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The effects of polymer-controlled hydration on nuclear magnetic resonance parameters Lees, Irene 1993

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THE EFFECTS OF POLYMER-CONTROLLED HYDRATION ONNUCLEAR MAGNETIC RESONANCE PARAMETERS.Irene M. LeesB. Sc. (Physics), University of New Brunswick, 1991A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAApril 1993© Irene M. LeesIn presenting this thesis in partial fulfilment of the requirements for an advanced degreeat the University of British Columbia, I agree that the Library shall make it freelyavailable for reference and study. I further agree that permission for extensive copyingof this thesis for scholarly purposes may be granted by the head of my department orby his or her representatives. It is understood that copying or publication of this thesisfor financial gain shall not be allowed without my written permission.Department of PhysicsThe University of British Columbia1956 Main MallVancouver, CanadaDate: 3o ) j4Q3AbstractThe polymer polyethylene glycol (PEG) was used to control the amount of hydrationin lipid bilayers. These bilayers were composed of either 1,2-dimyristoyl-sn-glycero-3-phophocholine (DMPC) or 1,2-dipalmitoyl-sn-glycero-3-phophocholine (DPPC) andoriented between glass slides. These lipids were deuterated in the headgroup to allowtheir study with 2H Nuclear Magnetic Resonance (NMR). Specifically, the quadrupolarsplitting (Avg ), the gel to liquid crystalline phase transition temperature (T n,), thespin-lattice relaxation times and the spin-spin relaxation times were investigated asthe membrane was dehydrated. Both Avg and Tn, are hydration dependent but nosystematic change in the relaxation times was noted as a function of the water contentof the sample. The spin-spin relaxation times did show an orientation dependence. Theanalysis led to the proposal that thickness fluctuations and thermal undulations of themembrane were two possible mechanisms for this relaxation.iiTable of ContentsAbstract^ iiList of Tables^ vList of Figures^ viAcknowledgments^ vii1 Introduction 12 Lipid Bilayers 32.1 Properties of Lipid Bilayers ^ 32.2 Motions within Lipid Bilayers 42.3 Hydration ^ 53 Theory 83.1 Spectra of Bilayers ^ 83.2 Relaxation ^ 93.3 Orientation Dependence of Relaxation ^ 94 Experimental Procedure 114.1 Equipment ^ 114.2 Data Acquisition 114.2.1^Quadrupolar Echo ^ 114.2.2^Inversion Recovery 13iii4.2.3 T 2q, Measurements ^  134.2.4 Jeener-Broekaert  144.3 Sample Preparation ^  154.4 Depaking ^  165 Results^ 175.1 Quadrupolar Splitting ^  175.2 Transition Temperature  205.3 Longitudinal Relaxation Times ^  235.4 Transverse Relaxation Time  265.5 Errors ^  316 Discussion^ 327 Conclusion^ 37Bibliography^ 38ivList of Tables3.1 Legendre Coefficients for Slow Motions ^ 104.1 Example ri values ^ 154.2 r1 Values Used in Experiments ^ 155.1 Quadrupolar Splittings for DMPC 195.2 Transition Temperature for DMPC ^ 205.3 Average T iz ^ 265.4 T2 Fits to Legendre Polynomials ^ 285.5 T2 Fits to (P 2 (cos0)) 2 and sin e 0 cos2 0 296.1 Conversion of wt. % PEG to H 2 O molecules ^ 33List of Figures2.1 Structure of DPPC ^ 44.1 Stack Plot of Temperature ^ 125.1 Quadrupolar Splitting for DPPC ^ 185.2 Transition Temperature for DPPC 215.3 Relation Between T v., and wt. % PEG ^ 225.4 Zeeman Spin-Lattice Relaxation Times for DPPC^ 235.5 Zeeman and Quadrupolar Spin-Lattice Relaxation Times for DMPC 255.6 Longitudinal Relaxation Times for DMPC ^ 275.7 T2 Fits ^ 30viAcknowledgmentsI would like to thank my supervisor, Dr. Myer Bloom, for all his help and support onthis project. I felt that I have learnt a lot over the past two years.I would also like to thank Clare Morrison for all her help since many of the ideascame from the work that she was doing. I would also like to express my gratitude toher since she took time out of her busy schedule to show me how things worked in thelab.The Room 100 bunch was a great pleasure to work with since everyone is so openand friendly. It made the more tedious portions of the two years much more endurableand the exciting parts much more fun. Good luck to all of you in the future.I would also like to thank the people who helped me out by proof reading my thesis,namely Jeff and Jeff. I hope there aren't too many mistakes left in it.Finally, I would like to thank my parents who started me out at a young age on theroad to science and gave me support from the beginning.viiChapter 1IntroductionIn the past, there have been numerous experiments looking into the effects of hydrationon phospholipid bilayers. These experiments include the study of changes in spin-latticerelaxation rates [Ulri 90], measurement of the quadrupolar splittings of the deuteriumnuclei [Bech 91] and the determination of the gel to liquid crystalline transition temper-ature [Jurg 83], all as a function of the water content of the sample. Other experimentshave shown that polymers can be used to change the hydration of a bilayer [LeNe 77].Polyethylene glycol (PEG) is a polymer which is known to form many hydrogen bondsand therefore water binds to the polymer surface. In fact, at 38 wt. % PEG and above,no free water exists in the mixture. This fact makes PEG ideal as a dehydrating agentin membrane experiments since it is easy to control and may simply be added to thesample. This polymer has been used as a dehydrating agent in other experiments suchas protein crystallization and membrane fusion [MacD 85] but so far it has not beenused in conjunction with NMR relaxation studies of membranes. Furthermore, severalstudies have shown that PEG, with a sufficiently high molecular weight, is excludedfrom the surface of bilayers and therefore does not physically enter the membranethereby causing bilayer disruption [Arno 90]. This fact is also supported by consistentNMR results between samples with and without PEG added.The initial findings support the theory that PEG can be used to dehydrate mem-branes since the NMR results using PEG are similar to results using other methods ofmembrane dehydration. Since the addition of a polymer to a lipid sample is relatively1Chapter 1. Introduction^ 2simple, this method of dehydrating should prove useful in the future in studying theeffects of low water content on the properties of lipid bilayers.Chapter 2Lipid Bilayers2.1 Properties of Lipid BilayersThe main function of a membrane is to compartmentalize different areas of cells and toserve as a semi-permeable barrier. Cell membranes are composed of lipids and proteins,where the lipids provide the structure and the proteins carry out the functions of themembrane such as ion transport, energy production, etc. In this study, only modelmembranes were used since real cell membranes are much more complicated and resultsare difficult to interpret.A model membrane composed of only one type of lipid was used. Lipids are am-phiphilic in nature (i.e. they have both a hydrophobic and a hydrophilic domain).Therefore, when placed in water, they tend to form bilayers with the hydrophilic polarheadgroup facing out towards the water and the hydrophobic tails facing the inside ofthe bilayer. The strain on the ends of the bilayer due to the hydrophobic core com-ing into contact with the surrounding water causes the bilayers to fold into sphericalvesicles.The two types of lipids used in this study were 1,2-dimyristoyl-sn-glycero-3-phospho-choline (DMPC) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). These lipidswere deuterated in the a, # and 7 positions of the headgroup defined in Figure 2.1.DMPC has a very similar structure except that the chains are 14 carbons long insteadof 16 carbons.3Chapter 2. Lipid Bilayers^ 4CH, CH2 CH2 CH,^CH, CH2 CH,ZNVN/X7 X/i/NZXCH3 CH2 CH, CH2^CH2 CH2 CH2^\CH,^(y) +N(CD3)3//C=0 (II) \CD20^(a)/ CD2CH3 CH CH2 CH CH2 CH2 CH CH 2^CH—CHi—OP03-X7/77/77 i:° \CH2 CH2 CH2 CH2 CH2 CH2 CH2^C^CH2ii0Figure 2.1: Structure of DPPCThe structure of DPPC is shown as well as the thirteendeuterons associated to the a, and -y positions.One fundamental property of lipids is a phase transition from a gel phase at lowtemperature, involving slow lateral diffusion of the lipids and excitation of very fewtrans-gauche isomerizations in the hydrocarbon chains, to the liquid crystalline phaseat high temperature, where faster lateral diffusion is allowed and many kinks are formedalong the hydrocarbon chains. This phase transition can be monitored using NMR sinceeach phase has a distinct spectral signature.2.2 Motions within Lipid BilayersThere are many different types of motions in bilayers which occur over a wide rangeof timescales. Such motions include lateral diffusion (i.e. lipids moving in the plane ofthe bilayer), rotational diffusion about the long axis of the lipid molecule, lipid flip-flopfrom one side of the bilayer to the other, trans-gauche isomerization in the hydrocarbonchains, headgroup motions, movement of the lipids into or out of the plane of the bilayerand thermal undulations [Pfei 89]. Many of these motions contribute to the relaxationrates in NMR and therefore measurement of different relaxation times can be used todetermine the time scales of the lipid motions.Chapter 2. Lipid Bilayers^ 5One type of motion which is important in NMR spectra of powder samples is lat-eral diffusion of the lipids around the vesicle. This diffusion causes complications inthe interpretation of the spin-spin relaxation times (T 2 ) since a variety of angles aresampled by the lipid during the length of the experiment. Since T2 times are orienta-tion dependent, the true T2 relaxation rate can not be determined. In order to removethe effects of diffusion, bilayers are oriented between glass plates so that movement ofthe lipids will only be along one plane. The lateral diffusion will now no longer affectthe spectrum since the angle between the bilayer normal and the main magnetic fieldwill not change as the lipids diffuse. This allows the study of other types of motions inthe membrane.2.3 HydrationIn recent years, several groups have looked into the interactions of water with bilayers.There appear to be three water layers associated with a fully hydrated bilayer [Fine 74].The first is a layer of water very strongly bound to the headgroups. There is also anintermediate water phase where water is present between the stacked bilayers. Thissecond layer is quite free to move but it is rapidly exchanged with the bound water.Finally, there is a bulk water phase where water has unrestricted movement and is notdirectly associated with the bilayer. The actual number of water molecules associatedwith each of these three phases varies from lipid to lipid depending on the size andcharge of the headgroup.A previous study [Bush 80] showed that for DPPC, the first two water moleculesadded to the lipid separate and shield the phosphate charges from one another. Also,their results indicate that these water molecules are not strongly hydrogen bondedto the phosphate oxygen atoms but instead the PO4 group is free to rotate. TheChapter 2. Lipid Bilayers^ 6conformation of the headgroup seemed to be determined from the first four or fivewater molecules added to the lipid since after this, no further headgroup reorientationoccurs. This is not consistent with other findings [Bech 91] which indicate that a changein the headgroup orientation does occur at higher levels of hydration.In vivo biological membranes are found in a state of full hydration, defined asthe state where no change in any of the physical properties of the membrane occurswith the addition of water. Therefore, experiments which attempt to mimic in vivosituations should also use fully hydrated membranes. Actual methods of obtaining afully hydrated membrane seem to be under dispute.When using oriented samples, it is not possible to add a large amount of bulk waterto the sample since the lipids detach from the glass slides and form vesicles therebyruining the orientation of the sample. Therefore, there is some problem in achieving fullhydration in these bilayers. The most common way of getting a hydrated membraneis to leave the lipids in a water saturated vapour for a varying length of time (fromhours to days) so that the bilayer absorbs water. Recent studies [Rand 89] have shownthat this method does not lead to full hydration. In fact, only a 35 wt. % hydrationis achieved whereas full hydration is estimated at greater than 50 wt. % hydration.Thus, a new method needs to be developed in order to ensure full hydration in orientedbilayers.In this study, a polymer (PEG) was used to hydrate the membrane. PEG has thechemical structure(—CH2 — CH2 — 0— )nand water is found hydrogen bonded to the oxygen. Since both the membrane andthe polymer competed for the water in the sample, the addition of bulk water withoutthe lipids forming vesicles and sample orientation being lost was allowed. With onlyChapter 2. Lipid Bilayers^ 7a small amount of PEG added to the sample, the membrane was very close to fullhydration. Larger amounts of polymer can also be added to dehydrate the membraneso that studies on water depleted bilayers can be carried out.Although PEG was not used as a dehydrating agent, studies on dehydrated powderbilayers have been done in the past [Bech 91,Ulri 90,Jurg 83]. Therefore, this studywas compared to previous results to determine whether PEG produced the same effectswhen used for bilayer dehydration.One effect of bilayer dehydration is a change in the transition temperature fromthe gel to the liquid crystalline phase. The phase diagram for DPPC at low waterconcentrations has been determined [Jurg 83]. Another group [Cevc 85] theorized thatat low water concentrations, the shift in transition temperature from that of a fullyhydrated bilayer was directly proportional to the number of water molecules associatedwith each lipid.Bechinger and Seelig [Bech 91] recently determined the effects of dehydration on thequadrupolar splitting of deuterons in the headgroup of 1-palmitoyl-2-oleoyl -sn-glycero-3-phosphocholine (POPC). The changes in Av are attributed to conformational changesin the headgroup due to lower amounts of water in the surrounding environment.Another study evaluated the effect of hydration on spin-lattice relaxation times (TO[Ulri 90]. The results showed an almost linear increase in the T i relaxation times aswater was added until full hydration was achieved at approximately 22 water moleculesper lipid after which the relaxation times levelled off to their value at full hydration.Chapter 3Theory3.1 Spectra of BilayersIn nuclei with spin greater than one, there is an interaction between the quadrupolemoment and the local electric field gradient at the nucleus. This is the dominant effecton the 211 NMR spectra.The 211 NMR spectrum of an immobilized C- 2H bond making an angle 0 withrespect to the main magnetic field is a doublet with splitting 2w(®) wherew(0) = w qP2 (cos 0) = w q (3 cos t 0 — 1)/2^(3.1)In the case of deuterium, (f,-7, '2-_ 125kHz. (Note that the influence of a small deviationfrom axial symmetry was neglected in writing Eq. 3.1 [Davi 83].)In the presence of axially symmetric motions fast on the NMR timescale, thequadrupolar splittings only depend on 9 (the angle between the magnetic field andthe surface normal of the bilayer). Therefore,W(9) =< w(0) > fastmotions = Wq■SCD(3COS 2 9 — 1)/2^(3.2)where Scp is known as the order parameter and is equal toSCD =< (3COS 2 13 — 1)/2 >fastmotions •^ (3.3)Here, 0 is defined as the angle between the surface normal of the bilayer and the C- 2 Hbond.8Chapter 3. Theory^ 93.2 RelaxationThere are two different types of relaxation that occur in NMR. The first is known asspin-lattice or longitudinal relaxation and it is characterized by a relaxation time T i .This relaxation is due to spin flips which cause one or two quanta of Zeeman energyto be exchanged between the spin and the lattice. These processes involve spectraldensities associated with frequencies near the Larmor frequency w = w o and twice theLarmor frequency w = 2w„, respectively. The second is known as spin-spin relaxationand it is characterized by a relaxation time T2. This relaxation is due to the loss ofphase memory by the spins due to thermally driven fluctuations in the quadrupolarsplittings. T i is affected by fast motions on the NMR timescale whereas T2 is affectedby both fast and slow motions. It can be shown that T2 <T1.3.3 Orientation Dependence of RelaxationA general expression for the orientation dependence of T i (Tiz, T iq or T 2 ) for fastmotions has been derived by Morrison and Bloom [Morr 93a]. It takes the form,=a(i) Y (0 0) ,p even^ (3.4)p=0 q=-p pq PqFor the case of axial symmetry (which is present in liquid crystalline or fluid lipidbilayer systems), this equation can be reduced to a sum of even Legendre polynomialsup to order 4, ie.1 = a, + a2P2 (cos 0) + a4P4 (cos 0)T (3.5)The coefficients are functions of order parameters and correlation times and indicatethe types of motion present in the system.Chapter 3. Theory^ 10Table 3.1: Legendre Polynomial Coefficients for Example MotionsMotion Parameter Valueao 0.20(P2(cos 6)) 2 a2 0.29a4 0.51sin2 0 cos2 0a,a20.130.095a4 -0.23For special mechanisms of slow motion, specific orientation dependences of the re-laxation rates can be derived. Two such mechanisms are surface undulations whose an-gular dependence is predicted to be proportional to sin 2 0 cos 2 0 [Bloo 91a] and thicknessfluctuations proportional to (P 2 (cos 9)) 2 providing that they occur without any changein membrane orientation [Bloom, private communication]. These two expressions canbe rewritten to be expressed as a sum of Legendre polynomials with specific coefficients(see Table 3.1).Chapter 4Experimental Procedure4.1 EquipmentThe equipment used to obtain all experimental data was a home-built spectrometer[Ster 85] at 46 MHz. The 90° pulse length was equal to 4 its and the dwell time was setto 5 its. The signal was acquired in quadrature with cyclops phase cycling to increasethe signal to noise ratio [Davi 79].The temperature was regulated with a Bruker Model BV T1000 temperature con-troller and was measured to an accuracy of +0.5 degrees.The sample orientation was controlled using a home-built goniometer accurate to+0.5 degrees.4.2 Data AcquisitionIn order to determine the parameters under study, a variety of pulse sequences wereapplied. These enabled the quadrupolar splitting, the transition temperature, the spin-lattice relaxation times and the transverse relaxation time to be measured.4.2.1 Quadrupolar EchoThe quadrupolar echo pulse sequence used was90; — 7 - 901' — twhere a value of T = 50 tts was used for spectroscopic measurements.11Chapter 4. Experimental Procedure^ 12Figure 4.1: Transition TemperatureA stacked plot showing the determination of the transition tem-perature is presented. In this case, T m was taken as 50°C sinceat this temperature the peaks became very sharp. This illus-trative plot was done for the 60 wt. % PEG sample of DPPC.The spectra found from this pulse sequence were used to measure the quadrupolarsplitting for the three deuteron positions. The spectra were also used to determine thetransition temperature for the sample with an accuracy of +0.5°C. The actual value ofthe transition temperature was taken as the temperature at which the outer peaks inthe spectrum became much sharper and narrower (Figure 4.1). The temperature wasincreased in 1°C steps.Chapter 4. Experimental Procedure^ 134.2.2 Inversion RecoveryThe Zeeman energy spin lattice relaxation time, T iz , was measured using an inversionrecovery pulse sequence,180; — 7-1 — 90; — r2 — 901 — tThe signal was actually modified by subtracting the inverted spectrum from the quadru-polar spectrum obtained in the absence of the 180° inverting pulse. This gave a signalwhich was maximum at 7-1 = 0 and decayed to zero as 7-1 increased. Ten 7-1 valuesranging from 1 ms to 90 ms were used. The value of 7-2 remained constant at 50 ,as.The intensity of the deuteron peaks from the spectra were determined for each 7by Fourier transforming from the peak of the echo. These intensities were fit to anexponential curveM = mo e -r/Tizwhere M is the signal intensity and T i , is the longitudinal relaxation time.4.2.3 T2 q, MeasurementsThe transverse relaxation time, T 2ge , was determined using a quadrupolar echo sequencewith varying values of T,90; — T - 90: - tThe values of the nine T used were between 50 as and 4 ms.Again, the intensity of the FT spectrum was determined for each T for each deuteronposition. These values were then fit to the exponentialm = mo e-211T2 qewhere M is the signal intensity. The transverse relaxation time, T 2qe , could then bedetermined from the graph.Chapter 4. Experimental Procedure^ 144.2.4 Jeener-BroekaertThe Jeener-Broekaert pulse sequence [teen 67] was used to measure the quadrupolarrelaxation time for the DMPC sample. This pulse sequence consists of90° — 7-1 — 45; — T2 — 45; — tDifferent values of T1 cause a modulation proportional to sin(w gri ) in the amplitudeof the signal [Bloo 91b], where w g is equal to 271-Avg . Therefore, if7rwqri = 2then the signal will be a maximum. This is equivalent to chosing T 1 values accordingto1T1 = 4^Avgwhere Avg is the quadrupolar splitting frequency of the deuterons. In order to avoidrunning three experiments for the three types of deuterons each with different Avg , theT1 value had to be optimized for all three deuterons at once. To do this, the T 1 valuewas calculated for each deuteron at a specific angle. The experimental T 1 value wasthen chosen close to the optimum values for a and # since the 7 deuterons had a muchlarger signal and could afford the reduced intensity. An example of a choice of T i isshown in Table 4.1 where T1 was chosen as 50 its since it is intermediate to all threeindividual values although biased towards a and /3. The actual T1 value for each bilayerorientation used is shown in Table 4.2. The T2 times ranged from 1 ms to 150 ms.The spectra were obtained by Fourier transforming the FID signal from the firstzero crossing. The T ig relaxation times were found for each deuteron position by fittingthe FT intensities to an exponential (i.e. the same procedure used in the determinationof Tiz).Chapter 4. Experimental Procedure^ 15Table 4.1: Example of a chosen r 1 value for 0° orientationDeuteron Ay calculated -ri chosen Tia 6.379 39 iis0 5.383 46 /is 50 /is-y 1.256 199 itsTable 4.2: Jeener Broekaert pulse sequence ri valuesAngle 0 1-1 (is)0° 5015° 5030° 6045° 13075° 13090° 804.3 Sample PreparationDPPC-d13 and DMPC-d 13 , specifically deuterated in the a, 13 and -y positions of theheadgroup, were purchased from Avanti Polar Lipids Inc. (Birmingham, Al.). Thetwo different molecular weights of PEG (3000 and 8000) were purchased from SigmaChemical Company (St. Louis, MO, U.S.A.).The powder sample was made by dissolving 50 mg of DMPC in 1 mL of chloroform.Most of the chloroform was then evaporated to produce a thin film of lipid at the bottomof the test tube. The sample was then placed in a lyophilizer overnight to pump offthe rest of the chloroform. The sample was freeze-thawed by cooling in liquid nitrogenfor half an hour, then heating above T,„, and vortexing. This was done three times andthen approximately 500 iaL of deuterium depleted water was added. The solution wasthen transferred to an NMR tube (10 mm o.d.) and placed in the spectrometer forstudy.Oriented samples were prepared by dissolving 10 mg of lipid for the DPPC or 20Chapter 4. Experimental Procedure^ 16mg for the DMPC in 100 FL or 200 FL of chloroform, respectively. The lipid wasthen spread on approximately 20 glass slides (of dimensions 5 mm x 1.5 mm) and thechloroform was removed by pumping overnight. The samples were then hydrated at50°C in a water saturated vapour environment for 48 hours. The slides were stackedand wrapped with teflon tape to squeeze the slides together. Next, the samples wereplaced inside an NMR tube (10 mm o.d.) and were again placed in the water saturatedvapour for another 24 hours. Approximately 500 FL of PEG-water solution was addedto immerse the slides and the sample was left for 24 hours to allow the water to reachequilibrium between the PEG and the lipids. The samples were sealed and placed inthe NMR probe where the experiments were carried out.The PEG solutions were made by adding PEG to deuterium depleted water atconcentrations varying between 5 wt. % and 80 wt. %. These solutions were heatedslightly to ensure that the PEG was fully and uniformly dissolved. The definition ofweight % was taken as the mass of the PEG over the total mass of the solution (i.e.the mass of the PEG plus the mass of the water) times 100%.4.4 DepakingDePaking was performed using the DePaking procedure [Ster 83] on the spectra ac-quired from the powder sample in order to resolve the individual peaks of the threedeuteron positions.Chapter 5Results5.1 Quadrupolar SplittingThe quadrupolar splitting (Avg ) for each of the a, 3 and -y deuterons was determinedfor the DPPC samples at a variety of PEG concentrations (Figure 5.1). All the DPPCexperiments were carried out at the 0° orientation. The results show that Av g for thea position increases as the bilayer hydration decreases. The opposite is true for the 13deuterons where Avg increases as the amount of water in the bilayer decreases. Forthe 7 deuterons, Avg remains constant as water is removed from the lipids. Whencomparing the results for the 3000 and 8000 molecular weight PEG, there appears tobe very little difference between the quadrupolar splittings. This would tend to indicatethat both polymers are dehydrating the membrane by the same amount.When examining the DMPC samples, the splitting associated with the dePakedpowder spectrum peaks (which is equivalent to the 0° orientation) was also determinedand used as a comparison between a fully hydrated system and a system with differentlevels of dehydration (Table 5.1). These quadrupolar splittings are equivalent toAvg = vg Scr) 2where Sap was defined in chapter 3 as the order parameter and vg is 125 kHz for C-D bonds [Davi 83]. For low PEG concentrations, the quadrupolar splittings betweenthe powder samples and the PEG-treated samples at 0° were approximately the same,indicating that full hydration was present as far as Avg can measure.3 cos 2 0 — 1(5.1)17Chapter 5. Results^ 1810 1 I^I*^*8 — Air--*^*A^A* •..------, *^A * AN 6 — A=........-- A^4 A• A• • •A^c. A<1 4 —•A AA2 —o^A *^A^t o^0^oo I^I 10^20 40^60^80wt. % PEGFigure 5.1: Quadrupolar Splitting for DPPCThe quadrupolar splitting are shown for the deuterons of DPPCfor both the 3000 and 8000 molecular weight PEG. The opensymbols refer to the 8000 mw PEG and the solid symbols to the3000 mw PEG. From top to bottom, the Av g correspond to thea, /3 and -y deuterons. The samples were all placed at the 0°orientation.Chapter 5. Results^ 19Table 5.1: Quadrupolar splittings for DMPCOrientation Deuteron Avg (kHz)dePakedpowder(0°)a/376.3365.3441.2985 wt. % 50 wt. %a 6.379 7.5050° /3 5.383 4.7057 1.256 1.227a 5.975 6.89815° /3 5.008 4.4747 1.184 1.126a 4.315 5.12430° 0 3.622 3.3207 0.847 0.852a 2.511 2.42545° /3 2.078 1.5597 0.505 0.404a 2.006 2.194750 /3 1.689 1.4147 0.419 0.376a 3.132 3.57990° /3 2.612 2.3537 0.621 0.621Chapter 5. Results^ 20Table 5.2: Transition Temperatures for DMPCsample Tm (°C)powder 245 wt. % 2410 wt. % 2450 wt. % 285.2 Transition TemperatureThe transition temperature, T ni , from the gel phase to the liquid crystalline phase forthe bilayer is hydration dependent (Figure 5.2). As the amount of water associated withthe lipid bilayer decreases, the transition temperature rises. The transition temperatureis unaffected by only slight dehydration since T n, remains constant for samples withup to 30 wt. % PEG. At higher PEG concentrations, the transition temperature doesrise as the level of dehydration increases in the membrane. There appears to be littledifference in the effects of 3000 and 8000 molecular weight on transition temperaturewhich again indicates that both polymers seem to affect the membrane in the samemanner. There appears to be a direct relationship between the transition temperatureand the square of the PEG concentration (Figure 5.3).For the DMPC samples, the transition temperature was determined first so thateach sample could be maintained at a consistent number of degrees above T m during thesubsequent experiments. Therefore, the Avg , the T iz relaxation and the T 2q, relaxationexperiments were all done at sixteen degrees above the phase transition temperature.The transition temperature values for DMPC are shown in Table 5.2.Chapter 5. Results^ 21Figure 5.2: Transition Temperature for DPPCThe gel to liquid crystalline transition temperature in DPPC for3000 and 8000 molecular weight PEG is plotted as a function ofwt. % PEG. The open symbols refer to the 3000 mw PEG andthe solid symbols to the 8000 mw PEG.Chapter 5. Results^ 22(wt. % PEG) 2Figure 5.3: Transition Temperature vs (wt. % PEG) 2 for DPPCThe transition temperature for DPPC is plotted as a function of(wt. % PEG) 2 . A linear fit is made with a slope of 0.00178.Chapter 5. Results^ 235Q) 04070601ii^+^I ci20i1020^30I^I^I^I40 50 60 70^80wt.  % PEG1Figure 5.4: Spin-lattice Relaxation Times for DPPCThe Zeeman spin-lattice relaxation times for DPPC are deter-mined as a function of the wt. % PEG. The triangles correspondto the a deuterons, the open circles to the # deuterons and thesolid circles to the y deuterons. The samples were at 0° orienta-tion.5.3 Longitudinal Relaxation TimesThe T 1, relaxation times were studied for both DPPC and DMPC and the T iq relax-ation times were found for DMPC. T iq was measured as well as T 1 ,, for the DMPCcase, in order to obtain a larger number of parameters which would lead to a moreaccurate determination of the motions present in the sample. These relaxation timeswere obtained as detailed in chapter 4.The results for the DPPC samples are shown in Figure 5.4. These results wereagain taken at 0° orientation only. There was a small decrease in the T 13 relaxationtime as the sample was dehydrated (approximately 20%).Chapter 5. Results^ 24For DMPC, the orientation dependence of the T i, and T iq relaxation times, reflect-ing the anisotropy, was determined for each deuterium position. The values indicatethat there is not much anisotropy since relaxation times vary only slightly with orienta-tion (Figure 5.5). At 5 wt. % PEG, the T i, relaxation times for the a and # deuteronswere quite similar with values around 25 ms but the -y deuteron had a longer relaxationtime at about 65 ms. The T iq relaxation times were longer than the T i , values butthe same general orientation dependence was observed. In this case, the T iq relaxationtimes for the a and /3 deuterons were both about 38 ms, while T iq was 105 ms forthe 'y deuteron. For the 50 wt. % sample, the relaxation times were slightly lower forboth T i, and T iq (by about 10%) but again only a slight anisotropy was noticed in theorientation dependence. It should be noted that theory predicts that= —, wor, < 1^ (5.2)which is consistent with the results here taking into account experimental error.The relaxation times of the powder sample were compared to the relaxation times ofthe PEG samples to see whether full hydration was achieved using a sample containingPEG. In order to compare these values, the T i, values for the oriented samples wereaveraged over orientation. A straight averaging was not done since the angles chosen forstudy were not at exact intervals of cos 0. Instead, a sin 0 weighted average was takenby fitting a straight line to the T i, vs sin 0 curve and then averaging points at equalintervals along this line. The results are shown in Table 5.3. Since the relaxation timesat low PEG concentration are similar to the ones from the powder sample, full hydrationis probably achieved for the 5 wt. % PEG sample insofar as can be ascertained by spin-lattice relaxation.Tiz 5Ti q^3Chapter 5. Results^ 25120cn100En0.).,_.E—■80I [ I 1——i,ii;10•---4-)coxco i i * I'75 60C4crE---■-ci 40 _c)0(Ti4 0E—. z •• • • 4 Aa A A A20 I I I I0^20^40^60^80^100angleFigure 5.5: Spin-lattice Relaxation Times for DMPCThe Zeeman and quadrupolar spin-lattice relaxation times forDMPC are plotted as a function of orientational angle 0. The solidsymbols correspond to the Zeeman relaxation times and the opensymbols correspond to the quadrupolar relaxation times. The re-laxation times from the bottom to the top correspond to the a, #and -y deuterons, respectively. The sample is at 5 wt. % PEG.Chapter 5. Results^ 26Table 5.3: Average value of T iz Relaxation Times for DMPCSample Position Average T i , (ms)powderaOP722.3 ± 127.4 ± 463.1 ± 3a 23 + 15 wt. % /3 26 ± 27 63 ± 1a 22.6 ± 210 wt. % fl 25.1 + 2-y 64.6 ± 0.9a 21 + 250 wt. % /3 24 + 27 60 + 25.4 Transverse Relaxation TimeThe orientational dependence of the transverse relaxation time was studied at variousdegrees of bilayer hydration. The relaxation times were again obtained as described insection 4.2.3.For the 5 wt. % sample, the relaxation times for each of the a, /3 and -y deuterons aresimilar in magnitude although the orientation dependence is slightly different (Figure5.6). This is also true of the 50 wt. % sample. The values of 1/T 2 were plotted versusthe angle and then fit to a sum of Legendre polynomials up to order four1— = a c, + a2P2 (cosi9) + a4P4 (cos 9).T2 (5.3)This gave three parameters shown in Table 5.4 for each of the deuteron positions. Thefits of the experimental data to this equation are reasonable as will be shown later inFigure 5.7D.In section 3.3, it was seen that specific types of motions could be represented bythe terms (P 2 (cos 9)) 2 and sine 9 cos2 O. From this theory, it was shown that theseIiChapter 5. Results^ 277.0 I I,....-., 6.0 —3Cil^5.0 —a)0•r■IEl4.0 --0O•,--1-1-1cdkCd 3.0 —7.5r40 iE'' 2.0 —L1.0 I I0^20^40^BOangleFigure 5.6: Longitudinal Relaxation Times for DMPCThe longitudinal relaxation times for DMPC are plotted as a func-tion of orientational angle. The triangles correspond to the adeuterons, the open circles to the /3 deuterons and the solid cir-cles to the -y deuterons. The sample is at 5 wt. % PEG.terms could also be represented by a sum of Legendre polynomials with the coefficientsa0 , a2 and a4 shown in Table 3.1. These coefficients indicate that the experimentaldata can not be fit simply to either (P 2 (cos 9)) 2 or sin e 9 cost 0 since in the case of theexperimental data, a4 is smaller than a2 while the theoretical values give a 4 larger thana2 .Therefore, a linear combination of the two angular dependences and an isotropicterm was fit to the data, i.e.1—,7, = a + b (P2 (cos 0)) 2 + 4c sine 0 cos t 0^(5.4)I 2I I80 100The values for the three parameters are shown in Table 5.5. The choice of 4c for theChapter 5. Results^ 28Table 5.4: Fitting of T2 to a sum of Legendre polynomialsSample Position Parameter Valuea, 0.28 ± 0.02a a2 0.19 ± 0.03a4 0.07 ± 0.04ao 0.24 ± 0.015 wt. % # a2 0.17 ± 0.02a4 0.04 ± 0.02a, 0.24 ± 0.027 a2 0.16 + 0.03a4 -0.04 ± 0.03ao 0.15 + 0.05a a2 0.5 ± 0.1a4 0.8 ± 0.4a, 0.11 + 0.0350 wt. % # a2 0.33 + 0.03a4 0.9 + 0.1ao 0.21 ± 0.037 a2 0.03 + 0.1a4 0.5 ± 0.3last coefficient was to add a normalization factor since (P 2 (cos0)) 2 has a maximumvalue of 1 and sin 2 0 cos 2 0 has a maximum value of 1/4. These values could have alsobeen attained by rewriting equation 5.3 in terms of equation 5.4 and determining thea, b and c parameters.In general, the fit of the previous equation to the data was reasonably close for allthe samples except for the -y deuteron at 50 wt. % which showed an entirely differentsort of orientation dependence (as can be seen from the unusual coefficients in Table5.4 and 5.5). The necessity of using a superposition of all motions is demonstrated inFigure 5.7. The best fit is plot D which includes all three parameters.Chapter 5. Results^ 29Table 5.5: Fitting of T2 to (P2(cos 9)) 2 and sin2 O cos t 0Sample Position Parameter Valuea 0.11 ± 0.05a b 0.45 ± 0.05c 0.15 + 0.05a 0.07 + 0.025 wt. % 11 b 0.38 ± 0.03c 0.17 ± 0.03a 0.08 + 0.047 b 0.27 ± 0.05c 0.20 + 0.04a 0.15 + 0.05a b 0.3 + 0.1c 0.1 + 0.1a 0.10 + 0.0510 wt. % # b 0.3 + 0.1c 0.2 ± 0.1a 0.11 ± 0.047 b 0.20 ± 0.05c 0.15 + 0.05a 0.15 ± 0.05a b 0.5 ± 0.1c 0.2 ± 0.1a 0.11 ± 0.0350 wt. % /3 b 0.33 ± 0.03c 0.22 ± 0.03a 0.21 ± 0.037 b 0.03 ± 0.1c 0.1 ± 0.05.15 I0.0^0.2^0.4^0.6^0.6^I . 0angle (rad)I . 6 1.4 I . 60.6^0.18^I. 0^1. 2angle (rad)0. 0^0.2 ^l2 ^o.•0.6^0.6^1.0angle (rad)•^1.5Chapter 5. Results^ 30.45D4.35 -FI-" 25 -.15 -15 ^0. oO. 0 0.2 0.5^0.8^1.0^1.2angle (rad)1. fiFigure 5.7: Orientation fits for T2 RelaxationThese are fits of2 vs angle for different angular dependences.The actual fits in the plots are; A: a + b P 2 (cos 0); B: a + csin2 0 cos2 0; C: b 11(cos 0) c sin 2 0 cos 2 0; and D: a + b 11(cos 0)c sin2 8 cos 2 0. These plots are fits for the 0 position of the 5wt. % sample.Chapter 5. Results^ 315.5 ErrorsThe relaxation times were all assumed to be single exponentials since the In of theFourier transformed intensities of each peak was very close to a straight line. A Gauss-Newton method of least-squared fitting was used to determine the standard errors inthe fits and these were used as the error in the relaxation times.Chapter 6DiscussionThe quadrupolar splittings of the a, /3 and 7 deuterons show different dependenceson water content (Figure 5.1). The Avg of the a deuterons tends to increase withaddition of PEG whereas Avg for the /3 deuterons decreases. The -y deuterons showno real change in Avg . These results agree with previous findings [Bech 91] on POPC(1-palmitoy1-2-oleoyl-sn-glycero-3-phosphocholine) with the a and p positions deuter-ated. Since the direction of the shift in Avg is different for the a and /3 deuterons, asimple increase or decrease in the disordering of the headgroup can not explain the re-sults. This would cause a shift of Av g in the same direction for all deuteron positions.Instead it is likely that a conformational change takes place in the average orienta-tion of the headgroup. Bechinger and Seelig [Bech 91] suggest that the +N end of thephosphocholine dipole moves towards the interior of the bilayer upon dehydration.The transition temperature increased as the amount of water in the bilayer decreased(Figure 5.2). As water is removed, motions such as rapid lateral diffusion and chaintrans-gauche isomerizations which characterize the liquid crystalline phase are inhibitedand more energy is required to get the same degree of motion as a fully hydrated lipid.Therefore, a higher temperature is needed to provide this energy in the liquid crystallinephase and thus the transition temperature increases. The results are consistent withmany other experiments [Jurg 83,Koda 82]. Using the phase diagram of DPPC at lowwater content [Jurg 83], the actual number of water molecules in my study could beestimated by comparing my transition temperatures with the ones found in that paper.32Chapter 6. Discussion^ 33Table 6.1: Conversion of wt. % PEG to no. of water molecules/lipidwt. % PEG no. H2 O molecules/lipid10 full hydration (>10)20 full hydration (>10)30 7.4 - full (>10)40 6.9 - 9.250 6.6 - 8.760 5.9 - 7.765 5.7 - 7.270 5.3 - 6.975 4.8 - 6.580 4.5 - 6.2The results show that the number of water molecules per lipid ranged from greaterthan 10 (ie. full hydration) for the 10 wt. % sample to between 4.5 and 6 for the 80wt. % sample (Table 6.1). The fact that full hydration is still present at 30 wt. %PEG is due to the insensitivity of NMR in measuring small changes in T n, close tofull hydration. The definition of full hydration is different here than elsewhere sincethe shift in transition temperature is insensitive to changes in the number of watermolecules per lipid greater than 10 (ie. 30 wt. % PEG). This means that as far as canbe measured from changes in the transition temperature, the sample is fully hydratedat 30 wt. % PEG or less.Another group [Cevc 85] did calculations on the change in T,T, as the bilayer de-hydrates and they found that the number of water molecules per lipid was directlyproportional to the temperature shift. In these experiments, it was found that the shiftin Tm was proportional to the square of the wt. % PEG (Figure 5.3). Also, Cevc andMarsh determined that the shift in Tn, is smaller for lipids with longer chain length.Since, my experiments with DMPC only involve samples at full hydration and at 50 wt.% PEG, investigation of the chain length dependence of T m is incomplete. ComparisonChapter 6. Discussion^ 34of only the 5 and 50 wt. % samples for both the DMPC and DPPC do show a similarshift in Tn, equal to 4 K. This results seems reasonable since the difference in chainlength is not great between the two lipids.The longitudinal relaxation rates showed a decrease in T lz by approximately 20%with the addition of a high wt. % PEG. This is surprising since another result ina similar system showed a linear increase in relaxation times upon addition of water[Ulri 90]. Their experiments on DOPC-d 9 (dioleoylphosphatidylcholine, deuterated inthe choline methyl groups) showed a change in T 1, relaxation times from 20 ms at5 water molecules per lipid to 65 ms for fully hydrated bilayers. One reason for thisvariation may be due to the difference in transition temperature between the two lipids.DOPC has a Tm of -20°C and the experiments by Ulrich et al were carried out at 30°C.DPPC has a transition temperature of 43°C and my experiments were done between5°C and 7°C above Tm .Neither T 1, nor T iq show much anisotropy for the different headgroup deuterons.Similar results have been obtained in DPPC [Bloo 91b].For the T2 relaxation times, the orientation dependence was fit to a superpositionof three mechanisms. In equation 5.4, the coefficient b represents fluctuation in thethickness of the bilayer or, equivalently, changes in the area of the lipids. The coefficientc represents undulations of the bilayer which causes a change in the director normalThe a coefficient represents motions which involve only single lipids, e.g. rotation aboutthe long axis of the lipid and motion of the lipid into and out of the bilayer. The fitof Eq. 5.4 to the experimental data gave positive values for each of the coefficients, anecessary condition to be satisfied on physical grounds. From the results of the DMPCoriented samples, it seems impossible to isolate one specific motion which dominates thespectrum. Instead, all three motions seem to contribute to the angular dependence oflongitudinal relaxation. Also, there does not appear to be any systematic suppressionChapter 6. Discussion^ 35or enhancement of one type of motion with membrane dehydration since there is noconsistent change in the a, b and c parameters between the 5 and 50 wt. % samples.It is possible that both of the motions proposed here are coupled and therefore thepresence of one automatically means the presence of another.A problem with this analysis is that P 2 (cos 9) 2 and sin 2 O cos' 0 are not orthogonal.Therefore, the errors associated with the a, b and c coefficients are dependent on oneanother which was not taken into account in the fitting routine. An orthogonal set forthis case is the even Legendre polynomials up to order four. These were fitted to thedata (Table 5.4) but specific motions can not, at this time, be determined from thecoefficients (which was the reason for the use of the other coefficients). The values forthe ao , a2 and a4 coefficients can be used to determine the values of a, b and c. Thecomparison between the calculated and fitted values of a, b and c was very close whichindicates that although the method of analysis may not be perfect, it is a good firststep in understanding lipid motions.Full hydration of the bilayer did seem to be achieved with a sample at 5 wt. % PEGsince its values of T n„ Ay and T i , relaxation times were close to the ones for the powdersample. This is similar to other results using PEG to hydrate the bilayer [Morr 93b]where again a 5 wt. % PEG sample was assumed to be fully hydrated. Unfortunately,even with the comparison of T i , relaxation times from the powder and oriented samples(which appears to be the most sensitive test for dehydration), full hydration can notbe directly measured. The 10 wt. % PEG sample also seemed to be at full hydrationwhen the same experimental parameters were examined. Therefore, even if the 10wt. % PEG sample is not quite fully hydrated (since the most sensitive test can onlymeasure changes in hydration after a certain number of water molecules are removedfrom the bilayer), the 5 wt. % sample which has even more water associated withthe bilayer should be at full hydration. This new method of adding a polymer to theChapter 6. Discussion^ 36surrounding solution seems to allow oriented bilayers to reach full hydration unlike theusual method of using water saturated vapour.Chapter 7ConclusionThe use of a polymer as a dehydrating agent seems to be very effective in controllingthe hydration of a membrane. My results for quadrupolar splitting and transitiontemperature show the same trends as other experiments which use different methodsfor dehydrating the bilayer. Also, it seems likely that full hydration is reached whenonly a small wt. % PEG solution is added to the bilayer.The main purpose of dehydrating the membrane was to look for changes in themotions of the lipids. This was done by measuring relaxation rates. The longitudinalrelaxation rates did not seem to show much change when water was removed from thesystem. The spin-spin relaxation rates also did not show any systematic change withthe addition of more PEG. The orientation dependence of the spin-spin relaxation timeswas used to determine the types of motions present in the bilayer. It was found thatone particular motion did not dominate this angular dependence but instead a sum ofthree motions could be used to fit the data reasonably well. Two of these motions arethickness fluctuations and thermal undulations of the bilayer. The third was a residualnon-isotropic component which was likely to arise from single lipid motion.With the development of this new technique for membrane dehydration, furtherexperiments on the effect of bilayer dehydration can be carried out relatively simply.37Bibliography[Arno 90] Arnold Klaus, Zschoernig Olaf, Barthel Dieter and Herold Wolfram. "Ex-clusion of poly(ethylene glycol) from liposome surfaces". (1990) Biochim.biophys. Acta 1022:303-310.[Bech 91] Bechinger B. and Seelig J. "Conformational changes of the phosphatidyl-choline headgroup due to membrane dehydration. A 2H-NMR study". (1991)Chem. Phys. Lipids 58:1-5.[Bloo 91a] Bloom, Myer and Evans, Evan. "Observation of surface undulations on themesoscopic length scale by NMR". (1991) In Biologically Inspired Physics(ed. L. Peliti), pp. 137-147. New York: Plenum Press. 171.[Bloo 91b] Bloom, M., Morrison, C., Sternin, E. and Thewalt, J. "Spin echoes and thedynamic properties of membranes". (1991) In Erwin Hahn - The Book (ed.D.M.S. Bagguley). London: Oxford University Press. 171.[Bush 80] Bush, S. Fowler, Adams, Ralph G. and Levin, Ira W. "Structural reorga-nization in lipid bilayer systems: effect of hydration and sterol addition onRaman spectra of dipalmitoylphosphatidylcholine multilayers". (1980) Bio-chemistry 19:4429-4436.[Cevc 85] Cevc, Gregor and Marsh, Derek. "Hydration of noncharged lipid bilayermembranes". (1985) Biophysical J. 47:21-31.38Bibliography^ 39[Davi 79] Davis, J.H. "Deuterium magnetic resonance study of the gel and liquid crys-talline phases of dipalmitoylphosphatidylcholine". (1979) Biophys. J. 27:339-358.[Davi 83] Davis, J.H. "The description of membrane lipid conformation, order anddynamics by 2H NMR". (1983) Biochim. biophys. Acta 737:117- 171.[Fine 74] Finer, E. G. and Darke A. "Phospholipid hydration studied by deuteronmagnetic resonance spectroscopy". (1974) Chem. Phys. Lipids 12:1-16.Peen 67] Jeener, J. and Broekaert, P. "Nuclear magnetic resonance in solids: thermo-dynamic effects of a pair of rf pulses". (1967) Phys. Rev. 157:232-240.[Jurg 83] Jiirgens E., HOhne G. and Sackmann E. "Calorimetric study of the dipalmi-toylphosphatidylcholine / water phase diagram". (1983) Ber. Bunsenges.Phys. Chem. 87:95-104.[Koda 82] Kodama, Michiko, Kuwabara, Mika and Seki, SylizO. "Successive phase-transition phenomena and phase diagram of the phosphatidylcholine-watersystem as revealed by differential scanning calorimetry". (1982) Biochim.biophys. Acta 689:567- 570.[LeNe 77] LeNeveu D. M., Rand R. P., Parsegian V. A. and Gingell D. "Measurementand modification of forces between lecithin bilayers". (1977) Biophysical J.18:209-229.[MacD 85] MacDonald Ruby I. "Membrane fusion due to dehydration by polyethyleneglycol, dextran, or sucrose". (1985) Biochemistry 24:4058-4066.[Morr 93a] Morrison, Clare and Bloom, Myer. "General orientation dependence ofNMR spin-lattice relaxation for spin-1". (1993) J. magn. Res. In press.Bibliography^ 40[Morr 93b] Morrison, Clare. "Polyethylene glycol as a hydration agent in oriented mem-brane bilayer samples". (1993) Biophys. J. In press.[Pfei 89] Pfeiffer, W., Henkel, Th., Sackmann, E., Knoll, W. and Richter, D. "Lo-cal dynamics of lipid bilayers studied by incoherent quasi-elastic neutronscattering". (1989) Europhys. Lett. 8:201-206.[Rand 89] Rand, R. P. and Parsegian, V. A. "Hydration forces between phospholipidbilayers". (1989) Biochim. biophys. Acta 988:351-376.[Ster 83] Sternin, E., Bloom, M. and MacKay, A. L. "De-pake-ing of NMR spectra".(1983) J. magn. Res. 55:274-282.[Ster 85] Sternin, E. "Data aquisition and processing: a systems approach". (1985)Rev. Sci. Instrum. 56:2043-2049.[Ulri 90] Ulrich A.S., Volke F. and Watts A. "The dependance of phospholipid head-group mobility on hydration as studied by deuterium-NMR spin-lattice re-laxation time measurements". (1990) Chem. Phys. Lipids 55:61-66.

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