THESIS LIBHXe-CILS MICHIGAN STATE UNIVERSITY EAST LANSING, MICH. 48824 This is to certify that the thesis entitled MICROCALORIMETRIC DETERMINATION OF THE THERMOELASTIC MEMBRANE PROPERTIES OF CELL-SIZE, UNILAMELLAR PHOSPHATIDYLCHOLINE LIPOSOMES presented by Thomas P. Gielda has been accepted towards fulfillment of the requirements for ' 0 Master 5 degree in Mechamcgl Eng1neer1ng AMI professor QnMQwC/mau as Date 2-16-84 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES “ RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. MICROCALORIMETRIC DETERMINATION OF THE THERMOELASTIC MEMBRANE PROPERTIES OF CELL-SIZE, UNILAMELLAR PHOSPHATIDYLCHOLINE LIPOSOMES By Thomas P. Gielda A Thesis Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 1984 ABSTRACT MICROCALORIMETRIC DETERMINATION OF THE THERMOELASTIC MEMBRANE PROPERTIES OF CELL-SIZE, UNILAMELLAR PHOSPHATIDYLCHOLINE LIPOSOMES By Thomas P. Gielda The thermoelastic properties of large unilamellar egg and soy L-a phosphatidylcholine vesicles were determined experimentally. In these experiments the vesicles were formed in low concentrations (32 mosm) of sulpho rhodamine G ex dye. This was performed to allow observation under phase contrast illumination. The isothermal compressibility modulii, KT’ were found to be 80.0 and 52.0 dynes/cm for the egg and soy phosphatidylcholine respectively. These values were found to be statistically different than the results of Kwok and Evans (198l). The thermal expansion coefficient, GT, of the soy L-a phosphatidylcholine vesicles was experimentally determined to be 3.6 X l0'3°C'1. This result is in agreement with earlier investigators. The experimental results were then used in the formation of a state plane for the vesicle. The experimental data were collected on a micro-vesicle aspiration system. The apparatus was designed, fabricated and character- iaed during the course of the investigation. ACKNOWLEDGEMENTS I would like to thank Dr. Robert Olien for his support in financing important equipment needs for this investigation. I would also like to recognize Dr. Bill Dunker, 0.0. and Ms. Vicki Rakowski, R.N. Their friendship, understanding and professional skills have allowed me to complete this work. Special thanks go to my adviser, Dr. John McGrath for providing the direction and insight required in undertaking this adventure. I express my deep appreciation for always being there when I needed him. However, I owe the most to my loving wife, Peggy, and my son, Benjamin. They were constant reminders as to what is really important in life. Without their understanding and love this work would never have been completed. ii TABLE OF CONTENTS Page LIST OF TABLES .................................................... vi LIST OF FIGURES ................................................... vii NOMENCLATURE ...................................................... x CHAPTER 1 INTRODUCTION ........................................... 1 1.1 Early Work ........................................ 2 2 MEMBRANE MECHANICS ..................................... 7 2.1 Derivation of Membrane.Mechanical Properties ...... 7 2.1.1 Isothermal Compressibility Modulus of the Membrane ............................ 8 . 2.1.2 Thermal Expansion Coefficient at Constant Tension ........................... 14 2.1.3 Tension and Surface Pressure in the Vesicle ................................ 15 2.1.4 Thermal Expansion Coefficient at Constant Surface Pressure .................. 19 2.1.5 Bending Modulus of the Membrane ............ 20 2.2 Tension and Pressure Differential Equations ....... 23 2.3 Summary ........................................... 25 3 EQUIPMENT AND PROCEDURES ............................... 26 3.1 Micropipette Fabrication .......................... 28 V 3.1.1 Manufacturing Process Background ........... 28 3.1.2 Micropipette Manufacturing Process ......... 30 3.2 Micromanipulator System ........................... 32 3.2.1 Integration of the Manipulator to the Microscope .......................... 32 3.2.2 Liposome Aspiration System ................. 36 3.3 Test Stage ........................................ 38 3.3.1 Next Generation Test Stage ................. 40 iii TABLE OF CONTENTS (Continued) CHAPTER 3.4 Liposome Formation ............................ 3.4.1 Materials .............................. 3.5 Bulk Compressibility Modulus Experimental Procedure ........................ 3.6 Thermal Expansion Coefficient Experimental Procedure ........................ 3.7 Experimental Sensitivity ...................... 3.8 Summary ....................................... 4 EXPERIMENTAL RESULTS ............................... 4.1 Isothermal Compressibility Modulus ............ 4.2 Thermal Expansion Coefficient at Constant Membrane Tension ..................... 4.3 Summary ....................................... 5 PHASE TRANSITIONS IN LIPOSOMES ..................... Background Information ........................ Single-Component Systems ...................... 5.1 5.2 Phase Change Experiments: 5.3 Phase Transition: Two-Component Systems ...... ' 5.4 Limitations ................................... 6 RECOMMENDATIONS FOR FUTURE WORK .................... 6.1 Osmotic Shrinkage Experiments ................. 6.2 Ice-Water Interface Experiments ............... 6.3 Summary ....................................... APPENDIX A--RELATION OF MEMBRANE TENSION TO SUCTION PRESSURE .. APPENDIX B--COMPUTER MODELLING AND DATA MANIPULATION .......... 8.1 Computer Modeling and Data Manipulation ....... 8.1.1 8.1.2 8.1.3 Computer Modeling ...................... Data Manipulation ...................... 81.2.1 Isothermal Compressibility Modulus ........................ 81.2.2 Coefficient of Expansion at Constant Membrane Tension ...... User Notes ............................. Page 44 44 45 48 49 51 52 52 59 6O 61 61 63 64 65 68 75 77 77 78 78 79 79 TABLE OF CONTENTS (Continued) . Page APPENDIX C--TEMPERATURE CONTROL PROGRAM FOR THE SECOND GENERATION TEST STAGE ...................... 86 C.1 Introduction ................................. 86 C.2 Thermal Analysis ............................. 87 C.2.1 Cooling Cycle ......................... 87 C.2.2 Heating Cycle ......................... 89 C.3 Computer Modeling and Control ................ 90 C.3.l Computer Modeling of the Microscope Stage ...................... 90 C.3.1.1 Description of Error Analysis Figures ............. 90 C.3.l.2 Summary of Parameter Studies ...................... 91 C.3.2 Computer Program for Temperature Control ............................... 98 C.4 Digital Control Hardware ..................... 102 C.4.l Analog-to-Digital Thermocouple Amplifier ............................. 102 C.4.2 Digital-to-Analog Power Amplifier ..... 108 C.5 Experimental Results ......................... 108 C.5.l Microscope Stage Characteristics ...... 108 C.5.2 Effect of Operation Parameter Variations ............................ 112 C.6 Conclusions .................................. 116 C.6.l Correlation of the Model to Experiments .......................... 116 C.6.2 Error Sources and Reduction .......... 116 APPENDIX D--EXPERIMENTAL UNCERTAINTY ......................... 118 0.1 Uncertainty Analysis for Isothermal Compressibility Modulus Experiment .......... 118 0.2 Uncertainty Analysis for the Thermal Expansion Coefficient ....................... 119 APPENDIX E--STATE PLANE GENERATION ........................... 120 BIBLIOGRAPHY ................................................. 121 TABLE 1.1 4.1 LIST OF TABLES Page A Summary of Previous Results Describing Various Thermoelastic Membrane Properties ......................................... 4 A Comparison of Current Results with Published Results for Isothermal Compressibility Modulus and Thermal Expansion Coefficient .............................. 53 vi LIST OF FIGURES FIGURE Page 1.1 Cross Section of a Liposome Membrane ................ 5 2.1 A Differential Membrane Element in the Plane of the Membrane Before and After Deformation ........ 10 2.2 A Schematic Representation of the State Plane (n-A) for a Typical Monolayer ....................... 17 2.3 Representation of Geometric Considerations Required to Determine the Membrane Bending Modulus from Micro-aspiration Experiments ,,,,,,,,,,, 22 3.1 Schematic of the Overall Experimental System ........ 27 3.2 Micropipette Schematic Illustrating Typical Sizes and Geometries ................................ 29 3.3 Equipment Used to Produce Flat-Ended : Micropipettes ....................................... 31 3.4 Photograph of Micromanipulator System Mounted on Microscope ....................................... 33 3.5 Photographic Detail of Manipulator, Micropipette and Sample Stage .................................... 35 3.6 Experimental Hydrostatic Set-Up Designed to Create and Measure the Suction Pressure Applied to Cells and Microvesicles .................. 37 3.7 Schematic of the Sample Stage Used to Hold the Sample as Hell as Control and Measure Temperature ......................................... 39 3.8 Test Stage Open-Loop Transfer Function (Temperature Difference as a Function of Input Current) ...................................... 41 3.9 Schematic of a Proposed Second-Generation Test Stage .......................................... 43 3.10 Illustration of Membrane Deformation in a Micropipetting Experiment ........................... 47 LIST OF FIGURES (Continued) FIGURE Page 4.1 A Typical Result for the Isothermal Compressibility Modulus Determination (Membrane Isotropic Tension as a Function of Normalized Area Change) .......................... 55 4.2 "State" Plane for the Liposome Membrane (Isotropic Tension as a Function of Temperature and Normalized Area Change) ............. 57 4.3 State Plane for the Liposome Membrane (Membrane Surface Pressure as a Function of Temperature and Normalized Area Change) .......... 58 5.1 Temperature of Onset and Completion of Solid-Liquid Separation in DMPC/DPPE Vesicles (Reproduced from Lee (1975)) ........................ 66 6.1 Schematic of the Interfacial Interaction between a Liposome and an Ice/Water Interface ............... 72 A.1 ‘ Membrane Deformation Schematic Used for Performing Membrane Force Balance ................... 76 C2.1 Schematic Representation of the First Law of Thermodynamics Applied to the Cryomicroscope Stage ............................................... 88 C2.2 Schematic Representation of the First Law of Thermodynamics for the Cooling Process ........... 88 C2.3 Schematic Representation of the First Law of Thermodynamics for the Heating Process ........... 88 C3.1 Predicted Controller Steady State Error as a Function of Coolant Temperature ................... 92 C3.2 Predicted Maximum Steady State Error as a Function of Temperature Sampling Rate ............... 92 C3.2b A Log-Log Representation of the Steady State Temperature Error as a Function of Temperature Sampling Frequency .................................. 93 viii LIST OF FIGURES (Continued) FIGURE Page C3.3 Predicted Maximum Steady State Error as a Function of Heater Input (HPC) ................ 94 C3.4 Simulated Response of the Cryomicroscope Stage to a 10°C Temperature Change ................. 94 C3.5 Simulated Response of the Cryomicroscope Stage to a Temperature Ramp of 80 C.min‘1 .......... 95 C3.6 Pressure as a Function of Volume for the Coolant Fluid in the Cryomicroscope Stage .......... 96 C3.7 Temperature Controller Flow Chart .................. 103 C4.l Electrical Schematic for Thermocouple Input Signal Conditioner ........................... 109 C4.2 Bode Plot for the Thermocouple Input Signal Conditioner (with Experimental Data) ............... 110 C4.3 Overall Schematic of Temperature Controller ........ 111 C5.1 Typical Experimental System Response to a Step Input Current to the Microscope Stage Heater ............................................. 113 C5.2 System Response as a Function of the Microscope Heater Driver Voltage ................... 114 C5.3 Maximum Temperature Rise as a Function of the Microscope Heater Driver Voltage ................... 114 C5.4 Measured Steady State Temperature Error as a Function of Set Point Temperature with Proportional Control ............................... 115 C5.5 Effect of Different Thermal Sink Temperatures on the Stage Cooling Rate ............. 115 —i| NOMENCLATURE Specific Heat at Constant Pressure Specific Heat at Constant Volume Thermal Expansion Coefficient at Constant Membrane Tension Thermal Expansion Coefficient at Constant Membrane Surface Pressure Helmholtz Free Energy Isotropic Compressibility Modulus Heat Membrane Transverse Shear Entropy Temperature Principal Tension in the ith Principal Axis Direction Isotropic Membrane Tension Maximum Membrane Shear Stress Nondimensional Area Change Deformation Variable Associated with Membrane Shear Intramembrane Tension Membrane Extension Ratio Membrane Surface Pressure CHAPTER 1 INTRODUCTION The purpose of this work was to determine the mechanical properties of egg and soy phosphatidylcholine (PC) cell-size, unilamellar vesicles: in particular, the isothermal compressibility modulus and the thermal expansion coefficient. This information is invaluable in the biophysical characterization of the lipid membrane. Once such properties of these simple model membrane systems are well-defined, the rationale is that these results and techniques can then be used in the study of much more' complicated membrane systems such as actual biological membranes. Aside from determining the basic biophysical properties of membranes, this work also represents the first step in the research program of the Bioengineering Transport Processes (BTP) Laboratory aimed at understand- ing how the mechanical properties of cell membranes are related to freezing injury. The results of this and future work in this area have many applica- tions. By knowing the membrane properties of healthy biological cells, these techniques can be used as diagnostic tools in the detection of cell abnormalities (i.e., cell malignancies). The characterization of the cell membrane can also be used in the design of artificial organs. The designer must know the limits of stress which can be placed on the cell as it flows through the organ. The membrane mechanical properties in this work were found by per- forming micropipette aspiration experiments on cell size, unilamellar lipid vesicles (liposomes). This experimental technique was first developed in the early 19505 by Mitchison and Swan. A sumary of earlier related work using micropipette aspiration techniques follows. 1.1 Early Work Mitchison and Swan (1954) were the first investigators to implement micropipette aspiration techniques to determine the mechani- cal properties of biological systems. In their work they attempted to determine the "stiffness" of the sea urchin egg membrane. The term "stiffness“ here refers to some measure of the membrane resistance to deformation. Further clarification of this point will be discussed below. Their experiments involved deformation of the egg at constant surface area. The results of their experiments yielded the shear modulus of the membrane, although they did not know it at the time. Instead, they stated that they had detennihed the elastic modulus of the membrane. Rand and Burton (1964) applied the same techniques of Mitchison and Swan to the red blood cell (RBC). They too were interested in determining the "stiffness" of the membrane. The results of these earlier investigators were not clarified until Skalak et a1., (1973) and Evans (1973) decomposed the membrane stiffness into the resistance to shearing deformation at constant area and the resistance to area dilitation or condensation. The theoretical basis for this decomposi- tion is discussed in detail in Evans and Waugh (1977) and Evans and Skalak (1980). Steponkus (1982) determined the compressibility modulus of the Secale Cereale L. cv. Puma protoplast. He found the compressi- bility modulus to be 230.0 dynes/cm. A summary of the results of the above-mentioned investigators are shown in Table 1.1. From the table it is observed that the early investiga- tors, Mitchison and Swan as well as Rand and Burton, were determining the shear modulus of the membrane, where the shear modulus is the membrane resistance to shape changes while at constant area. This is apparent since the values they calculated for their compressibility modulii are much smaller than the values obtained for the compressibility modulii. This is consistent with their experimental procedures since they did not induce membrane tensions large enough to produce area dilitations. Little work in this field has been done concerning liposomes, even though this represents an interesting and important model membrane since the membrane can be studied without the influence of the structure usually enclosed in a biological membrane. The membrane to be studied is shown in Figure 1.1 taken from Israelachvili et al., (1980). Kowk and Evans (1981) and Evans and Kwok (1982) have determined the com- pressibility modulii and the thermal expansion coefficients for egg PC and dimyristoyl PC (DMPC) vesicles. Their results are also in Table 1.1. In addition to the membrane mechanical properties, Evans and Kwok (1982) have been able to determine the phase transition temperature of DMPC vesicles by measuring the changes in their compressibility modulii of the DMPC vesicles with temperature. They have demonstrated that by assuming a Gaussian distribution for the transition temperature and performing a convolution of an idealized first order phase transi- tion, they obtain excellent correlation between predicted compressi- bility modulii and experimental data. They also report that by coupling mmwuemaogm mangaewz ovummpmosamgh mzowgm> mcwnwcomoo mp—zmma maow>mcm mo hemeasm < _.p open» annuaoaoam alum .>o .4 on-ouou cannon a. uazu .Nmadv sass as. negpm cco.c.aoo.c .\a .cmd-.oau .uo.oa« om mm Aumauv .s.>m as. nos. a~oo.o .\: 8.8:“ .no.oa«g usuaneos Ammodv .axsoa.an .\= .\e o.cn~ .. .u..~a dflco Aouadv gasdgx as. a»:.3...sa:m .x: o_o.a o.on: Gouda cam , afloo Remedy soauam as. o:.¢ .\2 «doo.o can gouge noofim u.m . mum 333 5.26 as. :82an {a $6qu {a £95 non Au \Sv azmnoammmoo Aao\..eaov Aao\.o:acv maasuox moaézmgfi $3533 4339 3.39. mega 2483336 zfifim use? mDDM>de memenEmz mEomoaPA a mo cowuomm mmcco P.F mezmwm I. O O 0.1. _ 1: a T Z . 1 caddy :pnuuooauaa : z i H00. 000 o l i Queue neon .eaaonoaauaa.aa.ogm unopaamna ooduon the convolution approach with the Clausius-Clapeyron equation for the membrane they can predict the transition temperatures of the vesicles. This investigation is intended to be the foundation for future work related to membrane mechanics in the BTP laboratory. In order to perform such research a complete microcalorimetry system is required. This apparatus consists of the manipulator, data acquisition and temperature controlling systems. The experimental apparatus must be designed and fabricated. In addition the apparatus must have the capability to perform thermal transition temperature experiments similar to Evans and Kwok. Therefore, a major objective of the present research is the development of a complete microcalorimetry experimental apparatus. A second major objective is the reproduction of published data for representative types of major experiments of interest to verify that the experimental system yields acceptable data. Finally the system will be used to determine previously un- published values of the isothermal compressibility modulus and the thermal expansion coefficient for soy PC vesicles. These data are useful with respect to defining the manner in which membrane composi- tion affects membrane mechanical properties. CHAPTER 2 MEMBRANE MECHANICS The strategy of this chapter will be to relate the membrane mechanical properties to the thermodynamic state of the membrane. This will be accomplished by relating the change in energy of the membrane to the Helmholtz function. This information will then be coupled to the data provided by the solution of the differential equa- tion for membrane surface pressure to yield the thermoelastic properties of the membrane, namely CT-and KT' The integration of the differential equation for the membrane surface pressure yields the state plane for the membrane. The variables of the state plane equation are surface pressure, area and temperature. This is directly analogous to pressure, volume and temperature of the more common three-dimensional thermoelastic system. 2.1 Derivation of Membrane Mechanical Properties The function of this section is to relate theoretically the two membrane mechanical properties, isothermal compressibility modulus and the thermal expansion coefficient, to readily measured properties (i.e., isotropic tension and membrane area changes). In addition to the above, differential equations for the changes in isotropic tension and surface pressure will be derived. These equations will then be inte- grated in Chapter 4 to yield an equation of state for the vesicle membrane, where the variables of state are surface pressure, area and temperature. The following analysis is based primarily on the works of Evans and Skalak (1980) and Evans and Waugh (1977). 7 2.l.l Isothermal Compressibility Modulus of the Membrane This section will demonstrate the extraction of the membrane compressibility modulus from experimentally measured membrane tension data. The first law is written in integral and differential form for a reversible process as: IdE = f(5Q + 5W) (2.1.1.1) dE = so + 511 (2.1.1.2) Where work done on the membrane brings about a positive change in energy. For a reversible process the differential amount of heat transfer involved in a process can be calculated from the differential change. in entropy: 60 = TdS From the second law of thermodynamics for a general process: dS'jidQ/T (2.1.1.3) Equation (2.1.1.2) is an exact differential in the energy E, and we assume that the process is energy conserving, therefore there exists a potential function as its solution. At this point a choice can be made as to what potential energy function will be used to describe the membrane system. The Helmholtz function will be used since the varia- bles in Equation (2.1.1.2) are internal energy, heat flux and entropy. The Gibbs Function would be used if enthalpy were a variable instead of internal energy. The Helmholtz function is defined as: F -_- E_ TS (2.1.1.4) The “ superscript defines the extensive property E or S taken on a per unit area basis. This is done since the first and second law are based on the entire liposome membrane system, while we are interested in elemental membrane area. If Equation (2.1.1.4) is differentiated, and we assume an isother- mal reversible process the equation can be written as: dF = at: = dE- Tds (2.1.1.5) Figure 2.1 depicts an elemental membrane area undergoing a small deformation. At constant temperature the potential energy function is dependent on two membrane deformation variables. The potential energy function is independent of temperature. A useful analogy is energy stored in a spring, where the spring constant is constant at all temperatures. Figure 2.1 represents an elemental membrane area at two different states. Note the two figures are related by: dxi = Aiai i = 1,2 (1) a is the measure of the change of area to condensation or dilitation. It is defined as: a = aA/A0 = XIXZ - 1 (2.1.1.6) (2) B is defined as the measure of the change of the membrane shape, at constant area (i.e., change of aspect ratio of a rectangle). It is defined as: lO copumeeommo gmuw< new mgowwm wcmgnemz on» mo many; on» cw ucwempm acmcnsmz —amu:mgmwmwo < F.N mesmwm «Sax u «.5 .2. .4 u I... put up 1...: -* , ‘rlllu .1 .1 1.1: 1... 1. -’---“fl3 ----.~-- «nu—hj Inn... .l.llllll an L .1111. 1111114 .— 11 B = (A? + A§)/(2x1x2) (2.1.1.7) where A] and A2 are the principal extension ratios of the material defined by the following relations: (2.1.1.8) X —-l II >2 —.l m —l X I >2 The position of Xi at a different state than the initial position, a1, is related by the extension ratio Ai' That is to say: X. 1 f(ai) _ -1 a1 - f (a1) The two functions are the inverse of each other. Incremental work was performed on the membrane. It was assumed that the work performed from state 1 to state 2 was isothermal and reversible. For Figure 2.1 the equation for incremental work can be written as: SW = [(T1dx2)6(dx1) + (Tzdx1)6(dx2)] (2.1.1.9) Where T1 and T2 are the principal tensions in the membrane. Using the definitions of the extension ratios, Equation (2.1.1.9) can be rewritten as: SW = [(T1x25x1) + (T2A162)]dA0 (2.1.1.10) As a result, for an isothermal, reversible process the Helmholtz potential energy function is defined as: 12 (dF)T = (TlxdeI) + (szldxz) = 50 (2.1.1.11) The differential change in the elastic potential energy function is dependent on the two deformation variables a and 8. Since a and a are dependent on the extension ratios the following differential equa- tions are formed: da = [Ba/8X11dA] + [ac/BAZJdAZ (2.1.1.12) d8 = [BB/BXIJdX] + [aa/axzjdxz For the isothermal case, the Helmholtz function is a function dependent only on a and 8. Equations (2.1.1.11) and (2.1.1.12) can be used to derive the relationships between the principal tensions and the derivatives of the Helmholtz function. TiAi = [(aF/aa)T’B(aa/axi) + (aF/33)T,a(ae/axi)] (2.1.1.13) i = 1,2 Using the definitions for a and 8 Equation (2.1.1.13) is rewritten as: _ ~ i+l 2 2 2 2 Ti - [(3F/36)T,8 + (-1) 1/(21112)(aF/33)T’a(x]-12)] (2.1.1.14) i = 1,2 The definitionsof the isotropic tension and the maximum shear resultant are: T'= 1/2 (T1 + T2) (2.1.1.15) Ts =1/2 11 T] - 1211 13 where the brackets denote the absolute value of the expression enclosed. Therefore: T = [aF/BGJT,B (2.1.1.16) _ ~ ~2 ~-2 Ts — 1/2(1+“)[3F/BB]T,a H A - x .H Using the above relations the tension resultants can then be incorporated into the exact differential of the Helmholtz potential energy function, at constant temperature. (a?)T = TOa + 215(1+a)di/i (2.1.1.17) Equation (2.1.1.17) is then expanded in a Taylor series about a equal to zero to yield: (F-F ) = Thu + Kaz/Z + 0(03) (2.1.1.18) The shear term does not contribute toward the isotropic tension component. Isotropic tension in the membrane is a by-product of area dilitation or condensation only. The membrane tension and the compressibility modulus of the membrane may then be defined as (assuming that T; is zero): T = BE/Ba = KTG KT 5 [aTVanT’a=o = [aZF/aa21T,a=o (2.1.1.19) 14 The value of KT is accurate only with a values close to zero. This limitation is imposed by neglecting the second order terms in the tension Equation (2.1.1.18). This limitation does not reduce the effectiveness of the model. Evans and Waugh (1977), Evans and Skalak (1980) and Kwok and Evans (1981) report lysis of the membrane at a values ranging from 2 to 3 percent. At values of a at 3 percent the second order error term for the expression for KT is approximately 4.5 x 10'9. 2.1.2 Thermal Expansion Coefficient at Constant Tension The surface area of a vesicle under tension is a function of temperature and isotropic membrane tension (see Section 2.2 for deve10pment): d—:-T+( 7 (3T T “W)T At constant tension, T} this equation simplifies to: do = (8T)T dT or 92.: (229.. dT 8T T (2.1.2.1) where CTi-T %) is the thermal expansion coefficient at constant membrane tension. Kwok and Evans (1981) and Evans and Kwok (1982) have found the value to be approximately 2.4 X 10'3/°C for egg lecithin. For '3°c. DMPC they report expansion coefficients of .4 - .6 X 10 It should be noted that Equation (2.1.2.1) cannot be used in the thermal transition region. Instead the Clausius-Clapeyron approach should be used as in Evans and Kwok (1982). 15 Evans and Kwok (1982) report changes in the compressibility modulus of an order of magnitude at the phase transition temperature. Evans and Kwok (1982) report that KT is 140 dyne/cm above the transi- tion point and 1100 dyne/cm below the transition point. This large change in the compressibility modulus at the phase transition emphasizes the need for the separate analysis performed by Evans and Kwok (1982) in the thermal transition region. Away from the thermal transition temperature CT-is given as: c-d“ 2122 T'(HT)T A. ("‘) CT-is a relatively easily obtainable quantity if the experiment is not performed in the thermal transition region. Later a relationship for the thermal expansion coefficient at constant surface pressure will be derived. 2.1.3 Tension and Surface Pressure in the Vesicle Tension in the liposome is related to the Helmholtz free energy density through the relation: [BF/BaJ-r = T = y - 1r (2.1.3.1) The tension in the membrane can be subdivided into two parts as in previous developments (Evans and Skalak (1980), Evans and Waugh (1977)). 16 y is taken to represent the intramembrane tension caused by the hydrophobic effect. The hydr0phobic effect is defined as the interfacial tension between the hydrocarbon tails of the lipid molecule and the aqueous environment. It is independent of a, but strongly dependent on temperature changes. The magnitude of y is related to the interfacial geometry of the amphiphilesand the aqueous environment (Defay and Prigogine (1966)). See Figure 1.1. n is defined as the surface pressure. It will be assumed to obey the two-dimensional gas equation (Evans and Waugh (1977)): nA = 4kT (2.1.3.2) The above assumption is based on the relation of the monolayer to the bilayer membrane. It must be noted that this assumption assumes that the liposome is in a state where the n-A curve is a hyperbola. From Figure 2.2. taken from Fendler (1981), note that all portions of the curve do not fit the hyperbolic form. Please note that Figure 2.2 is taken from monolayer data, however monolayer data can yield bilayer data. This is discussed in Chapter 5. When the vesicle is in the thermal transition region the above analysis is not applicable since there can be area changes at constant surface pressure and temperature. Further study of the vesicle in the thermal transition region is required to yield a complete analysis for the membrane. Tanford (1974) partitioned the Helmholtz free energy into two parts (see Figure 1.2). 17 cmxapozoz pmuwazh a so» Amuev mcmpa macaw use to copucucmmweamm umumsmgum < ~.N mczmwm Rodsoouol \ 33:80:55 _ ¢O>IIJ 0.0 >m ¢0b14322<3 . cwgom2<¢h wcammwc a 01¢ 20:0< maOumOcu.’ >(asa.9 mmucs ‘ Lamb f . _ u0 28 The experimental apparatus includes many improvements over the systems of previous investigators (Mitchison and Swan (1954), Rand and Burton (1964)). The current configuration is the first with on- line data acquisition and closed loop temperature control. However the system also has its shortcomings. Section 3.7 deals with the experimental uncertainties which are closely related to the shortcomings of the present system. At this time the experimental uncertainty is unacceptably high. The bulk of this uncertainty is due to the inability to accurately resolve the area changes in the liposomes. This effect will be discussed in detail in Section 3.7. The description of the experimental apparatus is subdivided into four components for the purpose of discussion: the micropipette, the manipulator system, liposome aspiration system, and the test stage itself. The remainder of the section covers experimental procedures . and uncertainties. 3.1 Micropipette Fabrication 3.1.1 Manufacturing Process Background The manufacturing of micropipettes, in the 7-13 micron inner diameter range, was a difficult task. The micropipettes must have a flat face on which the liposome muSt rest. (See Figure 3.2.) Previous attempts to manufacture these pipettes by some other investigators have involved a.quick fracture technique. This process is discussed in Evans, Waugh and Melnik (1976). Using this technique the stated production success percentage was less than 10 percent. Such high rejection rates led to alternative manufacturing processes. 29 nacho. and on any... 0.30%: 233.: 3.2- 0 mmpcameomw new mmNPm Pmuwazk mcwaogamzppH uwuwemcum muumavaocuwz ~.m mczmwm 2.3.2.... o..oa.u ooa.a .oonahuno . L 1.) 308383: a _ 2.33.! 25:01.. 30 Another manufacturing process, developed by the Fusion Research group of the University of Rochester and modified by Dr. R. Waugh, Radiation Biology and Biophysics Department of the University of Rochester Medical Center, was considered. Their technique involved the implementation of a sonicating bath to input ultrasonic energy into the glass pipette. This energy would then vibrate the glass tip, which was placed against a fine abrasive, and grind the tip to the desired diameter. 3.1.2 Micropipette Manufacturing Process The first step in the pipette manufacturing process is the pulling down of the 20 microliter Dade Accupipettes, l millimeter ' nominal 0.0., to needle tips. This task was accomplished at either of two locations on campus. The first was located at the Biochemistry Department Brown-Flaming horizontal pipette puller while the second was located at the Endocrine Research Laboratory. The Endocrine Research Laboratory Stoeling vertical pipette puller was shown to produce pipettes of more uniform and superior quality. This puller was therefore used routinely. The second step in the manufacturing process involved the grind- ing of the needle pointed pipette to the desired inner diameter. Figure 3.3 depicts the necessary equipment and fixtures. The ultra- sonic energy input into the glass pipette creates a vibration in the pipette, causing the tip to vibrate into a 600 grit aluminum oxide abrasive. The abrasive-glass interaction produced a grinding action which produces the desired flat-ended pipette. Typical sonification 31 .522: 3.6 8» x 606.9. mmupmapaocuwz nmucmupm—m moauoem o» vow: acmsapzcm m.m mgamwu 1 03.284 :56 6°. .uocuado oucoauauaa sauna: 5388 a 5 88858 3 Page L1 .029: 2.2.... .uonnoa o» nova: «o sedan. andaaamao an 83.. 5 3... a .32.: 32 times for the system range from 2 to 10 seconds. The success rate of this process is slightly higher than 80 percent. Any pipette that was not flat-ended was rejected. This represents an increase of 700 percent from the previous quick-fracture method. Once the pipettes are ground to the proper inner diameter all air must be excluded from the inside. Residual trapped air will cause compressibility problems in the pressure measurements which leads to erroneous measurements. All air is excluded from the micro- pipette by boiling the glassware for 20 minutes in distilled water. The pipettes must then be allowed to cool slowly to room temperature. The slow cooling ensured that all air was excluded from the interior of the pipette. In the course of the mechanical properties experimentsa frequently occurring problem was the lodging of lipid fragments in the pipette entrance. Previously this event would have required the changing of the pipette. However, this problem was solved by submerging the micropipette (without the holder shown in Figure 3.3) into the ultrasonic bath. The same level of ultrasonic energy which was used to grind the pipette can be used to free the lipid particles from the pipette entrance. This technique extends the working life of the pipette from a few hours to several weeks. 3.2 Micromanipulator System 3.2.1 Interfacing the Manipulator and the Microscope The Duke model C micromanipulator was used in these experiments. The manipulator was build and obtained from the Physiology Instrument Shop of the Duke University Medical School. Figure 3.4 displays the manipulator system as it appears in place on the microscope system. 33 Manipulator Body -~' Joystick Joystick Sensitivity Adjustment Figure 3.4 Photograph of Micromanipulator System Mounted on Microscope 34 The manipulator system consists of the joystick and the manipulator body shown in the foreground of Figure 3.4. The movement of pipettes, as shown in Figure 3.5, can be controlled in coarse and fine modes. The coarse adjustment controls are located on the manipulator body. These screw-driven controls provide coarse adjustment in all three axes of motion. Care must be taken when performing coarse adjustments not to dislocate any of the adjustment pins. The adjustment pins are located under the adjustment screws When the coarse adjustment screws are turned it forces the pin against a lever which in turn causes the pipette to pivot in a given direction. When an adjustment pin is dislocated the coarse adjustment in that direction does not function. When this occurs the manipulator outer covering must be removed and the adjustment pin realigned.‘ This Operation usually takes three or four hours to perform. : - - The Duke manipulator also has a joystick sensitivity adjustment (see Figure 3.4). By sliding the adjustable yoke of the joystick up or down the sensitivity of the pipette to joystick movements can be increased or decreased. This is a valuable tool when one is scanning the test chamber for suitable liposomes for experimentation. By keeping the joystick sensitivity high one can reduce the need for coarse adjustments. This allows for smoother system adjustment and reduces the induced vibrations from coarse adjustment. Figure 3.5 depicts the manipulator body attached to the Zeiss Universal Microscope. The plexiglass support fixture was specially designed for the Duke manipulator. The fixture allows rotation of the manipulator about its support rod and it keeps the manipulator 35 mmmum 39:3 28 $9,339.32 £32335: 05 :38 oEafmouof m.m 953... zoom asagfifix ca xoaonmoa wnnuooccoo 3:3 03.5 035565 . Atom hopaasaacuz ouuomaaoaoaz owaum .111 Susan 36 sufficiently removed from the microscope stage to eliminate physical interference problems. The plexiglass support is bolted to the microscope stage by two mounting screws. Care must be taken not to exert too great a load on the support fixture. Failure to do so will result in damage to the microscope stage and the support fixture (i.e., do not rest your hand on the support). 3.2.2 Liposome Aspiration System The suction pressures required for the compressibility modulus experiments were generated by the system shown in Figure 3.6. The suction pressures were measured by a Validyne DP-103-32 pressure transducer, coupled to a Validyne CP-lS carrier demodulator. The output of the transducer was :_5V over a pressure range of :_35.0 inches of water (i 8.72 X lo4 dyne/cmz; ==:_0.l atm). The output of the demodulator was then interfaced to the LSI-ll thru the I/O box and the A/D converter and to a panel meter for display. The pressure transducer was calibrated according to manufacturers specifications using a water manometer before the experiments were started. The accuracy of the pressure measurements was :_l40 dynes/cmz. The accuracy of the pressure measurements is based on the uncertainty of the trans- ducer and the uncertainty of therelative levels of the two reservoirs. The two-reservoir system was used to eliminate compressibility errors associated with a working fluid such as air. The system was shown to be reliable in producing low suction pressures. The suction pressure was adjusted to the 1 cc syringe. 37 mm.o.mm>ogu.z new mppmo op umwpaa< msammmga copuuzm on. asammmz u:m.mummgu op omcmmmma azuumm uwpmumogvzz .mpcmspgmaxm c.m mgamwm 39:02.0... 0 5:2; .3925 .333... .2333. «n.3— ao 2.3.; 35.3 no . pl fit l. fiIIIIIJ F» u N erllll .J ..ao.a.p. use: IIIIII Tcouahluv anomqam adopuouoz _ . can—5.52: .235...» :2.» o... :o.:... 9.; so... < a...» 90.553 21 2.3.3.... 4 2.2.... 2.... .0 2.0.0... 0.: a. .< 9.52:...- .o>o.. 3...... zeta-o: I 2.2.... 0.. Ill-l: [null 22.1.02: 2.... 0.. coco .3 zeta-cc 22.3.05; 2... ob $30.0 .3 . 33:... 38 Prior to each run the two reservoirs were open to the atmosphere. Then the air-water interface level in the reservoirs was brought to the height of the micropipette tip. This was a cumbersome and tedious process which could be eliminated with the incorporation of an inverted microscope. By incorporating an inverted microscope the level of the test chamber does not move with respect to the air-water interface in the reservoirs. With the current system, every time the sample is changed the water levels in the reservoirs must be realigned. When the reservoirs were brought to the proper height the pressure transducer read zero volts. With rebalancing complete the valve to reservoir one was closed. The experiments could then begin. 3.3 Test Stage The test stage used in this investigation is shown in Figure 3.7. Brass was chosen as the stage material since it has good thermal conductivity. The test chamber itself is located in the lower left hand corner as seen from the top view of the test stage. The 7x12 mm. test chamber could hold a 40 ul liposome sample. During operation the undersurface of the test chamber was covered with a l8xl8 mm. coverslip. The coverslip was held in place by capillary action and a light coat of vacuum grease between the brass stage and the glass coverslip. The liposome sample was then placed on the lower coverslip in the test chamber and then covered with a l2 mm. dia. coverslip. The micro- pippete was then positioned in the test chamberthrough the 1 mm thick opening in the y-z plane. Located to the side of the test chamber is the temperature heating/ cooling source. The Cambion model 801-1006-1 ceramic cascade module 39 mgsumcmasmh mgammmz vac .ogucou mo .sz mm mpasmm on» c.o: o» new: macaw opaEmm may mo uwacsmzom ~.m wgamwu so; can so; .5 N T:.|.o.om||. . .5... 32.553 .3 _> It .. .. .ON . OJ . L , . 6.3. .23.. a 1 J_ #- 025 c2950 er .II. Up a E. . odu IIIIIIOON m0 oanvm o.:.lF ndwn onanooum oonuaam cu omsnso .oznnneox olooomda osv hon onnum ounvm ‘ Eh 59 Again it must be reiterated that the state plane created is only valid when the vesicle is not in its thermal transition region. In this analysis the vesicle cannot have changes in area without changes in pressure or temperature. The effect of the Sulpho Rhodamine dye on the compressibility modulus of the liposomes was an apparent reduction in the membrane stiffness. Kowk and Evans (l981) report an average compressibility modulus for egg PC of l40 dynes cm.']. This value is 75 percent greater than the average value found in this investigation. Perform- ance of a null hypothesis test on the two compressibility modulii revealed they were statistically different at the 0.05 level of significance (Miller and Freund (l965)). The same type of statistical test was performed comparing the soy and egg compressibility modulii. The results revealed that the two modulii are statistically different at the 0.05 level of significance. 4.2 Thermal Expansion Coefficient at Constant Membrane Tension The thermal expansion coefficients as detailed in Chapter 3 were conducted on the soy PC lecithin. The results of these experiments are shown in Table 4.1. A total of l9 runs were conducted. Again the calculated experimental uncertainty was as large as the standard deviation of the sample. This result strongly suggests that before any further investigations are conducted higher power objective lenses should be employed with the microscope. The data for the soy PC suggest that the dye used has no effect on the thermal eXpansion coefficient. It is also apparent that the expansion coefficient does not vary appreciably with various lipid 60 materials. However, these conclusions cannot be asserted with con- fidence because the standard deviations are nearly as large as the measured average values (see Table 4.1). 4.3 Summary The isothermal compressibility modulus experiments were con- ducted on two lipid materials, egg and soy PC. The results were found to be statistically different from the work of Kwok and Evans (l981). They were also found to be different from each other. This finding suggests that the sulpho rhodamine dye used for liposome visualization is affecting the liposome membrane mechanical properties. Since there are no manufacturer's data available on the dye, the mechanism of change is unknown at this time. However, when the dye was used in the thermal expansion coefficient experiments it did not seem to change this membrane property. Clearly further work is needed to characterize the effect of the dye. CHAPTER 5 PHASE TRANSITIONS IN LIPOSOMES The purpose of this section is to form an outline for experiments leading to a greater understanding of phase transitiomsin liposomes. The development will not be limited to one-component systems. Two- component lipid mixtureswill be studied, and a method to construct their phase diagrams will be discussed. Baret (1981) compiled thermal phase transition data for many lipid materials. In his work he determines the thermal phase transi- tion temperature by many different techniques: differential scanning calorimetry, electron spin resonance, nuclear magnetic resonance, fluoresence. liaht absorbtion and scattering, X ray diffraction, dilatometry and Raman and infrared spectroscopy. In his work he studies both single and multi-component lipid systems. Baret also reports on the effect of lipid-protein interactions in the membrane. 5.1 Background Information Information on the phase transition of bilayer membranes is difficult to determine experimentally due to the nature of the lipo- some system. Therefore it is desirable to relate the wealth of avail- able data concerning monolayers to the bilayer. Nagle (1976), Blume (1979) and Gruen (T982) have developed analogies for the relation of the bilayer system to the monolayer. Nagle and Gruen suggest that a bilayer in the tension-free state is 61 62 similar to a monolayer with an externally applied pressure of 50 dynes cm.'1. The criteria used to equate the bilayer system to the monolayer system involves matching the area per molecule of each system. In addition, Gruen suggested that monolayers on an oil/water interface will not represent as close an analogy as a monolayer on an n-alkane/ water interface. Blume (1979) suggests that the lateral pressure in the monolayer be 30 dynes cm.’1 for an analogy between the monolayer and the bilayer. He reasons that at this surface pressure the absolute areas per molecule are equal for the monolayer and the bilayer. Lee (1975) performed fluorescence studies using chlorophyll a on small sonicated liposomes of various compositions, to determine their phase transition temperatures. Lee also demonstrated a method to construct phase diagrams, for two component systems, from fluorescent intensity measurements. Evans and Kwok (1982) studied the phase transi- tion of large unilamellar DMPC vesicles employing mechanical calorimetry. Their results were in close correlation with previously existing bi- layer transition data (Lee (1975)). ' Evans and Kwok (1982) employed a micromanipulator system to study the membrane phase transition. In their investigation they measured the relationship between the isothermal compressibility modulus and temperature. By monitoring the isothermal compressibility modulus and assuming a Gaussian thermal transition temperature distribution they predicted the thermal transition temperature. They verified their mechanical calorimetry study with differential scanning calorimetry. 63 5.2 Phase Change Experiments: Single Component Systems The phase change experiments should be conducted on pure lipids with sharply defined phase transition temperatures because the sharp phase transition will allow a clearer definition of the phase transition temperature. Yeager, et al., (1982) studied phase changes in cell-sized vesicles using light microscopy. His method involved determining the area changes by changes in the diameter of the liposomes. They report area changes of 23 percent during phase transition. However their method may miss the true onset of phase transition simply by not having sufficient optical resolution. (Note that their investigation was only interested in the main transition of the vesicle.) In contrast the manipulator system and the micropipette act as a mechano—optical amplifier. Very minute changes in the vesicle area will be apparent in the pipette. An area change of 0.5 percent can be resolved, for a 30 um diameter vesicle and a 6 um radius pipette. These experiments must be conducted on a test stage which has fine temperature control in order to achieve the temperature resolutions on the order of 0.1°C normally reported in phase transition work (Evans and Kwok (1982)). As the vesicle is warmed from below the phase transi- tion temperature one would expect to see the vesicle area increase. In the phase transition region, the vesicle area would increase markedly. As the vesicle passed out of the upper bound of phase transition the vesicle would increase its surface more slowly. By monitoring the increase in vesicles surface area one can determine the vesicle phase transition temperatures. By employing this technique the effect of the external environment on the phase transition of the liposome may be directly measured, instead of inferred from monolayer data. 64 To serve as a check on the method outlined above, the liposome could be tagged with a fluorescent probe which fluoresceses in the solid or liquid phase only. Therefore as the liposome was warmed above the phase transition temperature, the fluorescent intensity could be monitored with a photomultiplier yielding the phase transi- tion temperature. This type of technique has been used by Lee for bulk samples of small (nm) sonicated liposomes. It has never been applied to a cell sized liposome. Cell sized liposomes and fluorescent probes offer the additional advantage that the fraction of surface in the solid or liquid state could be ascertained visually using the segregation of phase-specific fluorescent probes as outlined above. These data could then be checked against data collected using the manipulator mechano-optical-amplifier. 5.3 Phase Transition: Two Component Systems Lee (1975) performed a series of experiments to determine the phase diagrams of multicomponent systems. His experiments, which were conducted on small sonicated vesicles, could be modified by using area change data from the manipulator system instead of fluo- rescent data. The new test system requires the mechano-optical amplifier detailed in Section 5.2. Lipid mixtures at various concentrations could be tested similarly to those in Section 5.2. During phase transition the temperature and the area would be measured. Since the thermal expansion coefficient is greater during phase change, by approximately one order of magnitude (Evans and Kwok (1982)), the onset and completion of transition is apparent. 65 By determining the onset and completion of phase transition at various lipid concentrations a phase diagram similar to Figure 5.1 from Lee (1975) can be constructed. Note that the ends of the diagram are not closed. This is expected since the process does not occur isothermally which means that some degree of uncertainty in determin- ing the initial onset and final completion of the phase transition will be included. By incorporating different fluorescent probes, which are lipid and phase selective, into the solid and liquid phase the composition of any phase and temperature could be found. This would be accom- plished by scanning the liposome with the photomultiplier and determin- ing the composition of the liposome by PMT output. Further investiga- tion into this phenomena is warranted. 5.4 Limitations At present the microscope system used does not have the necessary Optics to observe the phase transition. Since the dye used in Chapter 3 will not incorporate into the pure compound liposomes Hoffman modula- tion optics are required. The liposomes can be formed at the desired molar ratios (Lee (1975)). However, the actual composition of the liposomes proposed for the studies outlined in Section 5.3 should be verified experimentally. It is possible that the liposomes may not form as homogeneous mixtures. The liposomes may form configurations similar to bedquilts with patches of pure lecithin dispersed throughout. Or the lipids may not mix at all and form liposomes only of a specific lipid such that the liposome 66 flamempv was some umusuocammv mo_oemm> maao\uazo melee_paeaamm swaps vaom we cowuochou use ummco no assumemqeoh F.m mesmwm mama—x s . _ __ m.o v.5 v.c «.0 .1: m an”... om cm ml. :1 name u care on 1. “ram cm II -f “r v-—.. 67 membrane structures formed are at a different molar ratio than the initial bulk solution ratios used to form them. In order to experimentally verify the composition of the multi- component liposomes an electrophoresis apparatus should be constructed. However, since the PC head groups are zwitterionic (Lehninger (1970)) a probe must be attached to the specific lipids to allow phoresis. This is not an easy task, and much more consideration is warranted. In order to perform the experiments suggested in this section, the second generation test stage and its temperature controller must be employed. This controller has shown f_.5°C accuracy on the BTP Lab conduction stage and would need to be debugged further to allow realization of the theoretical accuracy of :_0.l°C predicted for this device. See Appendix C. CHAPTER 6 RECOMMENDATIONS FOR FUTURE WORK The micromanipulator system is an excellent tool to measure the volume and surface area changes in microscopic objects. This system should be employed to further the osmotic shrinkage work of Callow (1983) and Nowlen (1983). It can also be used in the fluoresence studies proposed in this thesis. Lastly, the system should be used to examine liposomes and other biological membranes at the ice-water and ice-aqueous solution interfaces. 6.1 Osmotic Shrinkage Experiments Nowlen (1983) reported difficulties in measuring the volume changes of liposome vesicles in osmotic shrink-swell experiments. He calculated the volume changes by measuring the changes in the liposome diameter. The liposome diameters were measured from photographs taken during the course of the experiment. The recommended experiments would be conducted in a modified dif- fusion chamber, to allow admittance of the pipette. Since the volume of the chamber will be greater than previous models, there may be sig- nificant concentration gradients in the sample chamber. To alleviate this problem it is suggested that two membranes be employed instead of one. By locating the dialysis membranes on the upper and lower sur- face of the chamber the Concentration gradients may be reduced. (See Nowlen (1983) for a complete description of the diffusion chamber.) 68 69 Once the pipette is in the chamber and a suitable liposome is found, it would be aspirated into the pipette at a low suction pres- sure. Then the initial diameter and projected length of the liposome would be recorded. Once the experiment is started the suction pressure in the pipette would take up all the excess membrane area produced by the liposome as a result of osmotic shrinkage. This accommodation of the excess membrane material would prevent necking of the liposome and it would always keep the liposome in spherical form. If the membrane area of the liposome is assumed constant the following relation can be used for the radius of the liposome at any time t: RL(t) = [(A(0) - ZnRPAL(t)(l-RPRC-1))/4n]'5 (5.1.1) Where A(0) is the surface area of the liposome at time t=0. Equation (6.1.1) depicts how the changes in volume can be measured much more accurately than in previous investigations. Equation (6.1.1) yields the radius of the liposome at any time t based upon the projected length and the radius of the pipette. The proposed system does have one feasibility problem. In this system the test chamber must be open to the environment to allow entrance of the pipette. Further work is needed in characterizing the solute time history in the proposed chamber. Another question is whether the mechano-opti cal system will react fast enough to keep up with the dynamics of the system. In the compressibility modulus experiments it was observed that the liposome reacted almost instantaneously to an increase in the suction pressure. As long as the increase in pressure 70 was not large enough to perform irreversible work on the membrane (i.e., in regimes where membrane viscosity, plasticity or failure occur). Therefore it is felt that if the suction pressure is suf- ficiently high to provide minimal membrane tension the system will react fast enough to accurately measure the changes in volume of the liposome. Also the effects of friction between the liposome and the glass micropipette can be minimized if the glassware is kept ultraclean. This can be accomplished by sonicating the micropipette in distilled water prior to use. In any case the osmotic dynamics have been reported by several investigators (Boroske, et al., (1981) and Callow (1983)) and these data could serve to check the possible deleterious effects of friction on the experiments suggested above. 6.2 Ice-Hater Interface Experiments These experiments will be invaluable in determining the stresses a biological membrane undergoes during freezing. They will attempt to yield the adhesion forces and the adhesion energies the membrane senses while in contact with an ice front (Olien (1972) and Olien and Smith (1977)). The first task involved in these experiments is the formation of the ice front. The ice front must be planar with respect to the lipo- some. This is essential in order to measure the contact angle between the ice and the membrane. The generation of such an ice front can be accomplished with the second generation test stage. This task can also be accomplished on some of the other conduction stages (Shabana (1983)), but these stages haVe no access site for the micropipette. 71 Once the ice front is established the liposome can be captured in a large bore pipette. Then the remaining liquid in the chamber can be drawn off and replaced with an inert fluid such as 3M FC-47. With this accomplished the liposome can be expelled from the pipette into the inert fluid and then captured again with a small bore pipette similar to those used in the previous experiments. Thus the temperature of the test chamber can then be lowered further as desired without further propagation of the ice front. Care must be taken not to form ice crystals in the liposome. The liposome can then be placed against the ice front and the contact angles measured (see Figure 6.1). The contact angle data can then be put into the equation: .5 = ((0"0015Yi-w" 2.00)(Y1ngm_w) + Y ) 4‘1E; (Ym-w(0'015(Yi-wYm-w) - cos(e) m-w (6.2.1) 1.)) taken from McGiver (1981) to yield the interfacial tensions of the various interfaces. Where Ym-w is the interfacial tension at the water-membrane interface, and Yi-w is the interfacial tension at the ice-water interface. 7 must be available or determined independently i-w to allow the solution of Equation (6.2.1). This analysis was applied to a video tape sequence of an egg PC liposome in distilled water in contact with an ice front (Callow (1983)). The value for 7 was given i-w by Dr. D. McGiver (1983) of the University of Western Ontario, as approximately 5.0 dynes/cm. When Equation (6.2.1) was solved for Ym-w 72 w mumycmucH cmumz\ouH cm van osomoard m :mmZHwn :owuumcoucm Pawuameoucfi on» we uwuceogum .ucoumzmoH .\\ oEOmoqu muuoafiaouow: O P.o mesmeu 73 the result was 77.0 dynes/cm. This is approximately twice the inter- facial tension of a monolayer on an oil-water interface. The value for y is in accordance to that predicted by Evans and Skalak (1980). The contact angles used in the calculation differed on each side of the membrane by no more than 3 degrees. The existence of possible adheSion forces between the membrane and the ice front can be tested by attempting to pull the vesicle from the ice front. By increasing the suction pressure the membrane tension is increased. If an attempt is made to pull the liposome off the ice front, and it just breaks away, a force balance can be performed to calculate the adhesive forces between the ice front and the liposome. The result of this type of proposed study would be a tabulation’ of the adhesive force as a function of the ice front temperature at the membrane-ice interface. These data would be useful for comparison with theory (Olien and Smith (1977)). These experiments could then be performed in various cryoprotective agents and their effects on the adhesive forces measured. Preliminary experiments were attempted using the existing test stage. However the test stage did not have the capability to form the ice front required. The test stage could not reach the low temperature required. 6.3 Summary The micromanipulator system offers an excellent opportunity to study the physical properties of the bilayer membranes in biological 74 cells and liposomes. It also allows one to observe how the membrane reacts to pertubations of its environment. This research has been intended to open the door to the characterization of the membrane and the relationship between the membrane state and the state of its environment. The experimental system has been developed and sugges- tions as to its further refinements and use have been made. APPENDICES APPENDIX A RELATION OF MEMBRANE TENSION TO SUCTION PRESSURE This appendix demonstrates the relation of suction pressure to the membrane isotropic tension. It will also relate the projected length of the aspirated vesicle to the change in area. Performing a force balance, in the axial direction, on Figure (A.1) yields: (PP - 11‘.)an2 TQnRP (A.1) 2 . (P0 " Pc)flRc - TZTTRC Subtracting the two equations eliminates the pressure inside the liposome to yield the following equation. AP = 2T[1/Rp - l/RC]= (Po - Pp) (A 2) which can be solved for T'in terms of measured data (Po, PP, RP’ RC)' The area change is related to the projected length (and other measured data) (Evans, Waugh and Melnik ( 1976)) by: aA = (2an)AL[1 - RP/RC] (A.3) 75 76 mucmpmm mono; oceansmz marscowgom com vow: ovumeosum :owumscowoo.ocmcneoz p.< acumen . TJIII'. .4-4u4< 59.0.. 023.0... 3...... .... .411 A.1 L ‘0 APPENDIX B COMPUTER MODELING AND DATA MANIPULATION 8.1 Computer Modeling and Data Manipulation In the course of this investigation, several computer programs were written to perform various tasks. Early in the study the finite element program ELAS was used in an attempt to model the beam compression test as described by Evans and Skalak (1980). This was attempted to allow greater understanding of the membrane and to attack the modeling problem from a finite element point of view. This effort failed since the program was not adaptable to the volume constraint inside the vesicle. During the beam compression experiments the vesicle can only deform in a way such that its volume remains constant. This volume constraint could not be satisfied in any finite element codes. The results produced from this effort was similar to that of placing a compression load on a thin hoop. The membrane deformed in such a way that there was a sharp bend or buckling at one point. This was not consistent with the experimental results of Evans and Skalak (1980). Therefore this effort was terminated. In the course of this investigation two main computer programs were written. One program was written to perform data reduction, while the other was written to act as a digital temperature controller. Both of the programs will be discussed in detail. The Fortran program DRED.FOR was written to reduce vesicle area, temperature and membrane tension data to allow calculation of the mechanical 77 78 properties of the membrane. The program was also designed to perform parameter variation studies on the isothermal compressibility modulus. Fortran program HTRCON.FOR was written to provide the control logic for temperature control of the second generation test stage. This program requires an LSI-ll with A/D, D/A and RTC capability. This temperature control system was not operational at the time the experiments in this study were performed. A new test stage employing this control program is in development and is discussed in detail in Chapter 3 and Appendix C. The control program HTRCON.FOR has been tested on the stage used by Shabana (1983) and proven useful. B.l.l Computer Modeling At the present, DRED.FOR will do parameter studies on the isothermal compressibility modulus. The user inputs compressibility modulii and the program will construct the tension versus nondimensional area curves. Figure 4.1 represents the tension as a function of the nondimensional area change of the membrane. The curve is generated from Equation (2.1.1.19). The a values range from O to 3 percent. The upper limit was chosen based on the results of Evans and Kwok (1981). They report membrane lysis at values of 3 percent. 3.1.2 Data Manipulation This section of the program DRED.FOR calculates the isothermal compressibility modulus (KT) and the thermal expansion coefficient, at constant tension (Cf) from experimental data. 79 8.1.2.1 Isothermal Compressibility Modulus The user inputs the suction pressure and the projected length of the vesicle in the pipette at several points. The program will then transform the raw data to tension and nondimensional area changes (Appendix A). The tension data is then input to a least squares routine to find the best fit straight line. The slope of this line is defined as the compressibility modulus. The program also performs statistical analysis to determine the coefficient of determination for the least squares linear fit. 8.1.2.2 Coefficient of Expansion at Constant Membrane Tension The coefficient of expansion is calculated using Equation (2.1.2.2). The user inputs two operation temperatures along with the corresponding compressibility modulii, suction pressures and projected lengths. With these data the coefficient of expansion at constant tension (or) is determined. 3.1.3 User Notes The driver program is DRED.FOR. Subroutine Comp.FOR is also required. The program is user-friendly and will prompt for all necessary data. Sample output and program listings follow. (.‘uflPU-‘a _/\_I .J‘ 0003 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0 0 a") 0 0 0 (1. 00000002") 00030000010000 0 1 000000000 IV .22 5-2 Tue 2”-3ec~83 14 +2 C4 P437 0C1 PRBQRAM DPED This program will calculate membrane mechanical properCies using data taken from mechanical experiments in the BTP lab The program operates in two modes. Mode 1 being calculation of membrane conditionsliie. Tension and p?0}éCtEd length of vesicle aspiration). the other will calculate the bolt compressibilitg; shear modulus: and thermal expansion coefficient from experimental data. Dimension arrags and make declarations. DIMENSION X(3&0);Y(350).XBilOQ),YB(100);ALPHA(30);TENSNiEO) DIMENSION DELTAL(SO) LOGICAL IANS REAL KIMU CDMMDN/BLKl/TENSN.NPTS:ALPHA.K.YINTRS.RP.RCIAIDELTAL:PI CDMMDN/BLKE/EXPANS:IRUNS Define variables. X = Position of vesicle in x direction. Y = Position of vesicle in 9 direction. XB = Position of vesicle in micro-pipette. Y8 = Position of vesicle in micro-pipette. ALPHA Nondimsional area change. TENSN Isotropic tension in vesicle. K = Bulk compressibiltg modulus. Shear modulus. Area of vesicle. .141592654 MU A PI = IRUNS = “UN 11 lRun counter. ~-“---“--_-‘~-———--.------‘--‘-“----—-.---~-‘---‘~‘~—I--—-’*--”--—-- --CI.-. NRITEC7,*)’DU YOU WANT A PARAMETER STUDY UR ARE YOU GOING’ NRITE(7:*)’TD INPUT EXPERIMENTAL DATA. IF THIS IS A’ NRITE(7;*)’PARAMETER STUDY TYPE YES.’ READ(7:10) IANS {Check if user is doing param. stdg. O FDRMAT(A1) IF(IANS.NE.’Y’) GDTD 55 .‘~—-——---——---—-—--I.--—----..--..-c--O_~-I.~--_uon_-—. ~—_-—--—-~——o-—*~--— Parameter study section. The user may vary the values of the mechanical properties of the membrane and then watch the variation in the expected experimental output. .-------*_‘--—--—*~-—’-—--“-——-~-_--‘-’—~’-'-..-~--_“-_—'--'-——-- _ _--—o— 0027 002 0030 0031 0032 0033 0034 0035 0036 0037 0038 003? 0041 L“: (3 m m 0 0 0 O 0 L”) 1‘.) h (d O C) ()00000()00L’30f‘1t’3000000000 ['3 0‘ O 81 o ',"\ .Y’ 1“: l . P.) .v I 0 Tue 2"Dec-S3 14:42.04 1‘ 3 I'J1 1 Read in phgsical parameters of experiment. NRITEi7.s)’ENTER BULK CQMPRESSIBILTY: DYNE/CM.’ READ{7.*) K NRITEi7iél’ENTER VESCICLE RADIUS IN MICRO METERS.’ READ(7,*) RC NRITEi7isl’ENTER PIPETTE RADIUS IN MICRO METERS.’ READi7:*) RP Calculate tension and proJected length of RP=RP*.0001 RC=RC*.OOOI NPTS=30 A=4.*PI#RC**2. SConvert to centimeters. {Convert to centimeters. iCalculate area of vesicle IF(IANS.NE.’Y’) DO 20 I=1:30 ALPHA(I)=I*.OOI TENSN(I)=K*ALPHA(I) DELTAL(I)=(A*ALPHA(I)/(2.*PI*RP*(1.~RP/RC)))*10000. CONTINUE GO TO 700 WRITE(7:*)’DO HRITE(7,*)’THE COMPRESSIBILITY MODULUS. READ(7.250) IANS FORMAT(A1) IF(IANS.EQ.’N’) CALL COMP GOTO 300 YOU WANT TO INPUT DATA TO CALCULATE ’ TYPE YES OR NO:’ GOTO 1100 ‘--*--*'—--~*--—--‘--"—-—I---O--‘--~-~---'-~_-~«---—‘-—--_D---~--- ——u---——u._--.."----_-——---—------I--—- —*——'~‘-——-—”—_—-‘“—~ -‘u‘-- DO 260 I=11NPTS SUMX= ALPHA(I) + SUMX SUMY= SUMY + TENSN(I) SUMXY= SUMXY + ALPHA(I)*TENSN(I) SUMXSQ=SUMXSQ + ALPHA(I)%*2. SUMYSO=SUMYSQ + TENSN(I)**2. CONTINUE XNUM=(SUMXY-SUMX*SUMY/NPTS)##2. XDENON=(SUHXSQ-((SUMX**2.l/NPTS)) XDEN2 = SUMYSQ’((SUMY**2.)/NPTS) COEDET= XNUM/(XDENOM*XDEN2) SUMX=O. SUMY=O. SUMXY=O. SUMXSG=0. IDATF=1 FOPTRAN iv CCE 5-2 Tce 27-Dec—83 14 £2 C4 PAS? CZ? C SUMYSQ=O C C Nrite results C 0043 70: NRITE(6.BOO) IRUNS 0044 800 FORMAT(/////’ Run number ’.12) C IF(IDATF.EQ.ll NRITE<61805l COEDET C305 FORMAT(!/’ The coefficient of determination = ’.f10.3) 0045 ifCIDATF.EO.1l WRITE(6,306) 0047 BLé FORMAT(//’ Experimental results!!!!!’) 0048 WRITE(6,810) K 0049 BIC FORMAT(/’ Bulk compressibiltg = ’.F10.3.’ Dgne/cm.’) 0050 RP=RP*IOQOO. 0051 NRITE(6,811) RP 0052 RC=RCe1OOOO. 0053 811 FORMAT(/’ Pipette radius=’.F5.1,’ Micro meters.’) 0054 WRITE(6.812) RC 0055 812 Format(/’ Vescicle radius =’.F5.2.’ Micro meters’) 0056 WRITE(6,820) 0057 820 FORMAT(////’ ’) 0058 NRITE(6.850) 0059 850 FORMAT(: Alpha ’.5x, ’ Tension ’.5x.’ PrOJ. Lng’) 0060 NR1TE(6,860) 0061 860 FORMAT<15X,’ Dune/Cm. ’15X.’ Micro-Metrs.’) 0062 NRITE(6.B70) 0063 870 FORMAT(//’ ') C C C 0064 900 D0 920 I=IINPTS 0065 wRITE<6.910) ALPHA(I).TENSN(I),DELTAL(I) 0066 910 FORMAT<3 = IPEEK("170420) EContents 0P RTC DR. IDLIST(9) = "170422 lLocation 0F BPR Reg. IDLIST<10)= IPEEK("170422 !Contents oF BPR Reg. IDLIST<11)= "440 ELocation oF RTC Int. IDLIST(12)= IPEEK("440) !Contents of RTC Int. IDLIST<13)= 0 35nd 0F list Flag. Set initial conditions. IVEC = "440 ICNT = 1 IPRTY= "7 ID = 1 Call device. CALL DEVICE @musmmma on» ucmmoumou muon one .cfimm concasoamo can we mafia vHHOm one __Wmumn0fiuaocoo Hmcmwm yams“ mamsoooshonu on» How uoam doom c.ca Ii fl _ o o cqccd -_.—-——.. - _...- 11] ago ca nu- mama :oumcfiauma III. mane .3 "am cmppogucou mcaumgmnemh we ovumsmzum ppmcw>o m.¢u mgzmwu ago 2 H am e ouofie Ho. 0 .uom 5:0 x ca om Hm Am om mocmumfimmu Houmoz II: .> ma I .mmmuao> Hm>fiuc 47 .Hmumm: mmoomouowz iIJ+ «“ unease <\a xwm O H ~\HHnHmA UHBdmeum mUH>mQ cor Ami .+ _V \zgnwcuso «\n .> .ma/HWWH/f H Hm _l .xm figofioa W50 UH. 112 to an exponential function, their respective correlation coefficients were greater than .90. The system time constants in the heating and cooling cycles were found to be 24 and 32 seconds, respectively. It should be noted that these experiments were not conducted on Tu's stage. However, since they were conducted on a much larger stage (Shabana, 1983) (larger thermal mass) one would expect the system time constants to be larger thaanu's,not smaller. Figure C5.4 is the steady state temperature error at set points from -40 to 40°C. In the current breadboarded configuration, the controller is able to maintain a worst case tolerance of :_.5°C. This error can be reduced and this will be discussed in Section 6. C.5.2 Effect of Operation Parameter Variations The dominant parameter in the operation of the cryomicroscope stage is the stage heater driving voltage: ~Figures CSiZ and C5.3 demonstrate the effect of the stage heater driving voltage on the system. Figure C5.2 is the time response of the system for various voltage settings. For these experiments the stage heater was subjected to the maximum power the controller would allow for the particu- lar heater driving voltage. This study allowed the definition of Figure C5.3. This figure plots the maximum AT the stage can experience for a given setting. The current configuration has this voltage set at 34.0 volts. The effects of various cooling liquids were recorded in Figure C5.5. It is interesting to note that the cooling rate is unchanged when going from liquid nitrogen to ethylene glycol. It should be"“ " noted that this effect could be the result of convection to the ambient environment. This effect was not studied in this project. 113 Aoomv mafia w: mm@.i is,mge.g 1. a .1. wees gismgmd ousuuuomfioa. 1; mid cmpmm: mamum maoomogupz on» op uemgezo wage" amum a on mmcoamma Ecumxm quemewgmaxm FmUVQzH _.mu «czar; . 114 H: 80.0 Ohms .37 R = ._ 0 Delta a’ §—- TCoolant 10.0 ? 717: T _ T(On.- ”A/ Figure 05.2 System Response as a Function of the Microscope Heater Driver Voltage 200 ° T a t— 3" ‘ . Max Delta __'_'r' RH: 80.0 Ohms 100 Qc I \ ‘ .1. if i i l ! 16 V. 20 V. 32 V. Figure C5.3 Maximum Temperature Rise as a Function of the Microscope Heater Driver Voltage 115 2 Microscope heater driver voltage. 32 V 3 ".5 0C , Coolant Liquid N2 A A"! '\ ?"" ‘\‘- , ’ = ‘ RH3 80. Ohms “n>” ' ._ A. ! -.N l l I I . l l l | neg ,/ a -40 0c 0 °C ~. /,«' 2 4o °c -— “A \ . x \ _- \ -— .A -.5 °c inn-.— Figure C5.4 Measured Steady State Temperature Error as a Function of Set Point Temperature with Proportional Control .. Figure cs,-'5 Effect of different coolants -\ on the cooling rate. 100 ° ‘ T . = 25 °c i?\ ambient .4, 0 Temperature ‘ ---------------------- Ethel. - Glycol 3 —10 c .—- \ . . . 3 ------------------- Liquid N2 @ -197 C .. (Seconds) Figure C5.5 Effect of Different Thermal Sink Temperatures on the Stage Cooling Rate 116 C.6 Conclusions C.6.l Correlation of the Model to Experiments The computer program HTRSIM.FOR provided valuable insight into the operation of the digital temperature controller. By performing parameter variation studies, it predicted the maximum source of error would come from the temperature sampling frequency. The simulation program predictions were verified by experiment. There was an order of magnitude reduction in steady state temperature error when the temperature sampling frequency was increased from 10 to l00 hz. This can be shown from Figure C3.2 and was verified by experiment. As stated previously, the optimal sampling rate, limited by thermocouple time constants, was 100 hz. However, the actual error was larger than the predicted error of the simulation studies. C.6.2 Error Sources and Reduction The simulation program estimated a controller accuracy of :_.l°C (Figure C3.4). The actual controller, in the breadboard state, was able to achieve an accuracy of : .5°C as its worst case. Upon analyzing the output of the thermocouple signal amplifier, it was determined that there was still substantial amounts of electro- magnetic noise in the signal. It should be noted that there are numerous filters in the system to remove these errors. This EM noise would cause substantial errors in the temperature the computer reads in the control program. It is felt these EM effectswould be eliminated if the controller was constructed on a PC board. There may have also ll7 been a problem of a floating ground since the breadboard ground may have been slightly different than the I/O box, which was used as the common ground. The slight changes in the grounds may have occurred from the distance the device was away from the I/D box and the corresponding cable length. The preceding work assumed the Action Pac was capable to accurately follow the actual temperature. The temperature control program sampled temperature at a frequency of 100 Hz. However, the time constant of the model 4l50 Action Pac was approximately 130 ms. This information was provided by the manufacturer. The large time constant of the Action Pac would induce further errors in the control program. A modified version of the 4l50 Action Pac which has a time constant of 5 ms. is available from Action Instruments Company of San Diego, California. The effects of the time constant of the_Action Pac will be felt more strongly when the temperature controller is operated in the dynamic mode. Since the controller will be used mainly for isothermal temperature work, the effects of the Action Pac are not as great. In order to optimize the controller performance, the following procedures should be initiated. First, when in operation, turn off all unnecessary sources of EM noise. Secondly, construct the controller on a PC board and house the board in a Faraday cage. Make all cable runs with grounded shielded cables especially from the Action Pac to the input of the thermocouple signal amplifier. Incorporate the modified Action Pac to allow for greater accuracy in the temperature measurements. When these modifications are made,the controller should operate well within its tolerance of :_.l°C. APPENDIX D EXPERIMENTAL UNCERTAINTY D.l Uncertainty Analysis for Isothermal Compressibility Modulus Experiment This uncertainty analysis is based upon the average experimental condition of the liposome. The average conditions are: T' = l.601 dynes/cm a = 0.023 AL = 5.6 um RL = 23.9 um RP .= 6.7 um AP = 3440.0 dynes/cm The resolution of our experimental apparatus is: d(AL) = 0.55 pm d(RP) = d(RL) = 0.55 um Using the relationship between aspiration pressure and membrane tension one can derive all the quantities of Equation (3.6.3). Results of this analysis reveals that the term: aT' _ dynes m (NAP) - i 0.05 cm 118 119 is the major source of error in Equation (3.6.3). Equation 3.6.4 can be solved if one uses Appendix A for the relation for a and incorporates the average properties mentioned earlier. The results of this analysis yield the fact that the terms: -—-32---C(R R ‘1 3a _1 p C ) and 7“” AL (HAL) a(R R ) p c are the major sources of error. Once do and d7 are found (Equation (3.6.l)) can be solved. 0.2 Uncertainty Analysis for the Thermal Expansion Coefficient Equation 3.6.2 is the expression for the uncertainty for Cf; do and dT must be determined using average conditions that are present during the experiment. da is the same as it was in Section 0.2. dT is j; 0.5°C. Finding the values for do and dT and using: (a - a ) CT: T: -"T'b’ (0.2.1) One can solve Equation (3.6.2) yielding dCT: The major source of experimental error was the term: 3 CT- —3;-da APPENDIX E STATE PLANE GENERATION Equations (4.l.l) and (4.1.3) were used to generate the state planes shown in Figures 4.2 and 4.3, respectively. T(a,T) = KTa - KT Car-(T - TREE) _ dv _ 1r(a,T) -no+d—(T - Tm.) - KT. + KT cT (T - Tm.) The state planes were created using parameters experimentally derived from Soy (R3) vesicles. Therefore: KT = 52.0 dynes/cm _ o"I 0f - 0.0036 C Tref = 25°C %%-= 0.2 dynes/cm - °C 1r = 70.0 dynes/cm Note the value for 5% was approximated. Little information is available on the quantity. no refers to the liposome in the stress free state (Evans and Skalak (l980)). 120 BIBLIOGRAPHY 10. 11. 12. 13. 14. 15. 16. BIBLIOGRAPHY Baret, J. F., (1983) "Progress in Surface and Membrane Science," 14, 291. Blume, A. (1979) Biochimica et Biophysica Acta, 557, 32. Boroske, M., Elwenspoek, F. (1981) Biophysical Journal, 34, 95. Callow, R. (1983) "Thermodynamic Modelling and Cryomicroscopy of Large Unilamellar Liposomes," M.S. Dissertation, Mechanical Engineering Department, Michigan State University. Defay, R. and Prigogine, I. (1966) Surface Tension and Absorption. John Wiley and Sons. New York, New York. Evans, E. and Kwok, R. (1982) Submitted to Biochemistry, unpublished manuscript. Evans, E. and Skalak, R. (1980) Mechanics and Thermodynamics of Biomembranes, CRC Press. Boca Raton, Florida. Evans, E., Waugh, R., and Melnik, L. (1976) Biophysical Journal, 16, 585. Evans, E. and Waugh, R. (1977) Journal of Colloid and Interface Science, 60, 286. Fendler, J. H. (1981) "Membrane Mimetic Chemistry," John Wiley and Sons. New York, New York. Gruen, D. and Wolfe, J. (1982) Biochimica et Biophysica Acta, 688, 512. Israelachvili, J. N., Marle, L. J. A. and Horn, R. G. (1980) Biophysics, 13, 121. Kwok, R. and Evans, E. (1981) Biophysical Journal, 35, 637. Lee, A. (1975) Biochimica et Biophysica Acta, 413, ll. Lehninger, A. (1970) Biochemistry, Worth Publishers,Inc. New York, New York. McGiver, J. L. (1981) Journal of Colloid and Interface Science, 83, 301. 121 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 122 Mitchison, J. L. and Swan, M. N. (1954) Journal of Experimental Biology, 31. 443. Nagle, J. F. (1976) J. Membrane Biology, 31, 233. Nowlen, S. (1983) "Non-Equilibrium Thermodynamic Modeling and Parameter Estimation of Phenomenological Coefficients Describing Coupled Transport Across a Membrane," M.S. Dissertation, Mechanical Engineering Department, Michigan State University. Olien, C. R. (1972) J. Theor. Biology, 33, 201. Olien, C. R. (1977) Plant Physiol. 39, 499. Rand, R. P. and Burton, A. C. (1964) Biophysical Journal, 5, 303. Reynolds, J. A., Gilbert, 0. B. (1974) Proc. Natl. Acad. Sci., U.S.A., 21, 2925. Shabana, M. (1983) "Cryomicroscope Investigation and Thermodynamic Modeling of the Freezing of Unfertilized Hamster Ova," M.S. Dissertation, Mechanical Engineering Department, Michigan State University. Steponkus (1982) Biochemica et Biophysica Acta. Submitted. Tanford, C. (1973) "The Hydrophobic Effect," John Wiley and Sons, New York, New York. . Tanford, C. (1974) Journal of Physical Chemistry, 13, 2469. Tu, S. M. (1983) "Computer Simulation of Two-Dimensional Transient Temperature Field in Cryomicroscope Conduction Stage," M.S. Dissertation, Mechanical Engineering Department, Michigan State University. Yager, P., Sheridan, J. P. and Peticolas, W. L. (1982) Biochemica et Biophysica Acta, 693, 485.