nd Dr. S. Rnnvre for their dvice nd ssistnce. This work ws supported by Ntionl Institutes of Helth grnt GM25862 nd Ntionl Science Foundtion grnt DMR8642. Computtions were performed t the Cornell Ntionl Supercomputer Fcility. Receivedfor publiction 6 September 1988 nd infinlform 16 November REFERENCES 1. Gershfeld, N. L Equilibrium studies of lecithincholesterol interctions. Biophys. J. 22: Mbrey, S., P. L. Mteo, nd J. M. Sturtevnt High sensitivity scnning clorimetric study of mixtures of cholesterol with dimyristroyl nd diplmitoylphosphtidylcholines. Biochemistry. 17: Shimshik, E. J., nd H. M. McConnell Lterl phse seprtion in phospholipid membrnes. Biochemistry. 12: Rubenstein, J. L. R., J. C. Owicki, nd H. M. McConnell Dynmic properties of binry mixtures of phosphtidylcholines nd cholesterol. Biochemistry. 19: Recktenwld, D. J., nd H. M. McConnell Phse equilibri in binry mixtures of phosphtidylcholine nd cholesterol. Biochemistry. 2: Presti, F. T., nd S. I. Chn Cholesterolphospholipid interction in membrnes. 1. Cholestne spin lbel studies of phse behvior of cholesterolphospholipid liposomes. Biochemistry. 21: Lentz, B. R., D. A. Brrow, nd M. Hoechli Cholesterolphosphtidylcholine interctions in multilmell vesicles. Biochemistry. 19: Copelnd, B. R. nd H. M. McConnell The rippled structure in bilyer membrnes of phosphtidylcholine nd binry mixtures of phosphtidylcholine nd cholesterol. Biochim. Biophys. Act. 599: Hui, S. W., nd N.B. He Moleculr orgniztion in cholesterollecithin bilyers by xry nd electron diffrction mesurements. Biochemistry. 22: Levin, I. W., E. Keihn, nd W. C. Hrris A Rmn spectroscopic study on the effect of cholesterol on lipid pcking in diether phosphtidylcholine bilyer dispersions. Biochim. Biophys. Act. 82: Knoll, W., G. Schmidt, K. Ibel, nd E. Sckmnn Smllngle neutron scttering study of lterl phse seprtion in dimyristroylphosphtidylcholinecholesterol mixed membrnes. Biochemistry. 24: Hinz, H.J., nd J. M. Sturtevnt Clorimetric studies of dilute queous suspensions of bilyers formed from synthetic Llecithins. J. Biol. Chem. 247: Ipson, J. H., G. K. Krlstrom,. E. Mouritsen, H. Wennerstrom, Shin nd Freed Dynmic Imging of Lterl Diffusion 549
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