<%BANNER%>

Development and Application of High-Field, High-Gradient Pulsed Field Gradient NMR for Studies of Diffusion Behavior of ...

Permanent Link: http://ufdc.ufl.edu/UFE0041203/00001

Material Information

Title: Development and Application of High-Field, High-Gradient Pulsed Field Gradient NMR for Studies of Diffusion Behavior of Lipids in Model Membranes
Physical Description: 1 online resource (112 p.)
Language: english
Creator: Sanders, Monica
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: diffusion, exchange, lipid, membrane, permeability, pfg, raft
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This work presents the development and application of a high-field, high-gradient pulsed field gradient nuclear magnetic resonance technique for studies of lipid lateral diffusion in planar-supported lipid bilayers composed of ternary mixtures of lipids intended to mimic the composition of eukaryotic cell membranes. Lipid rafts are small functional domains that exist in cell membranes. It is widely accepted that rafts participate in many cellular activities such as signal transduction. Lipid rafts in non-activated cells are believed to be smaller than around 200 nm in size and quite unstable. Liquid-ordered domains in model membranes share similar characteristics to lipid rafts. In these studies, domains as large as 10 ?m have been observed under certain conditions. However, recent data indicates that much smaller domains can also form and remain stable in these model membranes under certain conditions. In order to accurately characterize lateral transport of lipids in domain-forming model membranes and possibly extract information relevant to the study of lipid rafts, an experimental technique is required which has sufficient spatial resolution and does not disturb the membrane or any liquid-ordered domains which might exist. Pulsed field gradient nuclear magnetic resonance (PFG NMR) allows for the direct observation of molecular mean square displacements and their related diffusion coefficients in a manner which does not perturb the membrane since additives, such as fluorescently-labeled lipids, are unnecessary. In this work, the use of a high magnetic field strength (17.6 T) coupled with high magnetic field gradient strength of up to 30 T/m affords the use of smaller diffusion times under the conditions of the narrow-pulse approximation which allows for distortion-free monitoring of time-dependent and displacement-dependent diffusion behavior of lipids with superior signal-to-noise. Diffusion measurements conducted on membranes consisting of a mixture of DOPC, SM, and Chol show diffusion behavior which was independent of diffusion time, consistent with the presence of large liquid-ordered domains. Formation of smaller domains was observed in membranes consisting of DOPC, DPPC, and Chol near the miscibility transition temperature which manifests as time-dependent diffusion behavior of lipids. It was verified that this behavior was a consequence of lipid exchange between liquid-ordered domains and the surrounding liquid-disordered environment rather than an NMR relaxation effect. Dynamic Monte Carlo simulations were used in conjunction with time-dependent diffusion results to extract information about domain size and the permeability of the domain boundary. This is the first observation of time-dependent diffusion and estimation of such properties for lipid membranes of any composition.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Monica Sanders.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Vasenkov, Sergey.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041203:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041203/00001

Material Information

Title: Development and Application of High-Field, High-Gradient Pulsed Field Gradient NMR for Studies of Diffusion Behavior of Lipids in Model Membranes
Physical Description: 1 online resource (112 p.)
Language: english
Creator: Sanders, Monica
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: diffusion, exchange, lipid, membrane, permeability, pfg, raft
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This work presents the development and application of a high-field, high-gradient pulsed field gradient nuclear magnetic resonance technique for studies of lipid lateral diffusion in planar-supported lipid bilayers composed of ternary mixtures of lipids intended to mimic the composition of eukaryotic cell membranes. Lipid rafts are small functional domains that exist in cell membranes. It is widely accepted that rafts participate in many cellular activities such as signal transduction. Lipid rafts in non-activated cells are believed to be smaller than around 200 nm in size and quite unstable. Liquid-ordered domains in model membranes share similar characteristics to lipid rafts. In these studies, domains as large as 10 ?m have been observed under certain conditions. However, recent data indicates that much smaller domains can also form and remain stable in these model membranes under certain conditions. In order to accurately characterize lateral transport of lipids in domain-forming model membranes and possibly extract information relevant to the study of lipid rafts, an experimental technique is required which has sufficient spatial resolution and does not disturb the membrane or any liquid-ordered domains which might exist. Pulsed field gradient nuclear magnetic resonance (PFG NMR) allows for the direct observation of molecular mean square displacements and their related diffusion coefficients in a manner which does not perturb the membrane since additives, such as fluorescently-labeled lipids, are unnecessary. In this work, the use of a high magnetic field strength (17.6 T) coupled with high magnetic field gradient strength of up to 30 T/m affords the use of smaller diffusion times under the conditions of the narrow-pulse approximation which allows for distortion-free monitoring of time-dependent and displacement-dependent diffusion behavior of lipids with superior signal-to-noise. Diffusion measurements conducted on membranes consisting of a mixture of DOPC, SM, and Chol show diffusion behavior which was independent of diffusion time, consistent with the presence of large liquid-ordered domains. Formation of smaller domains was observed in membranes consisting of DOPC, DPPC, and Chol near the miscibility transition temperature which manifests as time-dependent diffusion behavior of lipids. It was verified that this behavior was a consequence of lipid exchange between liquid-ordered domains and the surrounding liquid-disordered environment rather than an NMR relaxation effect. Dynamic Monte Carlo simulations were used in conjunction with time-dependent diffusion results to extract information about domain size and the permeability of the domain boundary. This is the first observation of time-dependent diffusion and estimation of such properties for lipid membranes of any composition.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Monica Sanders.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Vasenkov, Sergey.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041203:00001


This item has the following downloads:


Full Text

PAGE 1

1 DEVELOPMENT AND APPLICATION OF HIGH FIELD, HIGH GRADIENT PULSED FIELD GRADIENT NMR FOR STUDIES OF DIFFUSION BEHAVIOR OF LIPIDS IN MODEL MEMBRANES By MONICA DANIELLE SANDERS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

PAGE 2

2 2009 Monica D. Sanders

PAGE 3

3 To my mother, who has relentlessly encouraged me throughout my life and has taught me the importance of hard wor k, education and independence

PAGE 4

4 ACKNOWLEDGMENTS I thank my committee chair, Dr. Sergey Vasenkov, for his constant guidance and support throughout my work, my lab partner, Amrish Menjoge, for his advice and friendship, the sta ff of the Advanced Magnetic Resonance Imaging and Spectroscopy facility, especially Dr. Dan Plant, for numerous discussions and technical support, and my collaborators which include Konstantin Ulrich for developmental studies, and Robert Mueller and Amrish Menjoge, for Monte Carlo simulation work.

PAGE 5

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 10 ABSTRACT ................................ ................................ ................................ ................... 14 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 16 Lipid Raft Model: Motivation for this Work ................................ .............................. 16 A Brief History of the Lipid Raft Hypothesis ................................ ...................... 16 Detection in Model Membranes ................................ ................................ ........ 18 Sizes of Model Rafts vs. Lipid Rafts in vivo ................................ ...................... 20 Studies of Lateral Diffusion in Biologically Relevant Systems .......................... 22 Description of Project ................................ ................................ ....................... 28 Description of the Pulsed Field Gradient NMR Method ................................ .......... 30 A Brief Overview of Nuclear Magnetic Resonance ................................ ........... 30 Pulsed Field Gradient NMR: Theory ................................ ............................... 36 Pulsed Field Gradient NMR: Application for Studies of Lipid Bilayers ............. 42 2 DEVELOPMENT OF DIFFUSION MEASUREMENTS IN LIPID BILAYERS USING HIGH FIELD, HIGH GRAIDENT PFG NMR ................................ ............... 46 Development Associated with Planar Supported Lipid Bilayer Samples ................ 46 Preparation of Planar Supported Multibilayer Stacks ................................ ....... 48 Orientation of Planar Supported Multibilayer Stacks at the Magic Angle ......... 52 Development Associated with PFG NMR Diffusion Experiments ............................ 54 Calibration Experiments ................................ ................................ ................... 55 Addressing Limitations Concerning Gradient Pulses ................................ ........ 59 Gradient pulse shape and delay for gradient recovery ............................... 60 Preemphasis adjustment and B 0 compensation ................................ ......... 62 Verification of Macrosc opic and Microscopic Orientation of Multibilayer Stacks ................................ ................................ ................................ ........... 63 Magnetic Susceptibility ................................ ................................ ..................... 67 3 DIFFUSION AND LIPID EXCHANGE INSIDE AND BETW EEN LIPID MEMBRANE DOMAINS ................................ ................................ ......................... 71 Studies of Lipid Bilayers with Large Liquid Ordered Domains ................................ 7 1

PAGE 6

6 Observation of Lipid Exchange Between D omains and Their Surroundings in Lipid Bilayers with Small Liquid Ordered Domains for Exchange Studies ........... 77 Diffusion Results ................................ ................................ .............................. 82 Time Dependent Diffusion Behavior ................................ ................................ 86 Relaxation Effects ................................ ................................ ............................ 88 Extracting Quantitative Information from the Lipid Exchange Data .................. 92 Dynamic Monte Carlo Simulations ................................ ................................ ... 95 4 SIGNIFICANCE AND FUTURE DIRECTIONS ................................ ..................... 102 LIST OF REFERENCES ................................ ................................ ............................. 105 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 112

PAGE 7

7 LIST OF TABLES Table page 3 1 Results from fi tting of the PFG NMR attenuation curves of DOPC/DPPC/Chol at different temperatures as seen in Figure 3 5 by Eq. 18. ................................ 85 3 2 The characteristic domain sizes as calculated by the fit of data in Fi gure 3 8 by Equation 19. ................................ ................................ ................................ ... 95 3 3 Domain Properties at Temperatures Near T m ................................ ..................... 99

PAGE 8

8 LIST OF FIGURES Figure page 1 1 Schematic of a lipid bilayer as described by the Fluid Mosaic Model. ................ 17 1 2 Schematic of a lipid bilayer as defined by the lipid raft hypothesis showing the existence of hi ghly ordered domains enriched in certain lipids and cholesterol. ................................ ................................ ................................ ......... 19 1 3 Schematic depicting two types of diffusion ................................ ......................... 24 1 4 Schematic representations of magnetization. ................................ ..................... 32 1 5 Illustration of the time domain free induction decay (FID) signal and the frequency domain NMR line after Fourier transformation (F.T.). ........................ 34 1 6 The PFG NMR spin echo sequence. ................................ ................................ .. 36 1 7 The PFG NMR stimulated echo sequence. ................................ ........................ 40 1 8 The PFG NMR stimulated echo longitudinal encode decode sequence. ............ 41 1 9 The PFG NMR thirteen interval pulse sequence ................................ ................ 42 1 10 Co mparison between the directions of measured and lateral diffusion ............... 44 2 1 Illustration of a PFG NMR sample consisting of many planar supported multibilayer stacks ................................ ................................ .............................. 49 2 2 Schematic of the magic angle insert. ................................ ................................ .. 54 2 3 Examples of PFG NMR attenuation plots for water and glycerin. ....................... 58 2 4 Proton decoupled 31 P NMR spectra of DOPC/SM/CHOL multibilayer stacks to study the orientation of lipids in the bilayers ................................ ................... 64 2 5 1 H NMR spectra of DOPC/SM/Chol multibilayer stack s to study the macroscopic orientation of the stack using the magic angle insert.. ................... 66 2 6 Examples of attenuation curves at different applied magnetic field strength to check for magnetic suscep tibility. ................................ ................................ ....... 69 3 1 1 H NMR spectra of DOPC/SM/Chol multibilayer stacks measured by the PFG NMR stimulated echo sequence at 750 MHz for different values of the gradient amplitude ( g ) at T = 303.2 K. ................................ ................................ 72 3 2 PFG NMR attenuation curves for DOPC/SM/Chol samples obtained at three diffusion times at low and high temperature at 750 MHz.. ................................ .. 74

PAGE 9

9 3 3 Lateral diffusivities of lipids in DOPC/SM/Chol multibilayer stacks plotted as a function of inverse temperature. ................................ ................................ ......... 76 3 4 1 H NMR spectra of DOPC/DPPC/Chol multibilayer stacks measured b y the PFG NMR stimulated echo sequence for different values of the gradient amplitude ( g ) at T = 307.8 K and T = 296.3 K at 750 MHz ................................ 79 3 5 Examples of diffusion attenuation curves obtained for D OPC/DPPC/Chol by the PFG NMR stimulated echo sequence at T = 307.8 K, T = 301.3 K, T = 300.7 K, T = 298.8 K, and T = 296.3 K at 750 MHz. ................................ ........... 83 3 6 Comparison of diffusion behavior at different effe ctive diffusion times for experiments conducted on DOPC/DPPC/Chol at T = 307.8 K, T = 301.6, T = 300.7, T = 298.9 K, and T = 296.3 K ................................ ................................ .. 87 3 7 T 1 NMR relaxation curves for DOPC/DPPC/Chol bilayers o btained using the PFG NMR STE sequence with g < 1 T/m for the range of relevant temperatures. ................................ ................................ ................................ ..... 89 3 8 The ratio of the time dependent effective diffusion coefficient of lipids in liquid ordered d omains relative to completely unrestricted diffusion in those domains as a function of ................................ ................................ 93 3 9 Two dimensional simulation model for lipid bilayer. ................................ ............ 97 3 10 Examples of fitting experimental data (points) by the results of dynamic Monte Carlo (MC) simulations (lines). ................................ .............................. 100

PAGE 10

10 LIST OF ABBREVIATION S AFM Atomic Force Microscopy CHOL Chole sterol DOPC 1,2 dioleoyl sn glycero 3 phosphocholine DPPC 1,2 dipalmitoyl sn glycero 3 phosphocholine ESR Electron Spin Resonance FCS Fluorescence Correlation Spectroscopy FID Free Induction Decay FRAP Fluorescence Recover After Photobleaching FRET Fluor escence Resonance Energy Transfer MAS NMR Magic Angle Spinning Nuclear Magnetic Resonance MSD Mean Square Displacement NMR Nuclear Magnetic Resonance PC Phosphocholine PFG NMR Pulsed Field Gradient Nuclear Magnetic Resonance PGSE PFG NMR Spin Echo Pulse Se quence STE PFG NMR Stimulated Echo Pulse Sequence STE LED PFG NMR Stimulated Echo Longitudinal Encode Decode Pulse Sequence SM Sphingomyelin SMT Single Molecule Tracking SPT Single Particle Tracking A(g) Signal measured as a function of magnetic field grad ient amplitude B e The amplitude of the field induced by currents from electrons in orbital clouds B ext The amplitude of the applied magnetic field from gradients

PAGE 11

11 B 0 The amplitude of the applied static magnetic field in NMR B 1 The amplitude of the applied f ield from a radiofrequency pulse in NMR c Concentration D Diffusion coefficient D H2O Measured diffusion coefficient of water D lit Known value of diffusion coefficient of water at room temperature D m Measured diffusion coefficient D o Diffusion coefficient f or lipids in liquid ordered domains Unrestricted diffusion inside liquid ordered domains E a Energy of activation g Magnetic field gradient amplitude g H2O Uncalibrated amplitude of gradient g act Actual amplitude of gradient applied fo r H 2 O calibration J Flux l Length of elementary diffusion step l d Liquid disordered l o Liquid ordered L Dimension of simulation lattice L o Dimension of simulation domain m Individual spin magnetization M z Magnetization vector along z axis M xy Transverse m agnetization (magnetization in xy plane) p bld Probability of an elementary diffusion through the domain boundary leading into the liquid ordered phase

PAGE 12

12 p blo Probability of an elementary diffusion through the domain boundary leading into the liquid disorder ed phase p ld Probability of an elementary diffusion step inside the liquid disordered phase in the x or y direction p lo Probability of an elementary diffusion step inside the liquid ordered domain in the x or y direction P Probability density r Position of molecule in space R Gas constant R lo Radius of liquid ordered domains t Time t eff Effective diffusion time T Temperature T m Miscibility transition temperature T 1 Spin lattice NMR relaxation Longitudinal NMR relaxation T 2 Spin spin NMR relaxation Tr ansverse NMR relaxation z Position of a nuclei along the z axis Domain boundary permeability The angle between the direction of the measured diffusivity and the direction of the lateral diffusion of lipids in t he bilayer The gyromagnetic ratio The relative number of molecules that started their trajectories inside l o domains and were outside the domains at time, t Duration of gradient pulse Chemical shift Angle between lipid dipole moments and direction of B 0 field

PAGE 13

13 Duration between and rf pulses in PFG NMR spin echo sequence Duration between first and second rf pulses in PFG NMR stimulated echo sequence Duration between second and third rf pulses in PFG NMR stimulated echo sequence Duration of radiofrequency pulse Magnetization phase Measured frequency Reference frequency Operation frequency of magnet Larmor frequency Tip angle Signal attenuation

PAGE 14

14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DEVELOPMEMT AND APPLICATION OF HIGH FIELD, HIGH GRADIENT PFG NMR STUDIES OF LIPID SELF DIFFUSION IN PLANAR SUPPRTED LIPID BILAYERS By Monica Danielle Sanders December 2009 Chair: Sergey Vasenkov Major: Chemical Engineering This work pres ents the development and application of a high field, high gradient pulsed field gradient nuclear magnetic resonance technique for studies of lipid lateral diffusion in planar supported lipid bilayers composed of ternary mixtures of lipids intended to mimi c the composition of eukaryotic cell membranes. Lipid rafts are small functional domains that exist in cell membranes. It is widely accepted that rafts participate in many cellular activities such as signal transduction. Lipid rafts in non activated cel ls are believed to be smaller than around 200 nm in size and quite unstable. Liquid ordered domains in model membranes share similar characteristics to lipid rafts. In these studies, domains as large as 10 m have been observed under certain conditions However, recent data indicates that much smaller domains can also form and remain stable in these model membranes under certain conditions. In order to accurately characterize lateral transport of lipids in domain forming model membranes and possibly extract information relevant to the study of lipid rafts, an experimental technique is required which has sufficient spatial resolution and does not disturb the membrane or any liquid ordered domains which might exist Pulsed field gradient nuclear magnetic resonance (PFG NMR) allows for the direct observation of molecular

PAGE 15

15 mean square displacements and the ir related diffusion coefficient s in a manner which does not perturb the membrane since additives such as f luorescently labeled lipids are unnecessary In this work, the use of a high magnetic field strength (17.6 T) coupled with high magnetic field gradient st rength of up to 30 T/m affords the use of smaller diffusion times under the conditions of the narrow pulse approximation which allows for distortion free monitoring of time dependent and displacement dependent diffusion behavior of lipids with superior signal to noise. Diffusion measurements conducted on membranes consisting of a mixture of DOPC, SM, an d Chol show diffusion behavior which was independent of diffusion time consistent with the presence of large liquid ordered domains. Formation of smaller domains was observed in membranes consisting of DOPC, DPPC, and Chol near the miscibility transition temperature which manifests as time dependent diffusion behavior of lipids. It was verified that this behavior was a consequence of lipid exchange between liquid ordered domains and the surrounding liquid disordered environment rather than an NMR relaxat ion effect Dynamic Monte Carlo simulations were used in conjunction with time dependent diffusion results to extract information about domain size and the permeability of the domain boundary. This is the first observation of time dependent diffusion and estimation of such properties for lipid membranes of any composition

PAGE 16

16 CHAPTER 1 INTRODUCTION Lipid Raft Model: Motivation for this Work A Brief History of the Lipid Raft Hypothesis Biological membranes of eukaryotic cells are complex systems which cannot be described as structurally homogeneous over a broad range of lengths scales ranging from nanometers to microns. Understanding the structural heterogeneity is crucial to attaining a more fundamental understanding of the role of membrane comp osition and organization in many important cellular events Lateral organization of biological membranes has been attracting an increasing amount of attention in the scientific 1 This model, developed by Sin ger and Nicolson, describes the lipid bilayer of the cell membrane as a neutral two dimensional solvent that serve s as an effective barrier for molecular exchange but does not influence membrane protein function. 2 Singer and work explains the connection between free energy requirements and lipid protein orientation by showing how membrane molecules orient themselves into bilayers so that hydrophobic and hydrophilic interactions are maximized in order to minimize the free energ y state of the system. 1 The flu id mosaic model suggests a random distribution of proteins and lipids in the membrane. (See Figure 1 1) Shortly after this 3 From then on, the focus on the organization of the lipid components in membranes grew. Over the past decade, our understanding of lipid membrane organization has b een further enhanced by the proposal of the lipid raft hypothesis. 4 This hypothesis postulates the existence of small, functional domains in

PAGE 17

17 Figure 1 1. Schematic of a lipid bilayer as described by the Fluid Mosaic Model. 1 Colored molecules are intended to represent the random distribution of differe nt types of lipids as originally postulated in this model. Grey molecules represent the proteins associated with the membrane which were also believed to be randomly distributed in the bilayer. membranes of eukaryotic cell with unique lipid and protein compositions. This paradigm arose from studies of polarized epithelial cells which examined the selective delivery of lipids to the apical and basolateral surfaces of these cells. 5 Early studies concluded that the two leaflets of the cell membrane are different in terms of composition and this difference originates in the Golgi complex where lipids are sorted and clustered before delivery to their destination. They also proposed that membrane proteins are included in these clusters and are transported together with the lipids via transpor t vesic l e s. 5 The lipid raft hypoth esis postulates that on the surface of cell membranes, particular clusters organize into domains know as lipid rafts. It has been suggested that lipid rafts serve as platforms that play a role in many cellular functions such as signal transduction. 2 It is also widely hypothesized that lipid rafts play a role in the survival of cancer cells and the ability of viruses to penetrate cell membranes. 6 11 Changes in

PAGE 18

18 membrane composition leading to modi fications of the raft properties have been explored as an attractive new strategy to fight lipid raft related cancer and viral diseases. 12 The s uccess of this approach would be en hanced by detailed knowledge of the structural and dynamic properties of lipid rafts. Detection in Model Membranes Studies preformed for the purpose of characterizing the organization and dynamic properties of lipids in biological membranes are conducted b oth in vivo and using synthesized model membranes. In vivo studies are complicated by the sheer complexity of the cell membrane. Studies using model membranes can provide a fundamental understanding of intrinsic cell membrane properties by observing char acteristic structure, dynamics and organization in less complex, multi component lipid bilayers. The lipid raft hypothesis suggests a close link 13,14 between lipid rafts and the liqui d ordered ( l o ) phase 15 which can be easily observed in cholesterol and sphingolipid rich model membranes. 13,16 19 (see Figure 1 2) For these model membranes, the l o phase is observed at temperatures above a melting point transition temperature, viz. the temperature at which there is a change in the physical state of the lipids from a gel to liquid crystalline fluid phase. Liquid crystalline phases are differen tiated into two states (or phases): liquid disordered and liquid ordered. The liquid disordered ( l d ) phase is characterized as having an abundance of lipids with the hydrocarbon chains that are mobile and head groups that are hydrated. The bilayer in the l d state is thinner and less dense when compared to that in the gel state 20 and order parameters for the fatty acid chains are typically > 0.25. Liquid ordered phases have a higher lipid density resulting in a stiffening of the hydrocarbon chains 21 as characterized by a thicker membrane and significantly higher order parameter. The l o phase is rich in

PAGE 19

19 Figure 1 2. Schematic of a lipid bilayer as defined by the lipid r aft hypothesis 4 show ing the existence of highly ordered domains enriched in certain lipids and cholesterol. The domains in this figure represent lipid rafts in the cell membrane and/or liquid ordered domains in model membranes. The domains are hypothesized to play key roles any many cellular activities. sphingolipids and cholesterol in comparison to the l d phase. For sterol free membranes, experimental data indicate that only the l d and gel phases can coexist. Addition of cholesterol can lead to the formation of domains, w hich exhibit a distinct l o phase. 15 Since lipid mixtures consisting of unsaturated and saturated phospholipids, sphingolipids and cholesterol can spontaneously form bilayers with clear domain separation u nder suitable conditions, they have been considered to be suitable model membranes to characterize the lipid organization and properties in cell membranes. 22,23 The development of these mod el membranes will be discussed further in Chapter 2. The observation of coexisting l o and l d liquid crystalline phases in synthetic lipid mixtures has triggered a number of very detailed investigations regarding the properties of liquid ordered domains i n model membranes by various experimental techniques.

PAGE 20

20 Many initial studies focused on detecting inhomogeneous lipid distribution, characterizing phase transitions and determining compositional effects in lipid mixtures. The most well known techniques su itable for such studies are fluorescence microscopy based techniques such as fluorescence quenching and fluorescence resonance energy transfer (FRET). 17,24 27 Fluorescence based techniques rely on the excitation o f a fluorescently tagged lipid to show the position and/or the distribution of membrane species of interest. These techniques have been used to investigate the role of cholesterol and other sterols in domain formation, to detect inhomogeneities in ternary mixtures of cholesterol, sphingolipid, and phosphocholine (PC), to generate phase diagrams for common ternary mixtures at physiologically relevant temperatures, 28 31 and to determine partition coefficients of fluor escent probes in l o and l d phases. 32,33 Other useful technique s include atomic force microscopy (AFM) 34 37 differential scanning calorimetry 38 40 and various nuclear magnetic resonance (NMR) a nd electron spin resonance (ESR) techniques. 41 46 Many of the studies detecting domains in model membranes indicate that these domains are very large (> 1 micron) and very stable. 47 Sizes of Model Rafts vs. Lipid Rafts in vivo There have been some questions raised about the discrepancy between the size of domains traditionally observed in model membranes and lipid rafts in cell me mbranes. Initially, lipid rafts were observed and characterized by detergent extraction of intact cell Lipids rafts are resistant to solubilization in non ionic detergents such as Triton X 100 at low temperatures (4C). Detergent extraction studies sho wed that certain proteins could partition into these domains as well. Lipid rafts were initially believed to be as large as 500 nm and stable based on detergent extraction experiments 48 In contrast more recent experimental evidence suggests that in many

PAGE 21

21 cases only very small ( < 200 nm), highly dynamic, and possibly unstable rafts can form in non activated cel ls. 3,49 52 Some researchers have expressed doubts about even the existence of lipid rafts as functional entities. 53 55 At the s ame time, experimental evidence which suppo rts the existence of such domains in vivo keeps accumulating. 56 63 It is also believed that small rafts can agglomerate and form larger platforms due to interactions between raft constituents (proteins and lipids) 20,52,64 67 With recent evidence that lipid raft sizes are smaller than l o domains in model membranes increasing, concerns as to the accuracy of representation by model membranes have been expressed. These conce rns do not directly refute the existence of lipid rafts in cells, but rather impress the importance of using caution when extending the results obtained with model membranes to lipid rafts in vivo Recent studies have observed l o domains on the order of 1 00 nm in model membranes using FRET, 24,25 AFM, 34,36,68 and solid state NMR. 43,45,46 These domains are consistently observed at physiological temperatures even when the same membrane system appear s to be homogeneous by other methods. 26 The size of the domain s observed has been demonstrated to vary as both a function of temperature and composition. 43,69 As the temperature of the raft containing bilayer is increas ed to approach the miscibility transition temperature of the lipid mixture T m large micron sized domains are replaced by smaller domains. Critical fluctuations on the length scale of <50 nanometers are expected when the system is very near T m 69 These fluctuati ons represent the formation and collapse of complexes consisting for the most part of a small number of cholesterol molecules and saturated lipids. 70 It has been suggested that critical fluctuations can be viewed as the onset of domain formation, 71 which is due to the affinity of chol esterol for and dynamic

PAGE 22

22 relationship with saturated lipids. 72 74 While, the study of raft like domains in model membranes and their relationship to the formation and function of lipid rafts in cell membranes is ongoing, i t is quite clear that exchange of lipids between rafts and their surroundings plays a key role in raft formation. With the focus shifting to much smaller length scales and the role of critical fluctuations in domain formation, it is necessary to employ experimental techniques appropriate for the detection of diffusion dynamics on submicrom eter length scales. First, many fluorescence based techniques which require attaching labels to lipid molecules, may be inappropriate for studies of structure and dynamics. It has been reported that fluorescent labels can affect the physical properties of small biomolecules, such as lipids, in membranes. 75 M icroscopy based techniques are limited b y the optical diffraction limit with t he smallest observ able length scale for these techniques is often much larger than the predicted size of domains. Methods such as single particle (molecule) tracking as well as improved fluorescence correlation spectroscopy (FCS) methods which allow the resolution to go be yond the optical diffraction limit provide better spatial resolution 34,36,76,77 but are still limited by the requirement of labels. To understand organization in these complex, sensitive system s i t is imperative to utilize an experimental technique with sufficient spatial resolution which will not perturb the membrane organization. NMR spectroscopy offer s an attractive alternative to techniques which require labels and underpins the studies in this work Studies of Lateral Diffusion in Biologically Relevant Systems The dynamics of lipids in biological and model membranes can be significantly affected by the presence of domains. Studies of lipid dynamics can give useful information about domain formation and stru cture as well as about the domain stability

PAGE 23

23 Of particular interest to this work, studies of lipid dynamics in domain forming membranes can give important information about molecular exchange between domains and their surroundings. Characterizing this li pid exchange can lead to a better understanding of lipid lateral dynamics and the structural properties of lipid rafts in cell membrane. Lateral diffusion is expected to play an important role in many membrane processes. In particular, the rate of reacti on between ligands (signaling molecules) and receptors might be controlled by lateral diffusion since these intermolecular events are often diffusion limited. The following section discusses the theoretical treatment of diffusion in lipid membrane focusin g on the fundamental of lateral self diffusion in detail. The fluid like properties of lipid bilayers are consequences of lipid mobility within the bilayer. Mobility in this case can be characterized by the two main modes of motion : changes in configu ration via vibrational and rotational motions of molecules within the bilayer, and translational motion which describes the lateral mobility of molecules 47 It is also p ossible for lipid molecules to exchange between the two leaflets of the bilayers ( lipid flip flop). This movement, however, is very infrequent having a much longer timescale than studies in this work These types of motions can be observed via longer time scale techniques to study the interaction and relationship between the two leaflets of the bilayer. However, the particular interest of this work is the manner in which lateral organization of lipids in biological membranes affects translational dynamics ( i.e. diffusion). Diffusion results from the process of stochastic thermal motion of the molecules and can be described by two basic modes : transport diffusion and self diffusion. (see Figure 1 3) Transport diffusion involves the movement of molecule s in order to reduce

PAGE 24

24 macroscopic concentration gradients (or gradients of chemical potential) while self diffusion occurs in the absence of macroscopic concentration (or chemical potential) gradients. The transport diffusion coefficient describes the rela tionship between the flux of molecules and a concentration or chemical potential gradient under non equilibrium conditions. In self diffusion, molecular transport is characterized by the random translational motion of molecules driven by thermal energy. Self diffusion occurs in liquid like systems such as lipid bilayers in t he absence of a macroscopic gradient of chemical potential. Self diffusion can be described and treated similarly to transport diffusion if one considers an uneven Figure 1 3. Sch ematic depicting two types of diffusion. A) transport diffusion under circumstances of a concentration gradient and B) self diffusion in the absence of a macroscopic concentration gradient. distribution of labeled and unlabeled molecules under conditions when overall molecular concentration remains the same at each point of the considered volume. Many experimental techniques suitable for studies of self diffusion involve the observation of

PAGE 25

25 labeled molecules in a sea of unlabeled but otherwise identical mo lecules. In these cases, the self a concentration gradient of labeled molecules. The diffusive flux of labeled molecules is (1) where D is the self diffusion coefficient, r is the position in space, t is the time and is the concentration of (labeled) molecules moving in one two or three dimension al space. By applying the principle of conservation of mass, the change in concentration with time at a certain position in space can be described as (2) (3) Thermal stochastic motion of molecules will cause the concentration gradient to approach the zero value with increasing diffusion time. The self diffusion ( D ) in Eq. 3 can be placed before the first gradient operator because this diffusivity is expected to be independent of position (since overall molecular concentration remains the same for all positions) Eq. 3 can be solved by replacing the spatially dependent concentration term with a term describing the probability that a molecule will diffuse from its initial position to the position after time t The solution gives a Gaussian distribution that is also known as dif fusion propagator.

PAGE 26

26 (4) where is the probability that a molecule with an initial position, r 0 will migrate to a final position, r after time t. This probability function is a function of the displacement ( r r 0 ) rather than the initial position. The Einstein relation can be easily derived from the diffusion propagator (Eq. 4). For two dimensional self diffusion in a plane such as the surface of the membrane bilayer this rel ation can be written as (5) where < r 2 > is the mean square displacement (MSD). 78 In a homogeneous sys tem where molecules diffuse in an unrestricted manner, the description above serves to give the true diffusion coefficient that describes the translational dynamics of the system. In this case, the diffusion coefficient is independent of the time that mol ecules are given to diffuse (observation time) and so the mean square displacement of molecules scales linearly with time. 79 Heterogeneous systems incorporate a complication related to the possibility of restriction of free diffusion due to the presences of obstacle s. For the case of lipid bilayers, this corresponds to a situation where domains are present in the bilayer. In cases of restricted or partially restricted diffusion inside of domains it is expected that the propagator will deviate from the Gaussian func tion. The effective diffusion coefficient as defined by Eq. 5 then becomes dependent on the observation time and the MSD no longer scales linearly with time. At sufficiently short observations times ( i.e. corresponding to displacements much smaller than the size of the domain), the diffusion coefficient should be unaffected by any restrictive domain boundaries. At moderate to

PAGE 27

27 large observation times, the molecule is allowed to reach the boundaries of the domain which affect their overall mean square dis placement and measured diffusion coefficient. Results showing time dependent dynamics can give information about the size of domains as well as the extent of exchange of molecules between these domains and their surroundings and the related permeability o f the domain boundaries. Experimental techniques capable of measuring translational dynamics of lipids in membranes include fluorescence recovery after photobleaching (FRAP) 80 82 fluorescence correlation spectrosc opy (FCS) 19,31,83 single particle (molecular) tracking 84 86 and pulsed field gradient NMR. 87 89 In addition to the properties di scussed earlier, lipids in the l o domains exhibit lower mobility in comparison with the surrounding l d phase. As mentioned previously, the focus of membrane research is shifting to much smaller length scales due to accumulating evidence of the existence o f nano sized domains both in vivo and in model membranes. In the presence of domains, membrane molecules such as lipids or proteins exhibit differences in diffusivities due to restricted diffusion and/or variations in local membrane properties such as mol ecular packing density. It is very important to utilize experimental techniques that can give information about dynamics over relevant length scales without altering the structural and dynamic properties of the membranes. With current attention focusing on conditions of bilayers very near the miscibility transition temperature, the length scales of interest are much smaller than the sizes of giant l o domains (around 10 microns) observed in model membranes. As mentioned before, fluorescence microscopy bas ed techniques are often limited by spatial resolution due to the optical diffraction but are also limited by the requirement for labels. Methods such as single particle (molecule) tracking and atomic

PAGE 28

28 force microscopy as well as improved FCS methods which allow the resolution to go beyond the optical diffraction limit provide better spatial resolution 34,36,68,76,77 but are still limited by the requirement of labels. Nuclear magnetic resonance spectroscopy offers an attractive alternative to experimental techniques that require the attachment of labels. NMR techniques such as magic angle spinning (MAS) NMR and pulsed field gradient (PFG) NMR spectroscopy as well as a combination of these two techniques (MAS PFG NM R) are used to detect membrane domains and/or study dynamics without perturbing the system with bulky labels. Current PFG NMR techniques to study diffusion are still however limited by spatial resolution. The spatial resolution of PFG NMR measurements is mostly determined by the strength of the magnetic field gradients. Recently used PFG NMR methods employ magnetic field gradients that correspond to spatial resolution comparable to that of some of the microscopy based techniques. The spatial re solutio n in these cases is not adequate for direct studies of nano sized domains. Current experimental techniques have contributed to the understanding of the structure and organization of biomembranes, however they are still unable to fulfill the requirements o f sufficient spatial resolution without perturbing environments. Description of Project This work describes the development and application of a high field, high gradient strength PFG NMR technique used to monitor lateral diffusion of lipids in planar supported membrane systems. The technological novelty of this work is related to achieving the s patial and temporal resolutions which are superior to those reported in previous PFG NMR studies of lipid membranes under the conditions when sufficiently larg e NMR signal of lipids can be easily recorded. The advantage of high field

PAGE 29

29 measurements is directly related to improved signal to noise. Application of stronger gradients allows for the use of smaller diffusion times under the conditions of the narrow pu lse approximation which allows for distortion free monitoring of time dependent and displacement depend ent diffusion behavior. Until now, the maximum strength of magnetic field gradients, which were applied in PFG NMR studies of lateral diffusion in lipid membranes, was in the range of just several teslas per meter. 87,90 In some special cases, a maximum gradient streng th of around 10 T/m was reached. 91 The maximum strength of magnetic field gradients applied in this work is 30 T/m. With the current experimental setup, it is possible to measure the displacement of lip ids over length scales relevant to the size of lipid rafts. The temporal resolution of PFG NMR measurements reported in this work are determined by the actual diffusion time used in a pulse sequence rather than the total time required to measure a single diffusivity. The former time intervals can be as small as 5 ms, while the latter can be greater than 1 hour. Results obtained by PFG NMR represent averages of numerous scans to produce data with satisfactory signal to noise ratios. A clear requirement fo r this type of study is that systems remain at steady state condition s during the measurements; t his requirement was always fulfilled for the studies reported in the present work. Simple estimates show that application of such strong field and gradient st rengths would increase the temporal and spatial resolutions of diffusion measurements to the extent that diffusion on length scales comparable with size of rafts (< 200 nm) can be directly measured. This was confirmed by the experimental results discussed below. The description of technological development in this work demonstrates that it is now feasible to employ high field, high gradient PFG NMR for diffusion studies in planar

PAGE 30

30 supported lipid membranes. Furthermore, the technique presents advantages ov er current methods in offer ing new details about lipid dynamics. Improvement in the spatial and temporal resolution of lipid diffusion measurements is important due to the following considerations. Detailed information on the influence of membrane inhomoge neities on translational dynamics of lipids in lipid membranes can be obtained only when probing diffusion for displacements comparable to the size of these inhomogeneities. For the limiting case of large displacements and diffusion time, most of the info rmation will be lost due to the averaging over the length scales much larger than the size of membrane inhomogeneities. In addition to a sufficiently high spatial resolution, it is also important to have the ability of monitoring diffusion over a broad ra nge of the mean square displacements (i.e., diffusion times). For molecular displacements comparable with the size of the inhomogeneities, the effective lateral diffusivities of lipids are expected to be dependent on diffusion time. Detailed knowledge of this time dependent diffusion is crucial to understanding the structure dynamics relationship in lipid membranes, i.e. molecular exchange of lipid molecules. In this work, new details of molecular exchange between domains and their surroundings as well a s permeability of the domain boundaries are extracted from the time dependent diffusion behavior. Description of the Pulsed Field Gradient NMR Method A Brief Overview of Nuclear Magnetic Resonance Nuclear magnetic resonance spectroscopy is a technique tha t exploits the inherent magnetic properties of certain atomic nuclei in order to obtain detailed information about the structure and dynamics of molecules. In the framework of classical theory, NMR spectroscopy can be understood by first considering that certain nuclei posses an

PAGE 31

31 intrinsic source of angular momentum known as nuclear spin angular momentum. For a macroscopic system consisting of many nuclei, the total angular momentum is a vector that represents the direction and magnitude of the sum of indi vidual spin angular momenta. Nuclei with non zero spin angular momentum also have an intrinsic magnetic moment. In a macroscopic system, alignment of magnetic spins of individual nuclei along the direction of the external magnetic field leads to a non ze ro net magnetization. (Figure 1 4A) The static magnetic field B 0 exerts a torque on the net magnetization which causes a precessive motion about the direction of the external magnetic field at a frequency know as the Larmor frequency, (6) where is the gyromagnetic ratio of the nucleus under observation and B 0 is the amplitude of the static magnetic field (Figure 1 4B). In NMR, the direction of the B 0 field is usually assumed to coincide with the z axis of the laboratory ( viz non rotating) coordinate system. Magnetic resonance can be achieved by applying an additional magnetic field B 1 that oscillates in the transverse ( x,y ) plane with the Larmor frequency. In NMR spectrometers, the applicatio n of a current through the rf coil at the Larmor frequency will rotate the net magnetization vector from the direction of the external magnetic field ( z axis) to the transverse plane (Figure 1 4C). The angle that the magnetization is rotated, or the tip a ngle, is give by (7) where is the tip angle and is the duration of the rf pulse or B 1 field. A tip angle of 90 will tip the net magnetization vecto r completely in the transverse xy plane, where the signal is detected. Detection will be discussed in detail later in this section.

PAGE 32

32 Figure 1 4. Schematic representations of magnetization. A) Alignment of individual magnetic moments in the presence of a static magnetic field. (B) The summation of individual magnetic moments to get a net magnetization and precession in the presence of a static magnetic field. (C) The excitation of a net magnetization vector precessing around the z axis by a radiofrequency pulse to create transverse magnetization.

PAGE 33

33 The excitation of magnetization by a transverse rf pulse guides the system into a non equilibrium state. The process by which the excited net magnetization vector returns to its equili brium position with time is known as NMR relaxation. There are two NMR relaxation mechanisms: spin lattice or longitudinal ( T 1 ) relaxation and spin spin or transverse ( T 2 ) relaxation At equilibrium ( i.e. before the rf pulse), the time average of the ma gnetization vector is oriented along the z direction while the transverse magnetization (magnetization in the xy plane) is zero. In a simple approximation spin lattice relaxation can be viewed as the process by which energy gained from the applied rf pul se is transferred from the excited nucleus (spin) to its surroundings (the lattice) in order to reach thermal equilibrium. This causes the z magnetization to return to its equilibrium value. T 1 relaxation can be described by (8) where M z ( t ) describes the magnetization in the z axis as a function of time, t M 0 is the equilibrium magnetization value in the z direction and T 1 is the spin lattice relaxation time. Spin lattice relaxation times depend on a number of macroscopic parameters including the strength of the B 0 field and temperature. Spin spin relaxation is the process that is related to the interactions between the nuclei (spins) themselves. Energy is exchanged between the spins which induce s light changes in their individual local magnetic fields causing a slight change in frequency. Immediately after excitation by the rf pulse, all spins are in phase coherence with each other ( i.e. they precess exactly at the same frequency and the accumula ted phase is 0). After some time when T 2 relaxation effects are significant, the spins lose coherence, which is reflected by the existence of phase differences for different nuclei. As a result, the transverse

PAGE 34

34 magnetization decays. T 2 NMR relaxation can be described by (9) where M xy ( t ) is the transverse magnetization in time, M xy,0 is the initial transverse magnetization after excitation, and T 2 is the spin spin relaxation time. This magnetization eventual ly decays to its equilibrium value of zero because of T 2 relaxation. As mention briefly above, the frequency of the signal is detected in the transverse plane. Immediately after the magnetization tipped into the transverse plane by the rf pulse, the si gnal starts to decay due to T 2 The decaying transverse magnetization that is recorded is referred to as a free induction decay (FID) which is converted from time domain signal to frequency domain signal using Fourier transformation (Figure 1 5). The fre quency of signal that is detected varies somewhat from the Larmor frequency. These slight variations are due to a phenomenon known as chemical shift. Electrons in orbital clouds exert currents which produce magnetic fields ( B e ). The existence of this add itional field leads to a slight deviation of the local magnetic field from the B 0 field. Nuclei with different local environments will experience Figure 1 5. Illustration of the time domain free induction decay (FID) signal and the frequency domain NMR line after Fourier transformation (F.T.).

PAGE 35

35 different effects due to differences in electron distribution, ( i.e. magnetic fields of ). As an example, signal from the 1 H nuclei in an H 2 O molecule will appear at a slightly different frequency than that for the same nuclei in a CH 3 molecule because of chemical shift. The frequency differences are sufficiently large to detect and distinguish nuclei in different environments. Chemical shifts expressed as frequency change are dependent on the strength of the magnetic field. To provide an unambiguous comparison of chemical shift that is independent of field strength, a ratio of the measured frequency shift to the operating frequency of the magnet is taken as (10) where is the chemical shift in ppm, is the measured frequency, is a reference frequency, and is the operating frequency of t he magnet. The reference frequency is usually taken as the frequency of a compound known as TMS. Because there is a standard reference used for chemical shift as well as a lack of dependence on magnetic field strength in ppm, chemical shift can be used u niversally to give important information about the composition of the molecule under observation. There are countless applications of nuclear magnetic resonance which include ways to determine physical, chemical, electronic, structural, and dynamic proper ties of molecules. This brief overview is intended to set up basic theory behind the application of interest used to study translational dynamics of lipid molecules, pulsed field gradient NMR.

PAGE 36

36 Pulsed Field Gradient NMR: Theory Pulsed field gradient NMR spectroscopy allows for direct measurements of mean square displacement (MSD) as well as of the related diffusivity and the diffusion propagator. The technique is based on the application of an external magnetic field with amplitude B ext which is superim posed on the B 0 field and which is heterogeneous along the z axis ( B ext = gz where g is the magnetic field gradient and z is the coordinate along the z axis). This magnetic field gradient g leads to a dependence of the Larmor frequency on the position of the nucleus. This frequency is described as (11) The application of magnetic field gradients allows for the detection of a change in nuclear position in the sample along the z direction. The PFG N MR spin echo sequence (Figure 1 6) was first used to measure self diffusion. 92 This sequence consists of two rf pulses ( and ) each followed by a gradient pulse. The first rf pulse creates transverse magnetization with phase accumulation of zero indicating complete phase coherence. The first gradient pulse Figure 1 6. The PFG NMR spin echo sequen ce. Two rf pulses create transverse magnetization and then flip the direction of the spin while magnetic field

PAGE 37

37 gradients of amplitude, g, and duration, are applied to label and unlabel the position of the nuclei. with amplitude g an d duration is applied which labels the location of the nuclei by dephasing the magnetization which assigns a non zero value for phase accumulation. The magnetization phase angle accumulated by each nuclear spin during the application of a gradient pulse is described as (12) assuming that their positions, z do not change during the time in which the gradients are applied. The durations of gradient pulses are relatively short so the assumptio n that no diffusion occurs during the time which the magnetization is dephased by the gradients is reasonable. The two gradient pulses are separated by a predetermined observation time known as the diffusion time ( ) in which the nuclei are expected to ch ange their position. Just before the second gradient pulse, a rf pulse reverses the direction of the precession. rephasing the magnetization and reads the change of the positions along the z directio n. The change in phase accumulation is described by (13) where z 1 is the position of the nucleus when the first gradient is applied, z 2 is its position when the second gradient is applied and If the nuclei do not change their positions during the diffusion time ( ), the change in phase accumulation due to the applied gradient g would be zero, and the spatially dependent term of the frequency would d isappear. In this case the measured NMR signal would not be reduced due to

PAGE 38

38 application of the gradients. 93 For the case when is not equal to zero, a non zero value of leads to attenuation of the measured NMR signal. The spin echo attenuation for all spins starting out at z 1 can be wri tten as (14) where the phase distribution for spins with an initial position z 1 This distribution term is determined by the distribution of (Eq. 4) and is described by a Gaussian function. Equation 14 can then be written as (15) where is the average of over the displacements This average is written in terms of mean square displacement a s (16) Eq.15 is expected to hold for any initial position. Hence, it describes the overall attenuation in a macroscopic sample. T he total spin echo attenuation for all spins due to the application of the gradient pulses is then (17) where t eff is the effective diffusion time. For cases such that the duration is much smaller t han the time between the application of the first gradient and that of the second ( i.e. ), the effective diffusion time can be taken as In a typical PFG NMR diffusion experiment, the attenuation of signal is measured as a function of one of the experimental parameters such as g or for the purpose of finding the experimental diffusion coefficient. Details on experimental procedures will be given later in the text.

PAGE 39

39 Equation 17 describes the relationship between experimental parameters such as effective diffusion time and gradient duration and amplitude with the diffusion coefficient, D and attenuation in the absence of NMR relaxation. For the PFG NMR spin echo sequence, the measured signal is reduced by a factor of due to T 2 relaxation. Under conditions where the NMR relaxation times are sufficiently long, terms that describe their effects for a given PFG NMR pulse sequence can be neglected as they have been in derivations up to this point. In some cases, these effects cannot be completely neglected. For this reason, it is more practical to measure the signal attenuation as a function of the amplitude of the gradient rather than the value of for diffusion experiments. In 1970, Tanner published a paper describing the stimulated echo (STE) sequence (Figure 1 7) as a useful tool for NMR diffusion studies for systems in which T 1 > T 2 94 In the stimulated echo sequence, the pulse from the spin echo sequence is split in to two pulses to redu ce the effects of T 2 NMR relaxation. The signal is reduced by and due to T 2 and T 1 respectively. The measured signal is susceptible to the affects of T 2 NMR relaxation while the magnetization is in the xy p lane. During the time interval between the latter pulses of the stimulated echo sequence, the signal is reduced only by T 1 NMR relaxation effects. This allows for studies of systems with significantly short T 2 times to be performed over a large range of diffusion times including diffusion times >> T 2 Long diffusion times are desirable in systems with low diffusivities since for short diffusion times even after application of the largest possible gradient, attenuation of the signal

PAGE 40

40 might not be sufficiently large to properly determine diffusivity(ies). In cases of restricted or partially restricted diffusion, there is a dependence of diffusion behavior on diffusion time and this should be studied over a range of diffusion times. 94 Under conditions of short T 2 times and/or requirements for long diffusion times, the PFG N MR stimulated echo sequence offers clear advantages over the PFG NMR spin echo sequence. T hus, t he PFG NMR stimulated echo sequence is one of the most common ly used diffusion pulse sequences that determine diffusivities of lipids in membranes. Figure 1 7. The PFG NMR stimulated echo sequence. This sequence stores the magnetization along the negative z axis by splitting the radiofrequency pulse in the standard spin echo sequence into two radiofrequency pulses This sequence is very advantageous for systems in which T 2 NMR relaxation time is much shorter than T 1 NMR relaxation time. The next PFG NMR diffusion sequence of interest to this work is the PFG NMR stimulated echo longitudinal encode decode sequence ( STE LED). A schematic of this sequence is shown in Figure 1 8. The advantage of this sequence is that it is designed to minimize effects of gradient eddy currents. Eddy currents are currents that are induced by changing magnetic fields. They can have v ery disturbing effects on diffusion experiments, especially when large magnetic field gradients are switched on or off. Normally, the gradient stabilization delay can be set to a value that is sufficiently long to

PAGE 41

41 allow for any eddy currents produced by the gradients to dissipate after the gradient is switched off. However, this delay increases the effect of T 2 because the T 2 NMR relaxation process remains during the gradient stabilization delay. The PFG NMR STE LED sequence applies an LED delay just be fore acquisition to allow for eddy currents to die out. Only T 1 NMR relaxation occurs during this delay. With this LED delay, the gradient stabilization time can be set to a value much smaller than that required for the standard STE sequence. This seque nce is most beneficial for use with samples that are limited by extremely short T 2 relaxation times. Figure 1 8. The PFG NMR stimulated echo longitudinal encode decode sequence. The sequence adds an additional delay at th e end of the standard PFG NMR stimulated echo sequence. During this delay, the magnetization is stored along the z axis and a spoil er gr adient can be applied to reduce any effects from eddy currents. The last PFG NMR diffusion sequence that is of inte rest to this work is known as the 13 interval sequence. This sequence incorporates alternating (bipolar) gradients in contrast to the previous sequence, where the gradients were strictly unipolar. This sequence is shown in Figure 1 9. Alternating pulsed field gradients are used to suppress susceptibility induced artifacts in diffusion experiments. Magnetic susceptibility is related to the manner in which an object causes distortions in the applied magnetic field due to the inherent and/or geometric prope rties of that object. 95 Samples that are heterogeneous in nature present a specific problem due to the

PAGE 42

42 existence of inhomogeneous internal magnetic fields even before the application of an external magnetic field. 96 Susceptibility induced inhomogeneities in the local field manifest themselves in various manners including phase shifts in the frequency domain and shifts in the spin echo position in the time domain. 97 These manifestations are dependent on the strength of the applied magnetic field. For this reason, the presence of susceptibility artifacts in NMR results can be tested by directly c omparing data from Figure 1 9. The PFG NMR thirteen interval pulse sequence. This pulse sequence uses alternating gradients to suppress artifacts induced by magnetic susceptibility. different B 0 field strengths. The coincidence of such data verifies t he absence of susceptibility artifacts, however it is not always convenient or possible to do diffusion experiments at multiple field strengths. The 13 interval sequence is intended to minimize susceptibility distortions of the PFG NMR data. Comparison of diffusion results obtained from a 13 interval sequence with those from more standard sequences such as the stimulated echo sequence can be used to verify that magnetic susceptibility effects are not distorting diffusion results. Pulsed Field Gradien t NMR: Application for Studies of Lipid Bilayers To measure diffusivity, PFG NMR signal A(g) obtained using one of the PFG NMR sequences above is measured as a function of the magnitude of applied field gradient ( g ) under conditions where all other sequ ence parameters are kept constant.

PAGE 43

43 For most cases, the amplitudes of the NMR lines in frequency domain spectra of lipids as well the area under these lines were used to measure signal to obtain the PFG NMR attenuation curves. It is also possible to use the attenuation of the amplitude of the signal in the time domain spectra to obtain PFG NMR curves. Both approaches can be used successfully for diffusion measurements. The advantage of the former approach is related to the possibility of measuring sepa rately diffusivities associated with different NMR lines, which can originate from different types of molecules in the studied samples. This is especially relevant for the case of lipid bilayers in which there are molecules such as water with a unique che mical shift and diffusivity contributing to the measured NMR signal alongside lipid molecules with different chemical shift and diffusivity. The diffusivities D are obtained from either a one exponential or two exponential fit of the PFG NMR attenuation c urves using (18) where A(g) is the measured signal for a given gradient strength, A(g=0) is the maximum gradient strength (signal for applied gradient amplitude of zero), and p i is the fr action of molecules diffusing with a diffusivity D i m The effective diffusion time ( t eff ) is equal to for the spin echo, stimulated echo sequence, and stimulated echo LED sequences and for the 13 interval sequ ence. 98,99 Eq. 18 is completely analogous to Eq. 17, however the sum of terms indicates the presence of more than one ensemble of molecules with distinct dynamics. A one exponential (monoexp onential) fit would indicate that there is one ensemble of molecules

PAGE 44

44 contributing to the overall signal yielding one single value of diffusivity. A two exponential (biexponential) fit indicates that two ensembles with unique values for the diffusion coef ficient as well as p i fractions contribute to the measured signal. Figure 1 10. Comparison between the directions of measured and lateral diffusion. The gradients ( g ) are oriented along the z axis hence any observation of the diffusion of lipids is ac tual diffusion along the direction in which the gradients are applied. The normal to the surface of the bilayers n is oriented at the angle Multiplying the measured diffusion coefficient ( D m ) by a factor of 1.5 yields the desired lateral diffusion coe fficient ( D ). The diffusivities determined by fitting the attenuation curves using equation 18 correspond to the diffusion along the direction, which coincides with the direction of the gradients and that of the B 0 field (Figure 1 10). This direction wa s different from that of

PAGE 45

45 diffusivities ( D m ) in the plane of the lipid bilayers for reasons associated with minimizing T 2 relaxation affects. This orientation of the bilayer normal n and the theory behind it will be discussed in de tail in Chapter 2. Ultimately, the measured diffusivities were multiplied by a factor (1/cos ) 2 = 1.5 to determine the true lateral diffusion of lipids along the bilayer 90 In this calculation we have assumed that the displacements of lipids in the direction perpendicular to the bilayer surface are negligibly small in comparison to the corresponding displacements along the bilayer surface. Detailed analysis of diffusion coefficients obtained f rom PFG NMR measurements will be discussed in more detail in the presentation of results in Chapter 3.

PAGE 46

46 CHAPTER 2 DEVELOPMENT OF DIFFUSION MEASUREMENTS IN LIPID BILA YERS USING HIGH FIELD, HIGH GRA D I ENT PFG NMR Development Associated with Planar Supported Lipid Bilayer Samples A wide variety of model membranes differing in composition and structure have been utilized extensively for studies of membrane dynamic and structural properties. The primary lipid components of biological and model membranes incl ude phospholipids, sphingolipids, and sterols. While membranes composed of a single lipid or binary mixtures of lipids have been well characterized, ternary mixtures of the three main membrane components represent a better model of the eukaryotic membrane. Common eukaryotic membranes are composed of about 50 mol% phospholipids and sphingolipids and up to 40 mol% of cholesterol. 22 Formation of domains have been found to be strongly promoted by the presenc e of two types of lipids with phase transition temperatures which are very different from each other. 22 Lipids that contain charged headgroups have also been incorporated into model membranes to mimic the charged nature of certain cell membranes. While lipid charge has been shown to have an effect on domain formation, this effect is not significant. 22 Lipids bilayers can be readily constructed in the for m of vesicles and planar structures. The use of lipid bilayers reconstituted on planar substrates is common practice for many of these studies of membranes. Planar supported bilayer samples are well defined and the absence of the orientational distributi on of the membrane planes in such samples offers many advantages for research. Membranes reconstituted on solid supports such as silica have been observed to retain the lateral fluidity associated with lipid membranes in vesicles and cell membranes. 100 These types of membrane samples are especially attractive to those interested in investigations of reconstituted functional membrane

PAGE 47

47 molecules such as proteins and receptors. 100 102 The potential for pl anar supported lipid bilayers to be used as biosensors gives a practical applicability to the membrane. For those interested in studies of translational dynamics of membrane constituents, planar supported membranes are advantageous because of the well def ined orientation of the bilayer plane. 101 In this work multibilayer stacks of lipid bilayers are reconstituted on solid support as shown i n See Figure 2 1. Each support holds on the order of 1000 bilayers each separated by a thin layer of water about 2 nm thick. 103,104 For studies of lateral diffusion, these samples offer an advantage over bilayers of vesicles, either unilamellar o r multilamellar, related to the absence of curvature of the bilayer. Curvature in the bilayer can complicate the interpretation of diffusion results which are obtained along a fixed microscopic direction coinciding with the direction of the applied gradie nts ( i.e. the measured diffusion coefficient for a lipid diffusing in a curved membrane could be smaller than the true diffusion coefficient due to misinterpretation of the measured mean square displacement). Also, planar membranes reconstituted on glass plates allows for the microscopic orientation of lipids in the bilayer to address problems associated with T 2 In contrast to samples where a single bilayer (or monolayer) is reconstituted on a solid support, the use of multibilayer stacks addresses any concerns associated with the influences of lipid support interactions. These effects can be neglected because the number of bilayers that are in contact with the solid supports are very small in comparison to the many thousands of bilayers between each s upport. Also, in comparison to these planar supported bilayers, the use of multibilayer stacks on solid support provides sufficiently large NMR signal for PFG NMR measurements.

PAGE 48

48 Preparation of Planar Supported Multibilayer Stacks PFG NMR studies were perfo rmed with multibilayer stacks supported on thin glass plates. The bilayer stacks were prepared from ternary lipid mixtures of either 1,2 dioleoyl sn glycero 3 phosphocholine, (DOPC, >99%), Chicken egg yolk sphingomyelin, (SM, >95%), and cholesterol, (CH OL, >99%) in equimolar proportions or DOPC, 1,2 dipalmitoyl sn glycero 3 phosphocholine (DPPC, >99%), and CHOL with the composition of 30% sterol and equimolar amounts of DOPC and DPPC. DOPC and DPPC were purchased from Avanti Polar Lipid, Inc. (Alabaster, AL, USA), while SM and cholesterol were supplied by Sigma Aldrich (St. Louis, MO, USA). Two protocols, which are adapted from the current literature, 91,105 are used for the preparation of model lipid membranes in this work. In both techniques a lipid film is deposited on thin glass plates, which is followed by hydration causing self orientation of the lipids into multibilayer stacks. The lipids are individually dissolved in solvents and combined using the appropriate volume ratios to create a final ternary lipid solution. This sol ution is deposited onto clean glass plates (55mm 2 or 67 mm 2 with a plate thickness of ~0.1 mm) obtained from Marienfeldt/Menzel (Lauda Knigshofen/Braunschweig, Germany) and the solvent is evaporated off overnight under high vacuum at ~313 K. Of the two methods employed here, the differences lie mainly in the solvents used to dissolve the lipids and in the way of introducing water into the system, i.e. either directly as liquid water or from the gas phase. The two techniques will be discussed separately from this point on. It was observed in this work that the PFG NMR data obtained with samples prepared using these two techniques were not influenced by the preparation method within the experimental uncertainty. Verification of the orientation of lipids in bilayers as well as reproducibility issues will be discussed in future text. In the first method, a

PAGE 49

49 solution of methanol:1 propanol (1:4 vol:vol) is used as the solvent. The ternary lipid solution was deposited on the glass plates to a sample mass of 8 9 g/mm 2 After Figure 2 1. Illustration of a PFG NMR sample consisting of many planar supported multibilayer stacks. The figure zooms in on the stack to show that many bilayers ( i.e. on the order of 1,000) are reconstituted on each glass plate. E ach bilayer is separated by a thin layer of free water about 2 nm thick. solvent evaporation, from 30 to 40 plates were stacked on top of each other and transferred to a hydration chamber filled with 2 H 2 O saturated with K 2 SO 4 The salt and 2 H 2 O were obtain ed from Sigma Aldrich (St. Louis, MO, USA) and Spectra Stable Isotopes (Columbia, MD, USA), respectively. In this method, the hydration takes place only from the gas phase ( i.e. indirectly) under the condition of a relative humidity of around 97%. The sa lt solution is used to keep the humidity slightly below 100% to

PAGE 50

50 ensure that condensation of liquid water domains on the glass plates with lipids does not occur. This prevents direct contact between the lipid films on glass plates and liquid 2 H 2 O. The sta ck was left in this environment for seven days at 313 K for equilibration. Once the stack is set up inside the NMR tube (see next section for details), pure 2 H 2 O is added to bring the sample to maximum (i.e. 100%) hydration and to keep it at this hydratio n. The second method uses a solution of chloroform:methanol (2:1 vol:vol) as the solvent. The ternary lipid solution was prepared as discussed above using three individual lipid stock solutions. A sublimable solid, i.e. naphthalene obtained from Cambri dge Isotope Laboratories (Andover, MA, USA), was then introduced into the lipid mixture in a naphthalene:lipid molar ratio of 1:1. The resulting solution was deposited onto the glass plates to a sample mass of 8.3 g/mm 2 After solvent evaporation, the p lates were left unstacked. They were hydrated from the gas phase in the presence of liquid 2 H 2 O saturated with K 2 SO 4 for 1 2 days inside of the hydration chamber. After the initial hydration step, pure liquid 2 H 2 O was directly added to the lipid bilayers using a syringe to achieve a final molar ratio of ~28 moles of water per mole of lipid. The direct hydration by pure 2 H 2 O is expected to bring the sample to maximum hydration of 100%. 35 40 plates were stacked and wrapped in parafilm. The stack was then held at 277 K for additional 1 2 days. Once the stacks were fully prepared and hydrated, they were transferred to an NMR tube with an external diameter of 10 mm (for studies using 750 MHz (17.6 T) PFG NMR spectrometer) or 7.5 mm (for studies using 400 MH z (9.4 T) and 125 MHz (2.9 T) PFG NMR spectrometers.

PAGE 51

51 Here, two protocols are presented for preparation of multibilayer stacks. Orientation of lipids in multibilayer stacks was verified using the first protocol described in this section. The second protoc ol gave sufficiently similar proton NMR spectra in terms of shape, linewidth, and chemical shift. This observation shows that also the second protocol results in preparation of samples of oriented multibilayer stacks because 1 H NMR spectra are sensitive t o the extent of the lipid self organization into oriented bilayers as will be discussed later. Most multibilayer stacks were prepared using the second protocol which uses the sublimable solid, naphthalene in order to promote better orientation. Naphtalen e is believed to randomly distribute among lipids when the solvent solution is dried on the glass. 105 After overnight vacuum drying, the solid is gone leaving the samples more amenable to hydration 105 providing a better extent of orientation and a more effective sample preparation protocol. It was observed that this method gave a better s ample preparation reproducibility yielding a lower probability of unusable samples where a significant fraction of lipids did not form the bilayers or were not ideally oriented in the bilayer. Sample preparation methods for bilayers reconstituted on glas s planar supports have been considered tedious 106 and very sensitive to solvent choice and hydration techniques 107 Evaluation and adaptation of protocols were based off of issues with lipid mixture spreadability and hydratio n issues. Great care was taken when using these protocols to prevent untimely solvent evaporation and contamination. Exposure to air was kept to a minimum to prevent lipid oxidation. Lipid oxidation is more likely to occur when lipids are directly expos ed to air, i.e. when there is no or vary little water or solvent. The lipids were stored in a way allowing minimizing the exposure to air and dry

PAGE 52

52 lipid mixtures ( i.e. after solvent evaporation and before hydration) were kept under vacuum whenever possib le. Mass spectroscopy measurements revealed no changes in the lipid composition of the lipid mixtures obtained from the bilayer samples used for diffusion measurements in comparison to the original lipid mixtures that were used to prepare the samples. Th ese measurements were performed by Konstantin Ulrich. Oxidation was seen to have an insignificant affect on the samples if proper measures were taken. Orientation of Planar Supported Multibilayer Stacks at the Magic Angle 1 H PFG NMR measurements of lipids in lipid membranes are complicated by rather short transversal ( T 2 ) NMR relaxation times and the related large line width in a frequency domain. Short T 2 times and the related line broadening are mainly caused by strong proton dipole dipole interactions i n lipids that are not completely averaged by molecular motion. In order to minimize the effects of dipole dipole interactions on T 2 times and the line width, the following main three options have been used or at least discussed in the literature: ( i ) PFG NMR studies can be carried out using oriented samples, i.e. multibilayer stacks oriented along the so respect to the direction of the applied magnetic field 88,90,91 ( ii ) PFG NMR c an be combined with a magic angle spinning (MAS) technique, 46,87,108,109 viz fast sample rotation along the direction given by the magic angle and ( iii ) PFG can be combined with multiple pulse homonuclear decoupli ng. 110 The MAS approach has proven to be an especially powerful method allowing for the discrimination between different membrane components. Unfortunately, it is not technically compatible with an application of commercially ava ilable high gradient systems. As it is not a trivial task to create reliable and reproducible magnetic field gradients of such high amplitudes, it is imperative to

PAGE 53

53 utilize what is available commercially. Similarly, approach ( iii ) is not compatible with t he application of high gradients because measurement artifacts are likely to occur if high gradient amplitudes necessary for submicron diffusion measurements are superimposed on the decoupling radiofrequency pulse sequence. 110 App roach ( i ) gives the possibility of adapting PFG NMR diffusion studies using high magnetic field gradient amplitudes for investigations of lipid transport in bilayers which are severely limited by short T 2 relaxation times. In order to minimize dipole dipol e effects on transverse relaxation, a sample insert had to be created to macroscopically orient the bilayers in NMR spectrometers. The stack of glass plates with bilayers should be oriented in such a way that the angle ( ) between the dipole moment of lipids and the direction of the applied magnetic field B 0 is very close to the so 2 1) in the Hamiltonian term describing the dipole dipole interaction approaches a zero value. To orient the bilayer stacks at the magic angle a special insert was originally developed by Konstantin Ulrich, a previous graduate student working for Dr. S. Vasenkov at the Universitt Leipzig in Leipzig, Germany. It was designed for use with 12 5 and 400 MHz spectrometers. The same approach was used to make inserts suitable for the current work using 750 MHz spectrometer. Figure 2 2 shows schematic presentation of the insert. The insert is made of plexiglass and fits into 10 mm NMR tubes used i n this study. The stacks were placed in the insert and inside the tube. Before sealing the NMR tube with a lipid sample, a few drops of excess 2 H 2 O are added on the tube walls above or below the sample to ensure that the relative humidity in the

PAGE 54

54 gas phas e surrounding the bilayers is 100%. Verification of macroscopic orientation of multibilayer stacks will be discussed in detail later in Chapter 2. Figure 2 2. Schematic of the magic angle insert. The insert orients the multibilayer stacks such that an gle ( ) between the dipole moment of the lipids and the direction of the external magnetic field ( B 0 ) is equal to the magic angle. Orientation at the magic angle leads to a minimization of dipole dipole interaction effects on T 2 NMR relaxation. Developme nt Associated with PFG NMR Diffusion Experiments The majority of measurements of self diffusion in model lipid bilayers were carried out on a wide bore Bruker PFG NMR spectrometer operating at a 1 H resonance frequency of 750 MHz (17.6 T). This spectromete r is located at the Advanced Magnetic

PAGE 55

55 Resonance Imaging and Spectroscopy (AMRIS) facility of University of Florida in Gainesville, Florida. A Diff60 probe with GREAT60 amplifier was used to generate high gradients for diffusion measurements using the 750 MHz spectrometer. Initial experiments were conducted at a lower frequency by and in collaboration with Konstantin Ulrich. These measurements were carried out using two different home made spectrometers: PFG NMR spectrometers FEGRIS NT and FEGRIS FT opera ting at a 1 H resonance frequency of 400 MHz and 125 MHz, respectively. Discussion of measurements conducted at 400 MHz and 125 MHz is limited to this section for early development and verification purposes. Acquisition of each proton spectrum using the P FG NMR sequences required up to 240 scans. The resulting ratios of signal to noise or to the background signal at small gradient strengths were around 300 for the measurements at 750 MHz and in the range of 50 for the measurements at 400 MHz and 125 MHz. Temperatures were varied in the range of 291 K to 310 K. The diffusion probes used at 750 MHz are suitable for PFG NMR measurements with gradient amplitudes up to 35 T/m, but a maximum of only 28 T/m was needed for most experiments. Calibration Experime nts Before carrying out diffusion measurements it is necessary to ensure that the amplitudes of the gradients generated by the gradient coils are known with a very high precision. The most common approach is to conduct PFG NMR experiments determining the diffusion coefficient for a species with a well known diffusivity. 111 1 H PFG NMR calibrations measurements were carried out with two liquids, water and glycerol. Figure 2 3A gives an example of an attenuation plot for diffusion experiments conducted in order to calc ulate the diffusion coefficient of a small amount of H 2 O in

PAGE 56

56 liquid D 2 O. Protonated water (H 2 O) is diluted in deuterated water (D 2 O) in order to decrease the number of NMR active nuclei under study and thus make the signal amplitude closer to that in lipid samples. The standard PFG NMR stimulated echo sequence was used with = 1.1 ms for two different diffusion times, t eff = 14.63 and 39.63 ms. The gradients were varied between 0.396 and 2.00 T/m. In similar experiments, the diffusion coefficient was me asured for t eff as large as 240 ms (not shown). The diffusivity of deuterated water at a given temperature is well known and can be used for the calibration of the applied gradient amplitudes. The relationship between gradient amplitude and diffusivity c an be found to be proportional according to the attenuation equation (Eq. 18) such that (18) where D H2O and D lit is the measured and literature values for the diffusion coeffici ent of the water sample, respectively, g H2O is the gradient amplitudes given by the software of the spectrometer (i.e. the gradient amplitude that was used to determine D H2O ) and g act is the actual gradient amplitudes. At room temperature (298.2 K), dif fusivity is expected to be 1.9 10 9 m 2 /s for pure D 2 O and 2.3 10 9 m 2 /s for pure H 2 O. Since the concentration for protonated water was sufficiently small, the value for pure deuterated water was used for calibrati on. The gradient calibration constant (GCC) must be adjusted such that results from diffusion experiments on water (H 2 O diluted in D 2 O) yield that value. This ensures that actual gradient amplitudes that are applied in diffusion experiments correspond to those used for the calculation of diffusion coefficients.

PAGE 57

57 The PFG NMR measurement of glycerin serves to verify the linearity of the gradients ( viz. proportionality between the actual gradient applied and the input value of the gradient as shown by the s oftware of the spectrometer) at large gradient amplitudes and durations. Figure 2 3B show examples of attenuation plots for diffusion experiments conducted for glycerin. The figure also shows the agreement of results obtained from the most standard PFG N MR diffusion sequence, the stimulated echo, with results obtained using the PFG NMR spin echo, stimulated echo LED, and the 13 interval sequences. These comparisons were performed to ensure that each sequence gave reliable results for a standard homogeneo us sample with a diffusivity similar to that in lipid samples. Verification of each sequence was conducted separately ( i.e. on different days), often using slightly different experimental parameters and sometimes different samples. Most of the results w ere obtained for each sequence with 3.0 ms, gradients ranging from 0.33 24.1 T/m, and t eff as small as 5 ms and as large as 240 ms. Each sequence produced results that were in agreement with the results obtained with the stimul ated echo sequence within the experimental uncertainty. The data then indicates that the sequences operate properly and do not produce disturbing artifacts, even at very large gradient strengths. The diffusivity of glycerol at room temperature is expecte d to be around 2 10 12 m 2 /s (similar to lipid samples). The experimental diffusion coefficients agreed with this value within experimental uncertainty. In the case of glycerin measurements the actual value of diffusivity is not of pr imary interest. Instead, the focus was on the shape of the attenuation curve. Measured attenuation curves should remain monoexponential (as is expected of homogeneous liquids) even with the use of large duration and amplitudes of the

PAGE 58

58 Figure 2 3. Exa mples of PFG NMR attenuation plots for water (A) and glycerin (B). The measured diffusion coefficient of water is compared to known values and used to calibrate gradient amplitudes. Experiments conducted on glycerin served to test the linearity of the gr adients at high magnetic field gradient amplitudes as well as to confirm the agreement of results obtained from different PFG NMR diffusion sequences.

PAGE 59

59 gradients used. In Figure 2 3B, it is seen that the attenuation of signal remain monoexponential throu ghout the range of gradients which are applied. Diffusion studies of glycerin at room temperature confirm that the gradients behave linearly even at high magnetic field gradient amplitudes and that there should be no artifacts in experiments associated wi th the choice of diffusion sequence. Addressing Limitations Concerning Gradient Pulses Studies of lipid self diffusion in heterogeneous lipid bilayers, especially those which form small liquid ordered domains as discussed in Chapter 1, involves the measu rement of short displacements as well as small diffusivities. In order to measure lipid diffusivities which are as low as 10 13 m 2 /s, it is necessary to apply gradients with sufficient amplitudes and/or pulse durations to measure an acceptable level of si gnal attenuation. The short T 2 NMR relaxation times of lipid molecules in bilayers limit the duration of the gradient pulse. Also, for studies observing anomalous or restricted diffusion, PFG NMR measurements fail to give correct information about dynami cs if the conditions of the narrow pulse approximation 112,113 are not fulfilled. These conditions are: ( i ) the trajecto ry length over the duration of the gradient ( i.e. MSD as defined by Eq. 5) has to be small in comparison with the size of restriction ( i.e. domain), and ( ii ) the effective diffusion time has to be sufficiently larger than the gradient pulse duration ( t ef f >> ). Large gradient amplitudes are applied to compensate for limitations on gradient pulse durations. The use of high gradients and relatively short gradient durations imposes complications when considering the relationship betwe en the input gradient pulse and the actual pulse that is applied in an experiment. These complications were addressed by adjusting the gradient shape, the delay for gradient recovery, and parameters used to account for eddy currents known as preemphasis

PAGE 60

60 a djustment. The development discussed in this section is novel for high field, high gradient PFG NMR studies used to measure lateral dynamics of lipids in model membranes. Gradient pulse shape and delay for gradient recovery Until now in this text, the gra dient pulse has been depicted as a perfect square shaped pulse. In reality, it is virtually impossible to apply a gradient such that the amplitude of the value rises instantaneously from zero to some arbitrary value. Pulsed field gradients are generated by pulses of electric current flowing through a gradient coil. Sharp rise and fall times ( i.e. rapid increase and decrease of current form the current source) 93 of a square pulse can create disturbing responses such as overshoot which are very erratic and cannot always be controlled and reproduced. These responses promote induct ion of eddy currents which cause measurement artifacts that are not always negligible in comparison to the actual data. It is important to have very consistent and reproducible gradient pulses in order to minimize artifacts and measure true diffusion beha vior. Shaped pulses are common alternatives to the generic square gradient pulse. Often, sine and trapezoidal shaped pulses allow for a more gradual climb towards the maximum gradient amplitude. 79 Eddy currents induced by the application of magnetic field gradien ts can be reduced by shaped gradient pulses but it is still important that the shape itself is free of distortion. In order to produce the optimal gradient pulse which is free from shape distortion and eddy current effects, it was necessary to explore vari ous types of shapes that would simultaneously ( i ) provide the quickest path to the full amplitude of the gradient, ( ii ) provide the largest area under the gradient pulse, and ( iii ) be sufficiently reproducible and free from distortions. In order to explor e the suitability of different shapes, a digital

PAGE 61

61 oscilloscope was used to directly observe the shapes of the gradient pulses. The oscilloscope gave information about the gradi ent pulse shape, which allowed for the observation of a difference (if any) betw een the shape prescribed by the software and the real shape of the gradient pulses. A pulse with a shape of a sine wave from 0 to was observed to be easily and accurately reproducible. It is most advantageous, however, for very short gradient duration s. For short durations, a sine wave will reach the full amplitude in a short amount of time and provides an efficient pulse area close to that for a square pulse. Longer pulses require shapes that have a sufficient plateau at full amplitude much like the square pulse. Trapezoidal shaped pulses provide the opportunity to designate ramp up, ramp down, and plateau durations. With this shape, it is possible to control and optimize each part of the shape. The linear ramps leading to and from the plateau cre ate a more gradual path in contrast to the instantaneous switching on and off of the square pulse. It was necessary to determine the minimum durations for the ramp up and ramp down portions of the shape that can be followed by the hardware and do not lea d to disturbing eddy currents. These values were found to be around 500 s for gradient amplitudes as large as 25 T/m, which was considered to be reasonable for experimental parameters. Next, the ramp curves were replaced individually by sine curves in an attempt to increase area under the gradient curve. The sine was preferred over the linear ramp up curve however the difference was not significant. Replacing the ramp down curve with a s ine induced distortions to the gradient shape. From these results, it was determined that the ideal gradient pulse shape was a trapezoid like shape with a sine ramp up and a linear ramp down. For

PAGE 62

62 many cases such as in the 13 interva l sequence as well as other diffusion measurements, a standard trapezoid (linear ramp up and down) was sufficient. In order to ensure that effects either from gradient shape distortion or induced eddy currents associated with the magnetic field gradients do not disturb diffusion measurement, it is necessary to let sufficient time pass after the last gradient pulse in the sequence is turned off and before data acquisition is started. According to observations from the oscilloscope, the delay for gradient recovery, which is that very time period between the end of the gradient pulse and the beginning of the rf pulse and/or data acquisition, must be larger than 500 s for experimental parameters used on lipid samples. To verify that the value of delay was s ufficient, a series of simple PFG NMR stimulated echo experiments with the gradient amplitudes as large as 25 T/m were carried out. The value of delay for gradient recovery was varied throughout this series of experiments. Using time intervals for delays for gradient recovery which are not sufficiently long can produce distortions in the shape in spectra as well as a reduction in amplitude. The minimum value for delay for gradient recovery is considered to be the value at which the shape and/or amplitude of the spectra stops changing. This value was determined to be at least 1 ms, which is much longer than observed with the oscilloscope. Preemphasis adjustment and B 0 compensation As mentioned previously, gradient pulse durations are often limited by sh ort T 2 NMR relaxation times. In the previous section, it was discussed how the gradient shape was optimized. The minimum delay for gradient recovery was found to be a rather long value of 1 ms. Preemphasis adjustment can be used to further improve gradi ent pulse

PAGE 63

63 shape and reduce the influence of eddy currents allowing for shorter gradient stabilization delays. Preemphasis adjustment applies corrections to the current at leading and tail edges of the gradient pulse. 79 These corrections exist in the form of three e xponential functions, with different amplitude and time constants and when optimized, can further reduce the effect of eddy currents. Optimization of preemphasis parameters for diffusion studies on lipid membranes was done in collaboration with a Bruker e ngineer. PFG NMR stimulated echo experiments similar to those described in the previous paragraph were conducted and showed that the new parameter optimization allowed for the use of delays for gradient recovery as small as 500 s. B 0 compensation was at tempted but did not provide appreciable benefits to diffusion experiments and was ultimately not implemented. Verification of Macroscopic and Microscopic Orientation of Multibilayer Stacks The orientation of the lipids in multibilayer stacks of an equimola r mixture DOPC/SM/CHOL prepared for diffusion measurements was characterized using 31 P NMR by Konstantin Ulrich. Figure 2 4 shows examples of proton decouple 31 P NMR frequency domain spectra, which were recorded for different values of the angle of orientation of a multibilayer stack with respect to the direction of the constant magnetic field B 0 (Figure 2 2). The angle was changed using the goniometer probe that allows performing measurements at different, well defined values of Each of the measured spectra consists of a single line with a half width around 6 ppm. The spectra in this figure collectively demonstrate that the majority of lipids in the sample are arrange in well oriented bilayers due to the following considerations: (i) the chemical shift of the lines depends on the values of as expected for macroscopically oriented lipid

PAGE 64

64 bilayers, and (ii) the line half widths, which are mostly determined by the chemical shift anisotropy, are sufficiently small, leading to the conclusion that there is insignificant distribution of orientati ons of individual lipid with respect to the bilayers normal. The signal from randomly oriented lipids in the sample is expected to be independent of Figure 2 4. Proton decoupled 31 P NMR spectra of DOPC/SM/CHOL multibilayer stacks to study the orienta tion of lipids in the bilayers. Each NMR line which was obtained by a Hahn echo sequence represents spectra for a different angle between the normal to the surface of the glass (which coincides with the direction of the dipole moment of the lipids formi ng bilayers) and the direction of B 0 field. The comparison shows that the signal of the lipids is dependent on which is not expected for randomly oriented lipids. This data was obtained by Konstantin Ulrich. and have a half width that is several time s larger than that of the lines in Figure 2 4. Within experimental uncertainty, no such signal was observed. On the basis of the data

PAGE 65

65 in Figure 2 4, it was estimated that more than 97% of lipids in the multibilayer stack samples are located in well orien ted bilayers. The extent of orientation is expected to be the same or similar within experimental uncertainty for samples prepared from different mixtures and/or by different protocols. Macroscopic orientation of the multibilayer stacks of an equimolar mixture of DOPC/SM/CHOL in the insert with respect to the direction of the B 0 field was verified using 1 H NMR. This characterization was also performed by Konstantin Ulrich. The orientation attained using the magic angle insert was determined by a compar ison with orientation obtained by a goniometer probe. For studies using the probe, the stacks were placed directly (i.e., without the insert) into a NMR tube and a goniometer probe was used to adjust the angle between the normal to the surface of the bilayers supports and the direction of the B 0 field. Figure 2 5 shows two set of frequency domain spectra comparing one from a multibilayer which was oriented as close as possible to the magic angle using a gonio meter probe (Fig. 2 5A) with one from a multibilayer oriented by the magic angle insert (Fig. 2 5B). 1 H NMR spectra in Figure 2 5 were obtained using the standard Hahn echo sequence with different separations ( ) between /2 and radiofrequency pulses. Under the measurement conditions of this sequence, the signal amplitude is reduced due to T 2 NMR relaxation by a factor of exp( 2 / T 2 ). Hence, dependence of the signal amplitude on allows for the evaluation of the characteristic values of T 2 which are mostly determined by the degree of deviation from the magic angle orientation. The spectra in Figure 2 5 show partially overlapping lines of the CH 2 groups of the hydrocarbon chains and of the CH 3 choline groups of the

PAGE 66

66 Figure 2 5. 1 H NMR spectra of DOPC/SM/Chol multibilayer stacks to study the macroscopic orientation of the stack using the magic angle insert. These spectra were recorded using the Hahn echo sequence for differe nt value of the duration between the first and second radiofrequency pulse, at 298 K. The stacks were aligned at the magic angle using a goniometer probe (A) and the specially designed insert shown in Fig. 2 3 (B). These data were obtained by Konstant in Ulrich. The insert has been adapted for high field, high gradient PFG NMR studies and the new insert yields similar orientational efficiency.

PAGE 67

67 headgroup at around 1 and 3 ppm, respectively. These lines can be assigned to both DOPC and SM. A line at around 4.7 ppm is assigned to a small amount of normal water. It is seen that the spectra in Figure 2 5A and their dependence on essentially coincide with those in Figure 2 5B. The data in Figure 2 5A were recording using a goniometer probe, which giv es magic angle orientation with precision of around 0.3. On the basis of comparison of these data with those in Figure 2 5B, it was concluded that the specially designed magic angle insert allows for the achievement of magic angle orientation with simila r precision. The magic angle insert developed by Konstantin Ulrich for studies of lateral diffusion of lipids in multibilayer stacks was adapted to the relevant studies of lateral diffusion with high field, high gradient PFG NMR. The new inserts are expe cted to function with similar precision. Magnetic Susceptibility Magnetic susceptibility can produce disturbing effects in our measurements. These effects are intensified as the strength of the magnetic field is increased. With the application of a stron g external magnetic field B 0 the susceptibility difference in the PFG NMR samples can yield additional magnetic field gradients, which are expected to be stronger for larger B 0 values. Similar diffusion experiments were conducted on multibilayer stacks o f lipids at three different B 0 strengths to verify the absence of such artifacts under our measurement conditions. Figure 2 6 shows examples of 1 H PFG NMR attenuation curves measured at different field strengths by the PFG NMR stimulated echo sequence for similar effective diffusion times and similar high and low temperatures. The effective diffusion time ( t eff ) and sample temperature were kept constant for the measurement of each curve. These studies were used to observe

PAGE 68

68 diffusion in a common ternary bi layer (DOPC/SM/Chol) under conditions where the system is expected to be compositionally homogeneous ( T > 298K) and heterogeneous ( T < 298 K). The details of diffusion results will be discussed in detail in Chapter 3. This section uses the results presen ted in Fig. 2 6 to confirm that magnetic susceptibility does not influence the data by comparing results obtained at different applied magnetic field strengths. The data in Figure 2 6 were obtained using the NMR spectrometers operating at a proton reson ance frequency of 750 and 400 MHz. For each attenuation curve, the initial, i.e. smallest gradient strength, was chosen in such a way that it was sufficiently small to ensure that there is no attenuation of the lipid signal and, at the same time, suffici ently high for suppression of any significant contribution of water to the measured signal. Such water suppression is possible because the diffusivity of water in the lateral direction is around 2 orders of magnitude larger than that of lipids. As a resu lt, even an application of relatively small gradients results in vanishing of the water signal under our experimental conditions. Suppression of the water signal is especially important for the measurements using the amplitude of the time domain signal (s ee solid and empty circles in Figure 2 6). For measurements at 400 MHz, the amplitude of the signal of time domains spectra were recorded and used to plot attenuation curves. Because of this method of processing, contributions of water and lipids to this time domain signal cannot be readily distinguished as it can be done on the basis of chemical shift difference. It is seen that the data in Figure 2 6, which were obtained at different B 0 strengths and for different types of data processing, i.e., proce ssing of either frequency domain or time domain spectra, show qualitatively and quantitatively similar behavior. Results from the fits of these types of attenuation plots also give similar

PAGE 69

69 Figure 2 6. Examples of attenuation curves at different appli ed magnetic field strength to check for magnetic susceptibility. The attenuation data was obtained by the PFG NMR stimulated echo sequence under the following conditions: (squares) the 1 H resonance frequency is equal to 750 MHz and = 1.89 ms and (circle s) the 1 H resonance frequency is equal to 400 MHz and = 1.35 ms. diffusion behavior. This implies that there is essentially no influence of the B 0 strength on the diffusion data. This observation is important in view of the possibility that our PFG NMR diffusion data could be distorted due to difference between the magnetic susceptibility of the glass plates, bilayers stacks, insert, and the gas phase in the PFG NMR samples. The existence of large susceptibility induced gradients would inevitably inter fere with our PFG NMR measurements. However, the results in Figure 2 6 show

PAGE 70

70 no evidence for such susceptibility effects because the diffusion data remain essentially the same for different B 0 values used in this work. The PFG NMR 13 interval sequence has also been used to obtain diffusion data for this type of sample. This sequence uses bipolar (alternating) pulsed field gradients in order to suppress susceptibility induced artifacts in diffusion experiments. The comparison of results (not shown) obtai ned using the PFG NMR 13 interval and STE sequences did not show any difference between results. Due to the coincidence in data at different B 0 field strengths as well as the coincidence between data obtained with these two sequences, we can conclude that under our experimental conditions the disturbing influence of the susceptibility effects on the diffusion data is negligibly small. It is also important to note the improvement in signal obtained at the high field. Low signal to noise at 400 MHz causes a significant amount of scatter in the data that is essentially eliminated with the increase in field strength to 750 MHz.

PAGE 71

71 CHAPTER 3 DIFFUSION AND LIPID EXCHANGE INSIDE AND BETWEEN LIPID MEMBRANE DOMAINS Studies of Lipid Bilayers with Large Liquid Orde red Domains The main purpose for studies of lateral diffusion in bilayers consisting of a ternary mixture of DOPC, sphingomyelin, and cholesterol was to demonstrate that it is feasible to adapt the PFG NMR technique using high field (17.6 T) and high gradi ents strengths (up to 30 T/m) for studies of lateral diffusion in model membranes. Diffusion and structural studies of bilayers and vesicles formed from equimolar mixtures of DOPC/SM/CHOL have been reported extensively in the literature which gives an app ropriate comparison for the verification of the new technique. 31,35,90 Application of high field NMR allows for measurements of samples with superior signal to noise ratio which can be crucial when collecting data from samples that have relatively weak NMR signal such as that of lipids in bilayers. The ratio of signal to noise is expected to increase with increasing applied field strength according to NMR theory. All data from this point on was collected at a hi gh field of 17.6 T corresponding to a proton frequency of 750 MHz. Application of high gradients allows for the use of sufficiently short diffusion times under the conditions of the narrow pulse approximation, which requires that the gradient duration is small in comparison to the diffusion time. Short diffusion times correspond to short observed displacements. As a result, application of strong gradients leads to the possibility of diffusion measurements over a wide range of length scales including subm icrometer length scales. The following discussion presents results of diffusion studies for the case in which domains are much larger than the experimentally measured lipid displacements. In membranes composed of a ternary

PAGE 72

72 mixture of DOPC/SM/Chol, domains have been observed to be as large as 10 m. 31,35 The largest displacement probed is on the order of 1 m. In this case, diffusion behavior is independent of diffusion time. Figure 3 1. 1 H NMR spectra of DOPC/SM/Chol multibilayer stacks measured by the PFG NMR stimulated echo sequence at 750 MHz for different values of the gradient amplitude ( g ) at T = 303.2 K. The inset shows the spectra obtained using the larger gradient strength scaled such that the intensities of the CH 3 lines match. Figure 3 1 shows examples of 1 H NMR spectra of the oriented multibilayer stacks of DOPC/SM/Chol measured by the stimulated echo PFG NMR sequence at 303.2 K under the measurement conditions used for diffusion studies at high field and high gradient strengths. The spec tra are from measurements at an initial gradient strength of

PAGE 73

73 1.96 T/m (solid) and an intermediate gradient strength of 14.46 (dashed). The spectra in Figure 3 1 show that under the measurement conditions at 750 MHz the spectral resolution allows distingui shing the NMR lines corresponding to CH 3 CH 2 and H 2 O. Each spectrum shows partially overlapping lines of the CH 2 groups of the hydrocarbon chains and of the CH 3 groups of the lipid headgroups at around 1 and 3 ppm, respectively. This signal originates from the phospholipids. No signal from CHOL can be observed due to the short T 2 NMR relaxation times of this rigid molecule. 90 A line at around 4.7 ppm is assigned to a small amount of normal water present in the sample. The smallest gradient strength ( i.e. 1.96 T/m) was chosen in such a way that it was sufficiently small to ensure that there is no attenuation of the lipid signal and at the same time, sufficiently high for suppression of any significant contribution of water to the measured signal. The spectra were obtained at a temperature well above the miscibility transition temperature, T m for this sample. Above the T m the bilayer is expected to be one homogeneous phase with a single l ipid diffusivity. The inset of Fig. 3 3A presents the two spectra superimposed where the spectrum obtained using the intermediate gradient strength is scaled such that the intensities of the CH 3 signals are equivalent. The coincidence in signal shape of the two spectra is nearly exact except for a small difference corresponding to the loss of the water line. This change is minor and does not significantly affect the measurement of lipid self diffusion. Figure 3 2 shows the examples of 1 H PFG NMR attenu ation curves. The attenuation data was measured by the PFG NMR stimulated echo sequence for different effective diffusion times at high and low temperatures at 750 MHz. During the measurement of each curve, these

PAGE 74

74 parameters ( t eff and T ) were kept constan t and the initial, i.e. smallest gradient strength, was chosen to be sufficiently small to ensure that there is no attenuation of the lipid Figure 3 2. PFG NMR attenuation curves for DOPC/SM/Chol samples obtained at three diffusion times at low and hi gh temperature at 750 MHz. At high temperatures, i.e. T > 298.2 K, the bilayers are expected to be homogeneous. At temperatures below 298.2 K, liquid ordered domains are expected to form. Analysis of the data shows that at the high temperature, there i s a single ensemble of lipids with one diffusion coefficient. To the contrary, at low temperatures there are two ensembles of lipids diffusing with different diffusivities. These two ensembles correspond to lipids diffusing inside and outside of liquid o rdered domains. These domains are large in comparison to the length scales of lipid displacements probed in the experiments. signal and, at the same time, sufficiently high for suppression of any significant contribution of water to the measured signal. In the presentation of Figure 3 2, the

PAGE 75

75 attenuation curves obtained for different diffusion times are expected to coincide if the diffusivity(ies) of the probed lipids remain the same with increasing or decreasing diffusion time and the corresponding value s of the mean square displacement. The data in this figure indicate that there is essentially no dependence of the attenuation curves and of the corresponding diffusion behavior on diffusion time. Such results were obtained for all measured temperatures. Fitting attenuation curves by Eq. 18 has shown that for temperatures lower than T = 298 K, the two exponential fit (Eq. 18 with n = 2, solid line) produces better results than the one exponential fit (Eq. 18 with n = 1, dashed line). At the same, time f or temperatures higher than T = 298 K, it has been sufficient to use the single exponential curves (solid line) to fit the experimental data satisfactorily (Fig. 3 2). In the latter case, the two exponential fit either produced two diffusivities, which we re identical within the uncertainty of the fitting procedure, or it gave an extremely small value (several percent) for one of the fractions, which was comparable to the fitting error. T = 298 K corresponds to the transition temperature for the liquid dis ordered liquid ordered phase coexistence, T m. Above this temperature, the bilayer is expected to be structurally homogeneous, i.e. no domains are formed. Monoexponential behavior corresponds to a single diffusivity for all lipids contributing to the me asured signal ( i.e. DOPC and SM). Figure 3 3 shows an Arrhenius type plot of the temperature dependence of diffusivities, which result from fitting the attenuation curves for different values of the constant magnetic field. There is agreement between d iffusion data collected at the three B 0 field strengths. Scatter in the diffusivity values at temperatures T < T m when two exponential fit of the attenuation curves becomes necessary is mostly associated

PAGE 76

76 with signal to noise limitations of measurements at the two lower proton resonance frequencies (see Fig. 2 6). These limitations are especially pronounced at large signal Figure 3 3. Lateral diffusivities of lipids in DOPC/SM/Chol multibilayer stacks plotted as a function of inverse temperature. Diff usivities are obtained from two exponential fit (filled symbols) and monoexponential fit (empty symbols) of PFG NMR attenuation curves measured at a proton resonance frequency of 125, 400, and 750 MHz. Also shown for comparison are diffusion coefficients (*) recorded by fluorescence correlation spectroscopy (FCS) in lipid membranes with the same composition (from ref 89). The solid line shows the best fit of the diffusivities measured at T > T m using the Arrhenius law with E a = 91kJ /mol. attenuation corresponding to diffusion in the liquid ordered phase. In comparison, the signal to noise ratio of the 1 H PFG NMR measurements at 750 MHz was appreciably

PAGE 77

77 better. It is important to note that no systematic changes in the measured diffusi vities were observed with increasing proton frequency. The results in Figure 3 3 were obtained with several different bilayer samples prepared in two different countries. Hence, under these circumstances, the agreement between the data in the figures can be considered to be satisfactory. Under these measurement conditions, the characteristic sizes of liquid ordered domains are expected to be in the range of much greater than 1 micron ( i.e., much larger than the root mean square displacements of lipids (E q. 5) for all effective diffusion times used). Hence, the possible influence of diffusion restrictions by the domain boundaries and of molecular exchange between different domains on the measured diffusivities can be ruled out. This conclusion is in agre ement with the observations that the diffusivities measured at each temperature do not depend on diffusion time. The values of diffusivities obtained by PFG NMR with high field and high gradient strengths in this section are in good agreement with those obtained using FCS 31 and PFG NMR with conventional gradient strenghts 90 in lipid membranes with the same or similar composition. This is demonstrated by the comparison of data from PFG NMR studies at high field and high gradient strengths and the previously reported FCS results in Figure 3 2. O bservation of Lipid Exchange Between Domains and Their Surroundings in Lipid Bilayers with Small Liquid Ordered Domains for Exchange Studies Domains on the order of 1 m or smaller, which is significantly smaller than those reported for other systems such as DOPC/SM/Chol discussed in the previous section, have been observed for model lipid membranes composed of a ternary mixture of DOPC/DPPC/Chol. 29,46 Smaller domains are often considered to be a better representation of lipid rafts and can be used to obtain new fundamental information

PAGE 78

78 about lipid dynamics in cell membranes. It is importan t to note that in comparison with the previous studies, PFG NMR at high field and high gradient strengths allows for the characterization of diffusion behavior under conditions of the narrow pulse approximation on a length scale as small as 100 nm, i.e. a much smaller length scale than in the previous similar measurements. The technique is then quite attractive for those interested in studying diffusion restrictions and inter domain exchange which can m). Diffusio n restrictions can be caused by the presence of transport barriers at the domain boundaries. High field, high gradient PFG NMR studies of time dependent diffusion behavior can give qualitative and quantitative information about the size of the domains, mo lecular exchange between domains and the surrounding disordered environment, and the permeability of the domain boundaries. Figure 3 4 shows examples of 1 H NMR spectra of the oriented stacks of bilayers measured by the stimulated echo PFG NMR sequence unde r the measurement conditions used for diffusion studies at high field and high gradient strengths. Both Figure 3 4A and 3 4B show spectra from measurements at an initial gradient strength (solid) and an intermediate gradient strength (dashed). Much like Fig. 3 1, each spectrum shows partially overlapping lines of the CH 2 groups of the hydrocarbon chains, the CH 3 groups of the lipid headgroups, and the normal water at around 1, 3 and 4.7 ppm, respectively. The smallest gradient strength ( i.e. 0.33 T/m) w as chosen in such a way that it was large enough to suppress most of the water signal but sufficiently small so that there was no attenuation of lipid signal at that gradient amplitude.

PAGE 79

79 Figure 3 4. 1 H NMR spectra of DOPC/DPPC/Chol multibilayer stacks measured by the PFG NMR stimulated echo sequence for different values of the gradient amplitude ( g ) at T = 307.8 K (A) and T = 296.3 K (B) at 750 MHz. For each set of spectra, the inset shows the spectra obtained using the larger gradient strength scaled such that the intensities of the CH 3 lines match.

PAGE 80

80 Figure 3 4A shows spectra obtained at T = 307.8 K, a temperature well above the miscibility transition temperature, T m for this sample, at gradient amplitudes of 0.33 and 12.13 T/m. The inset of Fig. 3 4A presents the two spectra superimposed where the spectrum obtained using the intermediate gradient strength is scaled such that the intensities of the CH 3 signals are equivalent. The superposition of spectra shows the same coincidence in shape of spectra as in Fig. 3 1 which would be expected for a homogeneous bilayer. Figure 3 4B shows spectra obtained at T = 296.3 K using gradient amplitudes of 0.33 and 15.73 T/m. The intermediate gradient strengths at each temperature correspond to approximately the sa me attenuation of signal. At lower temperatures, the diffusivities of lipids are smaller requiring larger gradient amplitudes to reach the same level of attenuation as that at higher temperatures. In the inset of Figure 3 4B, the two spectra are shown wi th the spectrum obtained using the intermediate gradient strength scaled such that the intensities of the CH 3 signals are equivalent. Unlike Fig. 3 4A, the spectra show that the shapes of the NMR spectra depend on the applied gradient strength. The line corresponding to the CH 2 groups appears to attenuate at a larger rate than the line for the CH 3 groups. This occurs because each spectrum obtained at this temperature is a superposition of signals coming from two components, a slow and a fast diffusion co mponent 90 corresponding to diffusion inside the l o and l d phases, respectively. 46,88 The l o domains are enriched in DPPC and characterized by a tighter packing and lower diffusivity of lipid s in comparison to the DOPC enriched l d phase. The NMR lines of CH 2 and CH 3 groups shown in Fig. 3 4B have different contributions from both phases. The change in shapes of the spectra that is seen in Fig. 3 4B is a

PAGE 81

81 consequence of a larger decrease of th e contribution from the phase with the highest diffusivity, i.e. l d phase, with increasing gradient strength. The spectra in Fig. 3 4 show that in all cases the amplitude of the choline CH 3 line is larger than the amplitude of the CH 2 line despite the fa ct that fewer protons contribute to the former line than to the latter. This results from the influence of T 2 NMR relaxation. 90 Under the measurements conditions of the PFG NMR stimulated echo sequence, signal amplitude is reduced due to T 2 NMR relaxation by a factor, exp( 2 / T 2 ). As already mentioned above, in lipid bilayers the rate of T 2 NMR relaxation is enhanced by proton dipole dipole interactions. Protons in the hydrocarbon chains of l ipids are expected to have shorter T 2 NMR relaxation times in the l o phase than in the l d phase due to increased packing order in the former phase. 88 In comparison to protons in the hydrocarbon chains, protons in the headgroups of lipids residing in both l o and l d phases have a higher flexibility with respect to reorientations. Hence, T 2 times of these protons are less sensitive to dipole dipole i nteractions resulting in larger T 2 values. T 2 NMR relaxation times were estimated by performing a series of STE experiments with g 0 T/m and varying the value of 1 the time between the first two pulses. These values were found to be on the order of ~ 6 ms and ~12 ms, for CH 2 and CH 3 respectively. Therefore the choline CH 3 line is used for obtaining diffusio n data at all temperatures. For selected experiments, the data was treated using the amplitudes of the CH 2 line in the attenuation plots in order to verify that diffusion coefficients, which were obtained from fitting the data by Eq. 18 would agree with t he corresponding data obtained using the CH 3 line. The only difference between the treatment of the two lines is the phase fractions obtained since the measured signal of the l o phase is more significantly

PAGE 82

82 reduced by T 2 While signal amplitude is reduced for both lines, the CH 3 line is a better representative of the signal unperturbed by the T 2 NMR relaxation process. Diffusion Results Figure 3 5 shows examples of 1 H PFG NMR attenuation curves measured by the PFG NMR stimulated echo sequence for different effective diffusion times at five different temperatures at a proton frequency of 750 MHz. Fitting the attenuation curves in Fig. 3 5A by Eq. 18 has shown that for T = 307.8 K, it is sufficient to use the one exponential curve (Eq. 18 with n = 1) in orde r to fit the experimental data satisfactorily. Single exponential behavior corresponds to a single diffusivity for all lipids contributing to the measured signal. In the presentation of Fig. 3 5, the curves obtained for different diffusion time are expec ted to coincide if the diffusivity of the probed lipids remains the same with increasing or decreasing diffusion time and the corresponding values for mean square displacement. The data in this Fig. 3 5A indicate that there is no dependence of the attenua tion curves and of the corresponding diffusion behavior on diffusion time at 307.8 K. Hence, it can be concluded that all probed lipids diffuse with the same diffusivity, which is independent of diffusion time in the measured range. Figure 3 5A displays o ne curve obtained by a sequence known as the PFG NMR stimulated echo longitudinal encode decode sequence (STE LED) measured with t eff = 4.24 ms. In comparison to the traditional PFG NMR STE sequence, this sequence has an additional delay before the data a cquisition to allow for a decay of eddy currents. 114 It is possible not only to compare results obtained using the PFG NMR STE and STE LED sequences to check for influence of eddy currents but a lso to obtain results using much smaller effective diffusion time (as low as 4.24 ms). In measurements with the former sequence, all essential parameters such as the total duration of the gradient

PAGE 83

83 Figure 3 5. Examples of diffusion attenuation curves obtained for DOPC/DPPC/Chol by the PFG NMR stimulated echo sequence at T = 307.8 K (A), T = 301.3 K (B), T = 300.7 K (C), T = 298.8 K (D), and T = 296.3 K (E) at 750 MHz. All attenuation curves were obtained by measuring the intensity of the choline spect ra. In part A, the solid line is a single exponential fit of all data in the figure. In parts B E, solid lines are individual two exponential fits of each curve using Eq. 18 with n = 2. The dashed lines show monoexponential curves corresponding to the i nitial decay of the measured attenuation curves.

PAGE 84

84 pulse, effective diffusion time, and temperature were kept the same or similar as in the measurements with the later sequence. As expected, no significant changes in the initial slope of attenuation curves (not shown) or the related effective diffusivity were observed when using the PFG NMR STE LED sequence. Figure 3 5E is a collection of attenuation curves similar to that shown in Fig. 3 5A for experiments conducted at 296.3 K, a temperature well below the T m for this mixture. These curves show pronounced deviations from the monoexponential behavior prescribed by Eq. 18 with n = 1 (dashed line). At the same time, fitting the attenuation curves by Eq. 18 with n = 2 produces satisfactory results (solid lines ). This biexponential behavior indicates the existence of two ensembles of lipids with different diffusion coefficients. The smaller diffusion coefficient can be assigned to the l o phase and the larger diffusion coefficient to the l d phase. For any part icular phase, the diffusivities of all lipid species present in that phase in multi component bilayers can be expected to be essentially the same or similar on the basis of the results of previous experimental studies. 87,115 This expectation is also confirmed by the data in Fig. 3 5A showing that the diffusion behavior is the same for all lipids contributing to the measured choline signal ( i.e. DOP C and DPPC). Figures 3 5B, 3 5C, and 3 5D show qualitatively similar attenuation curves measured at 301.6, 300.7, and 298.9 K, respectively. As in Fig. 3 5E, there is deviation from a single exponential fit of the initial slope (dashed lines) indicating that a two exponential fit using Eq. 18 with n = 2 (solid lines) provides a more appropriate description of the measured data. As the temperature approaches the T m for this mixture, the extent of deviation from the single exponential behavior becomes smal ler

PAGE 85

85 Table 3 1. Results from fitting of the PFG NMR attenuation curves of DOPC/DPPC/Chol at different temperatures as seen in Figure 3 5 by Eq. 18. T = 307.8 K t eff p o D o 10 12 p d D d 10 12 ms m 2 /s m 2 /s 8.24 1 4.7 0.5 14.24 1 4.7 0.5 29.2 4 1 4.7 0.5 59.24 1 4.6 0.5 179.24 1 4.5 0.4 T = 301.6 K t eff p o D o 10 12 p d D d 10 12 ms m 2 /s m 2 /s 8.24 0. 24 0.07 1.6 0.2 0.76 0.08 3.5 0.3 14.24 0.19 0.08 1.6 0.2 0.81 0.08 3.3 0.3 29.24 0.14 0.03 1.4 0.1 0. 87 0.09 3.2 0.3 59.24 0.11 0.04 1.3 0.3 0.89 0.09 3.1 0.3 179.24 0.02 0.02 1.0 0.4 0.97 0.10 2.9 0.3 T = 300.7 K t eff p o D o 10 12 p d D d 10 12 ms m 2 /s m 2 /s 8.24 0.69 0.11 1.8 0.2 0.31 0.11 4.3 0.8 14.24 0.62 0.12 1.8 0.2 0.38 0.12 4.2 0.8 29.24 0.52 0.18 1.6 0.2 0.48 0.18 3.8 0.7 59.24 0.41 0.14 1.5 0.2 0.59 0.14 3.3 0.5 179.24 0.21 0.15 1.2 0.5 0.79 0.15 2.8 0.3 239.24 0.17 0.12 1.1 0.4 0.83 0.12 2.8 0.3 T = 298.9 K t eff p o D o 10 12 p d D d 10 12 ms m 2 /s m 2 /s 8.24 0.73 0.07 1.7 0.2 0.27 0.03 4.1 0.4 14.24 0.61 0.08 1.6 0.2 0.39 0.08 3.6 0.6 59.24 0.49 0.05 1.5 0.2 0.49 0.05 3.4 0.3 179.24 0.18 0.08 1.1 0.2 0.82 0.08 2.6 0.3 239.24 0.15 0 .09 1.1 0.2 0.85 0.09 2.7 0.3 T = 296.3 K t eff p o D o 10 12 p d D d 10 12 ms m 2 /s m 2 /s 14.24 0.70 0.07 1.2 0.1 0.30 0.03 4.0 0.7 29.24 0.63 0.06 1.1 0.1 0.37 0.04 3.7 0.4 59.24 0.57 0.06 1.1 0.1 0.43 0.06 3.1 0.3 119.24 0.53 0.05 1.1 0.1 0.47 0.05 3.3 0.3 179.24 0.44 0.09 1.0 0.1 0.56 0.09 2.8 0.3 239.24 0.42 0.04 1.0 0.1 0.58 0.06 3.1 0.3

PAGE 86

86 (compare solid and dashed lines). This change could be a consequence of a change of diffusion coefficients phase fractions, or a combination of the two. There is also a noticeable change in diffusion behavior with increasing effective diffusion time. Table 3 1 reports the best fit results for the curves in Fig. 3 5, i.e. diffusivities and the corresponding fractions in l o and l d phases. The error of data in the table has contributions from a number of sources including uncertainties associated with the calibration of gradient strength, sample preparation, the reproducibility of the measured PFG NMR attenua tion curves, and the fitting of data using Eq. 18. For most measurements, the total error did not exceed 10%. In some cases, the reported uncertainty was larger than 10% due to a larger error associated with fitting the data by Eq. 18. Time Dependent D iffusion Behavior One very significant characteristic of the data in Figure 3 5 is the manner in which diffusion behavior changes with effective diffusion time at temperature below T m (see Fig. 3 5B thru 3 5E). Effective diffusion times are directly relat ed to the root mean square displacements of lipids according to the Einstein relation for two dimensional diffusion. Hence, the observed changes in the diffusion behavior can be directly attributed to the changes in the lipid displ acements. If the domains are much larger than the lipid displacements during the experimental observation time ( t eff ) or do not exist at all, the PFG NMR attenuation curve for different t eff values are expected to coincide with each other and give the sam e values of diffusivity within experimental error (see Fig. 3 5A). In the case that the size of domains is comparable to the lipid

PAGE 87

87 Figure 3 6. Comparison of diffusion behavior at different effective diffusion times for experiments conducted on DOPC/D PPC/Chol at T = 307.8 K (A), T = 301.6 (B), T = 300.7 (C), T = 298.9 K (D), and T = 296.3 K (E). The amplitudes of the columns show the phase fractions (left vertical axis) of the l o (red) and l d (blue) phases while the amplitude of the striped columns co rrespond to the diffusivities (right vertical axis) of the phases of solid columns on which they are superimposed.

PAGE 88

88 displacements, diffusion behavior is expected be dependent on the effective diffusion time. 116 Figure 3 6 illustrates diffusion behavior at small (14.24 ms) and large (179.24 ms) values of t eff for each temperature (below T m ) reported in Fig 3 5. In each case, the fraction of molecules attributed to the diffusion inside l o domains decreases with an increase in t eff which indicates an existence of exchange between the l o and l d phases. The data in Fig. 3 6 indicate that at the larger t eff most lipids diffuse either in the l d phase or diffuse a fraction of the diffusion time in the l o domains and the remaining fraction of diffusion time in the l d phase. The diffusivity values of lipids in the l d phase is ~2 3 times larger than that for the l o phase (Table 3 1). for this reason, lipids that spend even a small fraction of the observation time in the l d phase will be attributed to the l d phase fraction because their overall effective diffusivity will be closer to that of the l d rather than t he l o phase. The experimental observation that with increasing t eff the decrease in the fraction of lipids attributed to the l o phase is larger at T = 301.6 K than at lower temperatures (Fig. 3 6) indicates that the extent of exchange between the two phas es is greater at the former temperature. Relaxation Effects It is important to note that, in addition to the lipid exchange between different types of domains, the observed dependence of the diffusion behavior on diffusion time (Fig. 3 6) can be caused by an influence of the characteristic longitudinal NMR relaxation ( T 1 relaxation) on the measured PFG NMR signal. Such influence can arise if the T 1 times are sufficiently short and different for the proton signal of the choline groups of lipids located in d ifferent phases. In this case, the contribution to the measured PFG NMR STE signal from lipids with smaller T 1 would decrease with increasing diffusion time

PAGE 89

89 Figure 3 7. T 1 NMR relaxation curves for DOPC/DPPC/Chol bilayers obtained using the PFG NMR ST E sequence with g < 1 T/m for the range of relevant temperatures. 2 denotes the delay between the second and third pulses of the sequence. The delay between the first and second pulses of the PFG NMR STE sequ ence was kept constant at 3.65 ms.

PAGE 90

90 2 t eff ) relative to that corresponding to larger T 1 Figure 3 7 gives T 1 NMR relaxation curves measured for the line of the CH 3 choline group. The measurements were performed by the stim ulated echo sequence for the same temperature range as that used in diffusion measurements. A series of one dimensional PFG NMR STE experiments were carried out at each temperature using a gradient amplitude which was sufficiently small to ensure that the re was no attenuation of the lipid signal due to diffusion but sufficiently large to suppress water signal. The delay ( 2 ) between the second and third /2 radiofrequency pulses in the sequence was varied over a range that corresponds to the range of t eff values used in the PFG NMR STE diffusion measurements. During 2 signal amplitude is reduced by T 1 NMR relaxation by a factor, exp ( 2 / T 1 ). The normalized amplitude of the choline line was plotted against 2 along with the curve which were obtained by fitting each set of data with either a biexponential or triexponential curve. The T 1 NMR relaxation curves show non mo noexponential behavior at all temperatures including the highest temperature corresponding to the compositionally homogeneous bilayers (Fig. 3 7). For highly resolved spectra of lipid bilayers in which lines of different proton types ( i.e. choline, methy lene, etc.) do not overlap, monoexponential T 1 curves are expected for each type of protons. 117,118 Each type of protons is capable of having unique relaxation behavior. Under our experimental conditions, the lines of the choline and methylene groups, which are expected to have d ifferent T 1 values, show a significant overlap (Fig. 3 4). Hence, the non monoexponential behavior of the relaxation data at the highest temperature in Fig. 3 7 can be attributed to the existence of such overlap. With decreasing temperatures, the linewid th of both CH 3 choline and CH 2 groups become

PAGE 91

91 broader leading to a more pronounced overlap. 117 The deviation from monoexponential behavior is therefore expected to become larger as temperature is decreased from 307.8 to 296.3 K. This expectation is in agreement with the data in Fig. 3 7. In addition to the existence of signal overlap discussed above, the non monoexponential behavior of the T 1 plots at low temperatures can be related to the inhomogeneous na ture of the lipid bilayers exhibiting the existence of l o and l d phases. Clearly, the T 1 NMR times for the CH 3 choline group can be different in different types of phases. The later can contribute to the observed deviations of the T 1 plots at low tempera tures from the monoexponential behavior (see discussion below). From the results in Fig. 3 7, it can be concluded that for the same t eff the influence of T 1 NMR relaxation on the measured PFG NMR signal becomes larger with decreasing temperature. This is in agreement with the results of studies showing an increase in T 1 NMR relaxation rates of lipids in the same or similar types of lipid bilayers as the temperature decreases. 69,117,118 In addition, the difference between the values of T 1 in different phases can become more pronounced at smaller temperatures. The later is related to the expectation that many properties of the l o and l d phases, including NMR relaxation times, become more similar as the temperature is increased to approach the T m In agreement with this expectation, the deviations of the T 1 NMR relaxation curves in Fig. 3 7 from the monoexponential behavior become slightly less pronounced with increasing temperature. The discussion above suggests t hat the influence T 1 on the t eff dependence of the fractions of lipids with different diffusivities has to be smaller at the temperatures near the T m At the same time, the results in Table 3 1 and Figure 3 6 show that the t eff dependence of the fractions of lipids with different diffusivities is much

PAGE 92

92 stronger at larger temperatures than at smaller temperatures. Hence, we can conclude that the possible disturbing influence of T 1 NMR relaxation cannot be of large significance for the observed t eff dependen cies of the diffusion behavior at temperatures near the transition temperature. As a result, our experimental data at these temperature(s) can be used to obtain quantitative information on the exchange of lipids between different types of domains and on t he domain properties. In particular, we have attempted to estimate the permeability of the domains boundaries for diffusing lipids as well as the sizes of l o domains. Extracting Quantitative Information from the Lipid Exchange Data The discussion thus far concludes that time dependent diffusion behavior observed for DOPC/DPPC/SM multibilayer stacks is for the most part a consequence of the lipid exchange between the liquid ordered domains and the surrounding liquid disordered environment. Lipid exchange o ccurs over times scales comparable to the experimental effective diffusion times. Accordingly, this is indicative that the sizes of the domains are comparable to the length scales of the lipid displacements during the diffusion times used. In this case, the domain boundaries can act as barriers to lateral diffusion during measurements. Time dependent diffusion behavior studied in the presence of confining geometries can give important information about the domain itself. Mitra and colleagues 112,119 121 proposed a method which uses the short time limit of the diffusion data recorded in the presence of transport restrictions to extract information about the spatial extensions of such restrictions. In particular, t he perimeter to surface area of restricting two dimensional domains can be obtained using this formulism. In this formulism, represents the diffusivity of molecules for the

PAGE 93

93 limiting case of short diffusion times when the diffusion is not influenced by the domain boundaries. In the short time limit, molecules only sense the presence of the domain boundaries if they are within a distance of from the walls. Those molecules represent only a small fraction of the to tal number of molecules in the domain. This fraction, S / V p where S is the external surface area of the domain and V p is Figure 3 8. The ratio of the time dependent effective diffusion coefficient of lipids in liquid ordered domai ns relative to completely unrestricted diffusion in those domains as a function of Fitting of the data at short effective diffusion times by Equation 19 gives the surface to volume ratio of the domains.

PAGE 94

94 the volume of the domain, is of the same order as the deviation of the propagator from that of Gaussian propagator describing unrestricted diffusion. 120 For the ensemble of molecules that started their trajectories inside the domains and did not attempt to diffuse through the domain boundaries by the time t, the ratio of the effective diffusion coefficient at time t and is given by the short time limit by Mitra et al. 120 (19) where D o is the time dependent diffusivity of molecules in the domain and d is the dimensionality of the space where diffusion takes place. For the considered lateral diffusion in lipid bilayers, d = 2. The experimental values for were obtained from a linear extrapolation of D o vs. (not shown) to t = 0. Such type of extrapolation is frequently used to determine diffusivity in the limiting case of small diffusion times. 52,53 For applications of Eq. 19 to time dependent diffusion behavior of lipids in liquid ordered domains, the higher order terms are conside red to be negligible and the S / V p ratio is taken as the ratio of the surface perimeter to the surface area. Figure 3 8 shows the plot of the ratio of D o to as a function of for the two temperatures nearest to the transition temperature where T 1 NMR relaxation times are minimal, 300.7 and 301.6 K. For each temperature, initial data points were fitted by Equation 19 to obtain S/V p Data corresponding to higher effective diffusion times were excluded from the fi t to hold the short time limit requirement. For these calculations it was assumed that the liquid ordered domains were circular in shape and there was no distribution of domain size over the bilayer. Table 3 2 gives the radius at each temperature and the

PAGE 95

95 associated uncertainty. Because only initial data points were used for the fit, the uncertainty associated with relatively large using this method. Table 3 2. The characteristic domain sizes as calculated by the fit of data in Figure 3 8 by Equation 19. 300.7 K 301.6 K R lo nm 523 330 406 250 Once significant concern associated with this method is related to the observation that Eq. 19 was derived for molecules that never left the original l o domain by a given time t. At the same time, the corres ponding ensemble of molecules considered in the experiment also includes molecules that left the domains but returned back to the same domain at the time t (in addition to the molecules that never left the domain). Another significant concern is associate d with the assumption used to derive Eq. 19, i.e. namely the absence of transport barriers at the domain boundaries. The discussion in the next section demonstrates that comparison of the PFG NMR data with the corresponding results of dynamic Monte Carlo simulation provides a better approach to get information on the domain sizes and the permeabilities of the domain boundaries. Dynamic Monte Carlo Simulations Complementary dynamic Monte Carlo (MC) simulations of molecular diffusion on square lattice wer e performed to extract information on the permeability of the domain boundaries and domain sizes from the measured PFG NMR data. Such simulations as well as the procedure of fitting PFG NMR results by the corresponding results of simulations to estimate p ermeabilities and domain sizes were recently reported in several papers. 122 125 Collaborative dynamic Monte Carlo simulations were performed by fellow graduate and undergraduate students, Amrish Menjoge and Robert Mueller, working in the research group of Sergey Vasenkov at the University of Florida. Briefly,

PAGE 96

96 in complete analogy with the lattice described in reference 122, the two dimensional simulation lattice used in this work consists of four square domains rep resenting domains of liquid ordered phase ( l o ) that are surround by the inter domain lattice representing the liquid disordered ( l d ) phase (Figure 3 9). The fractions of the lattice area occupied by the l o and l d phases in the simulation lattice were chos en to approximately correspond to those of the respective lipid fractions obtained from PFG NMR diffusion measurements in Table 3 1. The size of the simulation lattice shown in Fig. 3 9 was L L ( L = 262 l where l is the length of the elementary diffusion step) and the size of the l o domains was L o L o ( L o = 92 l ). Lipid diffusion was simulated by random walk on this lattice. Periodic boundary conditions were applied at the lattice boundaries. The probability of an elementary diffusion step inside the l o domain in the x or y direction is denoted as p lo and that through the domain boundary leading into the l d phase is denoted as p blo p lo / p blo elementary diffusion step inside the l d phase in the x or y direction is denoted as p ld and that through the domain boundary leading into the l o is denoted as p bld The experimentally observed difference between diffusivities in the l o and l d phases was taken into account by choosing p ld / p lo = 2 resulting in p bld / p blo = 2. The starting points of 10,000 random walkers were randomly selected on the lattice. The N step walks ( N 10,000) were then generated for each random walker. The final simulations results reported here were the averages over 3 lattices with different configurations of the starting points. The quantities recorded in the simulations were the relative number of labeled random walkers, i.e. those that were inside an l o domain at time t = 0 and were

PAGE 97

97 Figure 3 9. Two dimensional simulation model for lipid bilayer. The periodic structure is organized by repetition of the simulation lattice of length L The square domains of length L o represent the liquid ordered phase ( l o ), and the surrounding inter domain latticed represents the liquid disordered phase ( l d ). The inset shows various jump probabilities and the elementary diffusion step used in the simulatio n model. 126 still inside the same domain at a later time t ( N(t) / N 0 where N 0 = N(t= 0 ) ), as well as normalized effective diffusivity of these random walkers, where is the diffusivity inside l o domains at sufficiently small time when the domain boundaries do not influence diffusion behavior. The diffusion time is definite as t = N where is the duration of the el ementary diffusion step. The effective diffusivity D o is calculated from the Einstein equation Eq. 5. Based on the formulism discussed in Ref. 122, the probability p blo can be used for calculation of the permeability of the domain boundaries for molecule s ( ) as (20)

PAGE 98

98 Varying p blo is thus equivalent to varying in our simulations. Figure 3 10 shows the results of fitting experimental data for T = 300.7 K with the corresponding results o f the dynamic Monte Carlo simulations outlined above. Such fitting procedure was recently introduced to determine surface permeability of nanoporous particles. 1 25 Fig. 3 10 plots the ratio of the effective diffusivity of lipid molecules residing in l o domains ( D o ) to the as a function of diffusion time. The simulated curves were obtained for the values of the permeability of domain boun dary, corresponding to a range between the limiting case when the domain boundary provides no transport barriers for lipid molecules ( = 1.1 10 3 m/s in Fig. 3 9), and a s almost two orders of magnitude smaller ( = 2.0 10 5 m/s in Fig. 3 9). Fig. 3 9A indicates that there is only an insignificant difference between the simulation results for different barrier permeabilities used These differences are especially small for values of the ratio close to 1. Fitting the initial experimental data points ( i.e. those at small times when does not affect D o ) to the simulated curves in Fig. 3 10A was used to determine the correlation between the experimental diffusion time and the diffusion time used in the simulation. The corresponding correlation between the length scales in the experiment and simulation was obtained by comparing the absolu te values of diffusivities at a fixed time. Fig. 3 10B shows a plot of the relative number of molecules which at initial time ( t = 0) have started their trajectories inside l o domains and were outside these domains by the time shown on the horizontal axis of the figure. Such dependencies are often referred to as tracer exchange curves. Since the relationship between the diffusion time in the experiment and simulation was already determined in Fig. 3

PAGE 99

99 paramet ers that can be used to adjust the correspondence between the experimental and simulation data in Fig. 3 10B. In contrast to the data in Fig. 3 10A, there is a 10B. It is seen in Fig. 3 10B that within the experimental uncertainty, the experimental data agrees with the simulation results obtained for 10 4 m/s. Hence, we estimate that the permeability of the l o domain bo undary to be equal to or greater than 5.0 10 4 m/s at 300.7 K. Using the relationship between the length scales in the experiment and simulations as well as the domain size used in the simulations, we estimate the domain radius ( R lo ) to be 930 290 nm at 300.7 K. These estimates for and R lo were obtained assuming that all domains are circular and there is no distribution over domain sizes as well as over permeabilities of the domain boundaries and intra domain diffusivities. The size of the square domains used in simulations was used to determine Table 3 3. Domain Properties at Temperatures Near T m 300.7 K 301.6 K m/s 10 4 10 4 R lo nm 930 290 73 0 310 the radius of the corresponding circular domains by equating the perimeter to area ratios for both domain shapes. Similar treatment of the experimental data recorded at 301.6 K resulted in 10 4 m/ s and R lo = 730 310 nm (Table 3 3). Uncertainties associated with the domain radius using this method were smaller in comparison to the previous Mitra formulism as fits were obtained using all data points instead of those obtained at short times.

PAGE 100

100 Fig ure 3 10. Examples of fitting experimental data (points) by the results of dynamic Monte Carlo (MC) simulations (lines). The data is fit for the following two dependencies: (A) time dependence of the ratio of the effective diffusivity of molecules in th e liquid ordered domains to the corresponding unrestricted diffusivity in these domains ( i.e. the diffusivity for the limiting case of small times) and (B) time dependence of the normalized fraction of molecules ( ) that started their trajectory inside t he domains but ended their trajectory outside of domains. Experimental data was obtained at 300.7 K. The results of MC simulations are shown for different permeability of the domain boundaries ( ).

PAGE 101

101 PFG NMR at high field and high gradient strength was use d to directly monitor the exchange of lipids between l o and l d phases that coexist in ternary lipid bilayers. This experimental option provides the possibility to monitor diffusion over length scales which are comparable to the size of l o domains in membr anes. Exchange was observed to occur over the time scales of the experimental diffusion times and was found to become more pronounced as the bilayers temperature was increased towards the miscibility transition temperature. The latter can be explained by an increase in diffusivity and some decrease in the characteristic domain sizes with an increase in temperature. Comparison of the experimental data and the corresponding results of dynamic Monte Carlo simulations allowed for the estimation of domain boun dary permeability and domain size at temperatures near the transition temperature. The observed size of domains is still quite large in comparison to the minimum displacement that can be observed with the proposed experimental setup. It is then quite pos sible and would be very interesting to use this technique to study the exchange of lipids between domains in systems that form even smaller, biologically relevant l o domains.

PAGE 102

102 CHAPTER 4 SIGNIFICANCE AND FUTURE DIRECTIONS The observation and analysis of li pid exchange between the liquid ordered domains and the surrounding liquid disordered phases of model lipid bilayers creates a new direction for studies aiming to understand the roles of lipid rafts in eukaryotic cell membrane. Characterizing the dynamics of lipids in the presence of domains is especially important when one considers the relationship between lipids diffusing inside domains with the transport of other domain associated molecules. The application of high field, high gradient pulsed field gr adient NMR allowed for the possibility to measure lateral diffusion over a broad range of mean square displacements, including displacements much smaller than those that previously were technically possible to record in model membranes using similar techni ques. The application of PFG NMR with high gradient strengths to observe lipid dynamics in multibilayer stacks required a significant amount of attention to development. This work shows that it is not only feasible to perform diffusion studies of lipids in bilayers with high field, high gradient PFG NMR but also to monitor lipid exchange between different membrane domains. Here, time dependent diffusion behavior was used to extract information about the characteristic permeability of the domain boundarie s. The latter property was obtained experimentally for the first time for any types of lipid membranes. The technique developed and used in this work can be used to perform time dependent studies over much smaller length scales. Composition and temperat ure are two major factors that influence the size of liquid ordered domains. These factors can be modified to change the characteristic domain size in the membrane. High field, high gradient PFG NMR can then be used to further study lipid exchange in sma ller domains.

PAGE 103

10 3 This experimental technique can also be adapted to more advanced studies of model lipid membranes containing membrane proteins and/or peptides. Influence of reconstitution of domain associated peptides into lipid bilayers on lateral transpo rt in these bilayers can be studied using PFG NMR at high field, and high gradient strengths. Lipid bilayers reconstituted on solid supports haven also been used to investigate electrical properties, enzymatic reactions, and pathogen attack. The techni que developed in this work can be utilized for applications which served to characterize the effects of any one of these biological processes on the dynamics of membrane associated molecules. The advantages of a non invasion experimental technique capable of extracting information about lateral diffusion over a broad range of diffusion times with superior spatial and temporal resolution would serve to benefit investigations of how these processes influence the translational dynamics of membrane molecules a s well as the local structure of the membrane. Model lipid bilayers reconstituted on planar supports as wells as on the pore walls of nanoporous and mesoporous membranes offer biomimetic environments for the study of molecular dynamics of the membrane con stituents. This work shows that PFG NMR with high field, high gradient can be adapted for diffusion studies in planar membranes to give new details about lipid dynamics and membrane structural properties. It also demonstrates the potential of the techniqu e to observe dynamics in other types of model membrane as well as the influence of certain membrane associated molecules and/or biological processes. The last consideration for future work using PFG NMR with high field and high gradient strengths is the po tential applications for studies of live cells, in vivo While one of the main advantages of NMR is that there is no requirement for bulky labels ( i.e.

PAGE 104

104 dyes) which have been found to disturb the membrane, labels in the form of certain NMR sensitive isotop es such as 13 C and 19 F can be incorporated into membrane molecules and utilized in a non invasive manner. Observation of diffusion of such labeled molecules in vivo using PFG NMR with high field and high gradient strengths can be feasible.

PAGE 105

105 LIST OF REFERE NCES (1) Singer, S. J.; Nicolson, G. L. Science 1972 175 720. (2) Simons, K.; Toomre, D. Nat. Rev. Mol. Cell. Biol. 2000 1 31. (3) Pike, L. J. J. Lipid Res. 2009 50 S323. (4) Simons, K.; Ikonen, E. Nature 1997 387 569. (5) S imons, K.; van Meer, G. Biochemistry 1988 27 6197. (6) Fantini, J.; Garmy, N.; Mahfoud, R.; Yahi, N. Expert Rev. Molec. Medicine 2002 20 1. (7) Wielgosz, M. M.; Rauch, D. A.; Jones, K. S.; Ruscetti, F. W.; Ratner, L. AIDS Res Hum Retroviruses 2005 2 1 43. (8) Aloia, R. C.; Tian, H.; Jensen, F. C. Proc. Natl. Acad. Sci. U S A 1993 90 5181. (9) Hill, J. M.; Steiner, I.; Matthews, K. E.; Trahan, S. G.; Foster, T. P.; Ball, M. J. Med Hypotheses 2005 64 53. (10) Freeman, M. R.; Solomon, K. R. J. Ce ll Biochem 2004 91 54. (11) Zhuang, L. Y.; Kim, J.; Adam, R. M.; Solomon, K. R.; Freeman, M. R. J. Clin Invest 2005 115 959. (12) Zaremberg, V.; Gajate, C.; Cacharro, L. M.; Mollinedo, F.; McMaster, C. R. J. Biol. Chem. 2005 280 38047. (13) Brown, D. A.; London, E. Annu. Rev. Cell Dev. Biol. 1998 14 111. (14) Reitveld, A.; Simons, K. Biochim. Biophys. Acta. 1998 1376 467. (15) Sankaram, M. B.; Thompson, T. E. Biochemistry 1990 29 10670. (16) Bagatolli, L. A.; Gratton, E. Biophys. J. 2000 78 290. (17) Ahmed, S. N.; Brown, D. A.; London, E. Biochemistry 1997 36 10944. (18) Dietrich, C.; Bagatolli, L. A.; Volvyk, Z. N.; Thompson, N. L.; Levi, M.; Jacobson, K.; Gratton, E. Biophys. J. 2001 80 1417. (19) Korlach, J.; Schwille, P.; Webb, W. W.; Feigenson, G. Proc. Natl. Acad. Sci. USA 1999 96 8461.

PAGE 106

106 (20) Mukherjee, S.; Maxfield, F. R. Annu. Rev. Cell Dev. Biol. 2004. 20:839 66 2004 20 839. (21) Mayor, S.; Rao, M. Traffic 2004 5 231. (22) Binder, W. H.; Barragan, V.; Menger, F. M. Angew. Chem. Int. Ed. 2003 42 5802 (23) McConnell, H. M.; Vrljic, M. Annu. Rev. Biophys. Biomol. Struct. 2003 32 469. (24) Silvius, J.; Nabi, I. R. Molec. Membrane Biol. 2006 23 5. (25) de Almeida, R. F. M.; Loura, L. S.; Fedorov, A.; Prieto, M. J. Mol. Biol. 2005 346 1109. (26) Silvius, J. R. Biophys. J. 2003 85 1034. (27) Loura, L. S.; Fedorov, A.; Prieto, M. Biophys. J. 2001 80 776. (28) de Almeida, R. F. M.; Fedorov, A.; Prieto, M. Biophys. J. 2003 85 2406. (29) Veatch, S. L.; Kell er, S. L. Biophys. J. 2003 85 3074. (30) Feigenson, G. W.; Buboltz, J. T. Biophys. J. 2001 80 2775. (31) Kahya, N.; Scherfeld, D.; Bacia, K.; Poolman, B.; Schwille, P. J. Biol. Chem. 2003 78 28109. (32) Dietrich, C.; Volovyk, Z. N.; Levi, M.; Thom pson, N. L.; Jacobson, K. PNAS 2001 98 10642. (33) Wang, T. Y.; Silvius, J. R. Biophys. J. 2003 84 367. (34) Yuan, C.; Furlong, J.; Burgos, P.; Johnston, L. J. Biophys. J. 2002 82 2526. (35) Rinia, H. A.; Snel, M. M. E.; van der Eerden, J. P. J. M .; de Kruijff, B. FEBS Letters 2001 501 92. (36) Tokumasu, F.; Jin, A. J.; Feigenson, G. W.; Dvorak, J. A. Biophys. J. 2003 84 2609. (37) Dufrne, Y. F.; Lee, G. U. Biochim. Biophys. Acta. 2000 1509 14. (38) Melchior, D. L. Science 1986 234 1577 (39) Epand, R. M. Biophysical Chemistry 2007 126 197.

PAGE 107

107 (40) McMullen, T. P. W.; McElhaney, R. N. Biochim. Biophys. Acta. 1995 1234 90. (41) Sankaram, M. B.; Marsh, D.; Gierasch, L. M.; Thompson, T. E. Biophys. J. 1994 66 1959. (42) Collado, M. I .; Goni, F. M.; Alonso, A.; Marsh, D. Biochemistry 2005 44 4911. (43) Veatch, S. L.; Polozov, I. V.; Gawrisch, K.; Keller, S. L. Biophys. J. 2004 86 2910. (44) Aussenac, F.; Tavares, M.; Dufourc, E. J. Biochemistry 2003 42 1383. (45) Holland, G. P .; McIntyre, S. K.; Alam, T. M. Biophys. J. 2006 90 4248. (46) Polozov, I. V.; Gawrisch, K. Biophys. J. 2006 90 2051. (47) Lipid Rafts and Cavaolae: From Membrane Biophysics to Cell Biology ; Fielding, C. J., Ed.; Wiley VCH: Weinheim, 2006. (48) Brow n, D. A.; Rose, J. K. Cell 1992 68 533. (49) Lommerse, P. H. M.; Spaink, H. P.; Schmidt, T. Biochim. Biophys. Acta. 2004 1664 119. (50) Kenworthy, A. K.; Nichols, B. J.; Remmert, C. L.; Hendrix, G. M.; Kumar, M.; Zimmerberg, J.; Lippincott Schwartz, J. J. Cell Biology 2004 165 735. (51) McMullen, T. P. W.; Lewis, R. N. A. H.; McElhaney, R. N. Curr. Opin. Colloid In. 2004 8 459. (52) Kusumi, A.; Ike, H.; Nakada, C.; Murase, K.; Fujiwara, T. Semin. Immunol. 2005 17 3. (53) Munro, S. Cell 2003 115 377. (54) Glebov, O.; Nichols, B. J. Nat. Cell Biol. 2004 6 238. (55) Nichols, B. Nature 2005 436 638. (56) Lenne, P. F.; Nicolas, A. Soft Matter 2009 5 (57) Brugger, B.; Glass, B.; Haberkant, P.; Leibrecht, I.; Wieland, F. T.; Krausslich, H. G. PNAS 2006 103 2641. (58) Meder, D.; Moreno, M. J.; Verkade, P.; Vaz, W. L. C.; Simons, K. PNAS 2006 103 329.

PAGE 108

108 (59) Swamy, M. J.; Ciani, L.; Ge, M.; Smith, A. K.; Holowka, D.; Baird, B.; Freed, J. H. Biophys. J. 2006 90 4452. (60) Sengupta, P. ; Baird, B.; Holowka, D. Semin. Cell Dev. Biol. 2007 18 583. (61) Eggeling, C.; Ringemann, C.; Medda, R.; Schwarzmann, G.; Sandhoff, K.; Polyakova, S.; Belov, V. N.; Hein, B.; von Middendorff, C.; Schonle, A.; Hell, S. W. Nature 2009 457 1159. (62) F abien, P.; Xavier, M.; Gopal, I.; Emmanuel, M.; Hsiao Ping, M.; Shimon, W. Traffic 2009 10 691. (63) Oelke, J.; Pasc, A.; Wixforth, A.; Konovalov, O.; Tanaka, M. Appl. Phys. Lett. 2008 93 213901. (64) Anderson, R. G. W.; Jacobson, K. Science 2002 29 6 1821. (65) Jacobson, K.; Mouritsen, O. G.; Anderson, R. G. W. Nat Cell Biol 2007 9 7. (66) Janes, P. W.; Ley, S. C.; Magee, A. I. J. Cell Biol. 1999 147 447. (67) Dykstra, M.; Cherukuri, A.; Sohn, H. W.; Tzeng, S. J.; Pierce, S. K. Annu. Rev. Imm unol. 2003 21 457. (68) Johnston, L. J. Langmuir 2007 23 5886. (69) Veatch, S. L.; Soubias, O.; Keller, S. L.; Gawrisch, K. Proc. Nat. Acad. Sci. 2007 104 17650. (70) Radhakrishnan, A.; McConnell, H. J. Chem. Phys. 2007 126 185101. (71) Nielsen L. K.; Bjornholm, T.; Mouritsen, O. G. Nature 2000 404 352. (72) Gomez, J.; Sagues, F.; Reigada, R. Phys. Rev. E 2008 77 021907. (73) Pandit, S. A.; Jakobsson, E.; Scott, H. L. Biophys. J. 2004 87 3312. (74) Garbs Putzel, G.; Schick, M. Biophys J. 2008 94 869. (75) Shaw, J. E.; Epand, R. F.; Epand, R. M.; Li, Z.; Bittman, R.; Yip, C. M. Biophys. J. 2006 90 2170. (76) Samiee, K. T.; Moran Mirabal, J. M.; Cheung, Y. K.; Craighead, H. G. Biophys. J. 2006 90 3288.

PAGE 109

109 (77) Edel, J. B.; Wu, M.; Baird, B.; Craighead, H. G. BBA Biomembranes 2005 1668 158. (78) Saffman, P. G.; Delbruck, M. Proc. Nat. Acad. Sci. U.S.A. 1975 72 3111. (79) Price, W. S. Concepts Magn. Reson. 1998 10 197. (80) Wu, E.; Jacobson, K.; Papahadjopoulos, D. Biochem istry 2002 16 3936. (81) Mullineaux, C.; Kirchhoff, H. Using Fluorescence Recovery After Photobleaching to Measure Lipid Diffusion in Membranes. In Methods in Membrane Lipids ; Dopico, A., Ed.; Humana Press, 2007; Vol. 400. (82) Okazaki, T.; Inaba, T.; Tatsu, Y.; Tero, R.; Urisu, T.; Morigaki, K. Langmuir 2008 25 345. (83) Schwille, P.; Korlach, J.; Webb, W. W. Cytometry 1999 36 176. (84) Saxton, M. J. Biophys. J. 1997 72 1744. (85) Selle, C.; Ruckerl, F.; Martin, D. S.; Forstner, M. B.; Kas, J. A. Phys. Chem. Chem. Phys. 2004 6 5535. (86) Dietrich, C.; Yang, B.; Fujiwara, T.; Kusumi, A.; Jacobson, K. Biophys. J. 2002 82 274. (87) Scheidt, H. A.; Huster, D.; Gawrisch, K. Biophys. J. 2005 89 2504. (88) Ordd, G.; Westerman, P. W.; Lindblo m, G. Biophys. J. 2005 89 315. (89) Lindblom, G.; Ordd, G.; Filippov, A. Chem. Phys. Lipids 2006 141 179. (90) Filippov, A.; Ordd, G.; Lindblom, G. Biophys. J. 2004 86 891. (91) Ordd, G.; Lindblom, G. Magn. Reson. Chem. 2004 42 123. (92) Hah n, E. L. Phys. Rev. 1950 80 580. (93) Stallmach, F.; Galvosas, P. Annu. Rep. NMR Spectrosc. 2007 61 (94) Tanner, J. E. J. Chem. Phys. 1970 52 2523. (95) Levitt, M. H. Spin Dynamics: Basics of Nuclear Magnetic Resonance ; John Wiley & Sons, LTD.: N ew York, 2001.

PAGE 110

110 (96) Vasenkov, S.; Galvosas, P.; Geier, O.; Nestle, N.; Stallmach, F.; Krger, J. J. Magn. Reson. 2001 149 228. (97) Galvosas, P.; Stallmach, F.; Seiffert, G.; Krger, J.; Kaess, U.; Majer, G. J. Magn. Reson. 2001 151 260. (98) Cotts, R. M.; Hoch, M. J. R.; Sun, T.; Markert, J. T. J. Magn. Reson. 1989 83 252. (99) Krger, J.; Ruthven, D. M. Diffusion in Zeolites and Other Microporous Solids ; Wiley & Sons: New York, 1992. (100) Boxer, S. G. Curr. Opin. Chem. Biol. 2000 4 704. (10 1) Sackmann, E. Science 1996 271 43. (102) Kalb, E.; Frey, S.; Tamm, L. K. Biochim. Biophys. Acta. 1992 1103 307. (103) Nollert, P.; Kiefer, H.; Jhnig, F. Biophys. J. 1995 69 1447. (104) Kuo, A. L.; Wade, C. G. Biochemistry 2002 18 2300. (105) Hallock, K. J.; Henzler Wildman, K.; Lee, D. K.; Ramamoorthy, A. Biophys. J. 2002 82 2499. (106) Gaede, H. C.; Luckett, K. M.; Polozov, I. V.; Gawrisch, K. Langmuir 2004 20 7711. (107) Lindblom, G.; Ordd, G. J. Disp. Sci. Technol. 2007 28 55. (1 08) Pampel, A.; Zick, K.; Glauner, H.; Engelke, F. J. Am. Chem. Soc. 2004 126 9534. (109) Polozov, I. V.; Gawrisch, K. Biophys. J. 2004 87 1741. (110) Dvinskikh, S. V.; Furo, I. J. Magn. Reson. 2000 144 142. (111) Sorland, G. H.; Dagfinn, A. Magn. Reson. Chem. 2002 40 S139. (112) Mitra, P.; Halperin, B. J. Magn. Reson. A 1995 113 94. (113) Malmborg, C.; Topgaard, D.; Soderman, O. J. Magn. Reson. 2004 169 85. (114) Gibbs, S. J.; Johnson, C. S. J. Magn. Reson. 1991 93 395. (115) Ordd, G. ; Lindblom, G. Spect. Int. J. 2005 19 191.

PAGE 111

111 (116) Lindblom, G.; Ordd, G. Biochim. Biophys. Acta. 2009 1788 234. (117) Kroon, P. A.; Kainosho, M.; Chan, S. I. Nature 1975 256 582. (118) Deese, A. J.; Dratz, E. A.; Hymel, L.; Fleischer, S. Biophys. J. 1982 37 207. (119) Mitra, P. P.; Sen, P. N.; Schwartz, L. M. Phys. Rev. B 1993 47 8565. (120) Mitra, P. P.; Sen, P. N.; Schwartz, L. M.; Le Doussal, P. Phys. Rev. Lett. 1992 68 3555. (121) Latour, L. L.; Mitra, P. P.; Kleinberg, R. L.; Sotak, C H. J. Magn. Reson. A 1993 101 342. (122) Krutyeva, M.; Krger, J. Langmuir 2008 24 10474. (123) Krutyeva, M.; Vasenkov, S.; Krger, J. Magn. Reson. Imag. 2007 25 567. (124) Krutyeva, M.; Vasenkov, S.; Yang, X.; Caro, J.; Krger, J. Microporous M esoporous Mat. 2007 104 89. (125) Krutyeva, M.; Yang, X.; Vasenkov, S.; Krger, J. J. Magn. Reson. 2007 185 300. (126) Sanders, M.; Mueller, R.; Menjoge, A.; Vasenkov, S. J. Phys. Chem. B 2009 113 14355.

PAGE 112

112 BIOGRAPHICAL SKETCH Monica Danielle Sa nders was born in Lubbock, Texas to James Kirk Sanders and Cynthia Sanders Buettner. She grew up in Moore, Oklahoma with her mother, stepfather, Rick Buettner, and younger brother, Kevin Buettner. She graduated from Moore High School in 2000 with valedic torian h onors. She earned her B.S. in chemical engineering (b iotechnology) and her minor in Spanish from the University of Oklahoma (OU) in 2005. Upon receiving her B.S., she attended graduate school at the University of Florida (UF), where she obtained her Doctorate in chemical e ngineering.