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Surface density of radiant sources measured by optical microscopy : correction for diffraction and focus… Knowles, David William 1986

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S U R F A C E DENS ITY OF R A D I A N T SOURCES M E A S U R E D B Y O P T I C A L M ICROSCOPY : C O R R E C T I O N F O R D I FFRACT ION A N D FOCUS L IMITATIONS by DAVID WILL IAM KNOWLES B.Sc. - Hon., University of New South Wales, Australia, 1982 A THESIS SUBMITTED IN PARTIAL F U L F I L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER ; OF SCIENCE in THE F A C U L T Y OF GRADUATE STUDIES DEPARTMENT OF PHYSICS We accept this thesis as conforming to the reauired standard THE UNIVERSITY OF BRITISH COLUMBIA October 3rd 1986 © David William Knowles, 1986 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia 1956 Main M a l l Vancouver, Canada V6T 1Y3 E-6 (.3/81) A B S T R A C T A new technique is introduced for the determination of the surface density of membrane bound components on living cells inuitro. This technique provides a simple conversion of fluorescence intensity to number density and involved the modelling of the spatial optical response of the microphotometer to account for the inherent diffraction and focus limitations of the system. A theoretical and experimental study was undertaken to examine the adsorption of a fluorescently labelled ligand (WGA) onto the membrane surface of a biological cell (the erythrocyte). W G A/red cell interaction was evaluated with a fluorescence microphometer. The microphotometer is a laser based fluorescence microscope in combination with intensified video imaging and digitizing equipment that produces fluorescence images with a resolution of 0.25Mm. The fluorescence conversion technique was used to characterize the adsorption of W G A on to the red cell surface. Individual cells were isolated and incubated in various bulk concentrations of fluorescenated W G A to determine the dependence of adsorbed concentration on bulk concentration and incubation time. The equilibrium g results gave a microscopic association constant of 2.95x10 liters/mole, a molecular binding ratio of one W G A molecule per glycophorin molecule on the red cell surface 5 and the number of glycophorin molecules per human red blood cell as ( 6 . 5 ± 0 . 3 ) x l 0 . ii TABLE OF CONTENTS Abstract i i List of Figures v List of Symbols vii Acknowledgements viii I. Introduction: Fluorescence Microphotometry and Biological Systems 1 A . Fluorescence Imaging 1 B. Image Analysis 2 C. A Model System 3 1. Membrane Structure and the Red Blood Cell 3 D. Application of the Fluorescence Intensity to Number Density Conversion Technique 5 II. Fourier Analysis and Physical Optics 8 A . The Fourier Transform 8 B. The Discrete Fourier Transform 11 C. Fourier Optics 11 D . The Optical Transfer Function 14 III. The Fluorescence Microphotometer 17 A . Introduction .". 17 B. Photometer Hardware ; 18 1. The Source of Radiation 18 2. The Optics and Microscope 18 3. Video Camera and Video Signal Multiplexing 20 4. The Microprocessor 21 5. The Hardware Interface 23 C. Photometer Software 25 1. Z80 Assembler Routines 25 D. Static Photometer Response 34 1. Introduction 34 2. Method:- Linearity, Invarience and Camera Gain 36 3. Results 37 4. Discussion and Conclusion 40 IV. Conversion of Fluorescence Intensity to Number Density:- 44 A . Introduction 44 1. Fluorescence Intensity to Number Density Conversion 45 B. The Molecular Surface Density Calibration Experiment 45 1. Experimental Procedure 45 C. The Theoretical Analysis Method 47 1. The Transfer Function 47 2. Multiplane Analysis including Focus Aberration 48 3. Discrete Numerical Analysis 50 4. The Theoretical Experiment 51 D. Results 52 E . Discussion 59 1. Frequency Domain Resolution 61 iii 2. A Calculation of the Optical Collection Depth 64 F. A Single Composite Transfer Function 67 1. Aim 67 2. Introduction 67 3. Method 68 4. Results 69 5. Disscussion 70 6. Conclusion 71 V. Specific Molecular Adsorption to Cell Surfaces 76 A. Introduction 76 1. The Molecular Interaction 76 2. The Scatchard Plot 77 B. Experimental Preparation 79 1. Chemical List 79 2. Pipette Preparation 80 3. Cell Preparation 81 C. The Experimental Procedure 81 1. Data Collection 83 D. Data Analysis 84 1. Sphere Surface Projection 86 2. The Application of Simple Discrete Fourier Optics 89 E. The Effect of the Fluorescent Label on the Wheat Germ 92 F. Kinetic and Equilibrium Behaviour of Red Cell/WGA Adsorption 93 G. Results 93 H. Discussion 95 Appendix 100 List of References 105 iv LIST OF FIGURES Number Title Page 1 The 321 Video Analyser Slow Scan Output 22 2 The Hardware Interface Schedule 24 3 Flow Chart of Data Acquisition/Display Software 26 4 A D A Voltage to 12 Bit Binary Conversion 31 5 The SSVS Lead Edge Synchronization 33 6 Laser and Incandescent Intensity Fluctuations 38 7 Output Voltage Verses Intensity 39 8 Intensifier Gain (INT) Response 41 9 Video Gain (AGC) Response 42 10 Experimental Projection of a Pipette Crossection 53 11 Theoretical Image and Object Projection of a Pipette Crossection 54 12 Theoretical and Experimental Dependence of Fluorescence Intensity on Internal Pipette Diameter 56 13 Linearity Constant Verses Transfer Cutoff 57 14 The Projection of a Cylinderical Object into 2 Dimensions Showing the Intensity Crossection 65 15 Intensity Verses Cylinderical Object Height 66 16 Frequency Spectra of the Theoretical Object Pipette Crossection 72 17 Frequency Spectra of the Theoretical Image Pipette Crossection 73 18 Multi Isofocal Analysis Composite Transfer Function 74 19 Incoherent Transfer Function at 2/im Out of Focus 75 20 The Projection of an Aspirated Red Cell into 2 Dimensions Showing the Intensity Crossection 85 21 Spherical Surface Crossection 88 v 22 Competitive Adsorption of FITC/WGA and WGA 94 23 Adsorption Kinetics of WGA onto the Human Erythrocyte 96 24 WGA/Red Cell Adsorption Isotherm 97 25 WGA/Red Cell Scatchard Plot 98 vi L I S T O F S Y M B O L S Ft Fourier Transform Function x Spatial Dimension f Frequency Dimension ir The ratio of circle circumference to its diameter i =V-i J The definite integral over all space spanned by x Af Elemental Frequency Unit Ax Elemental Spatial Unit T The Period of Oscilation A(x) Optical Pupil Function h(x) The Point Spread Function x =x/( X.d. ) Dimensionless Spatial Coordinate X Wavelength d. Image Distance M Magnification H^-, Coherent Transfer Function Hj Incoherent Transfer Function p = ^ c Dinnensionless Frequency f Optical Transfer Cutoff f(x) Derivative of f(x) p(x) Surface Density A(x) ( - 1 - x ; -1<X<1 0 ; otherwise Sinc(x) = (sin(7rx))/7rx vn ACKNOWLEDGEMENTS With great pleasure I thank: Dr. Evan Evans, my supervisor, for his encouragement and support. Dr. David Needham for many helpful discussions and his comments on this thesis. Andrew Leung for his experimental and technical assistance. Frances Ledwith for her sticky buns and all the yummiest things. The Girls of the Five for their protuberances fantastique. viii I. INTRODUCTION; F L U O R E S C E N C E MICROPHOTOMETRY A N D B I O L O G I C A L SYSTEMS Biologists are interested in the processes of ligand/cell interactions. Ligand is a term that refers to a wide range of biological macromolecules such as enzymes, hormones, growth factors and antibodies. Ligands, most of which are proteins, catalyse cell response by binding specifically to receptor proteins on the target cells they influence. These interactions control a host of physiological functions from gamete recognition and fusion through morphogensis, development and function of vital systems, growth, repair from injury and disease and the essential cellular metabolic processes. The characterization of such ligand/cell interactions is thus of great interest. A. F L U O R E S C E N C E IMAGING One method to study ligand interactions at the surface of the cell is to label the ligand with a fluorescent probe and view the conjugated ligand with a fluorescence microscope. This allows the direct imaging of the probe and results in a fluorescence intensity mapping of the ligand which can be related to ligand surface concentration. The state-of-the-art experimental equipment has been designed and assembled to study the interaction, number density and distribution of membrane bound proteins on single living cells invitro. The system is a laser based, microprocessor driven, fluorescence microphotometer [Koppel,1979, Peters et al.,1981; McGregor et al.,1984; Arndt-Jovin et al.,1985]. The new developement is its calibration on a macromolecular scale, and is capable of measuring the number density of fluorescently labelled molecules on the cell surface. This method allows one to look 1 Introduction: Fluorescence Microphotometry and Biological Systems / 2 directly at the ligand as it adsorbs to the red cell. Thus the resulting intensity map can be used to determine the distribution of ligand on the cell surface. B . I M A G E A N A L Y S I S The physics of this problem is the quantification of the surface density of ligand adsorbed on a cell. A technique is introduced for the simple conversion of fluorescence intensity to number density. It is a new technique which involves the encapsulation of a known concentration of fluorescent probe in a micropipette and the subsequent fluorescence analysis. The fluorescence intensity of a transverse pipette cross-section in such an experiment would have an intensity profile proportional to the projected cross-sectional volume of a cylinder (figure 10). One inherent problem is the size of the object in relation to the resolution of the system. Red blood cells for example, have an approximate average diameter of 5ym and the photometer has a band pass which attenuates spatial frequencies above 4jum *.f Thus the resolution of the S3'Stem, which is the minimum distance that two object points can be separated and still be seen as distinct in the image, is 0.25 ^ m . The effect, due to the nature of physical optics, is an image compromised by diffraction and focus limitations [Agard,1984] that cannot be used directly to determine surface density distribution. However, by using the theory of physical optics [Goodman, 1968], the resolving power of the system can be modelled and the distortions of the image caused by diffraction and focus aberration can be accounted for by a simple optical correction factor. tFrom the model presented in chapter 4. Introduction: Fluorescence Microphotometry and Biological Systems / 3 C. A MODEL SYSTEM Red blood cells and wheat germ agglutinin were used as a model of ligand/cell interaction. This system is widely studied. Much work has been carried out simply to characterize the interaction [Lovrien&Anderson,1980; Anderson&Lovrien,1981; Ketis&Grant,1982; Ketis et al.,1982; Grant&peters,1984], and other studies use the W G A as a probe to characterize the distribution of protein on the red cell surface[Evans&Leung,1984; Snoek,1985]. Wheat germ agglutinin is a protein extracted from wheat germ and is one of many such proteins which are termed lectins. Lectins have the ability to agglutinate red cells. The aggultination of red cells in the presence of wheat germ agglutinin is inhibited by the sugar N-acetylglucosamine [Sharon 1977]. This shows that wheat germ agglutinin binds specifically to this sugar and further that wheat germ agglutinin binds specifically to the membrane bound protein glycophorin since glycophorin contains N-acetylglucosamine. 1. Membrane Structure and the Red Blood Cell The human red blood cell is a remnant of a living cell, has no nucleus and thus cannot divide. It is filled with a solution of haemoglobin which is responsible for the transportation of oxygen to and carbondioxide from the metabolizing tissue of the body. One reason the red cell is studied so extensively is it's accessibility. Red cells can be extracted in small quantities from a simple finger prick. They also exist individually in the blood plasma thus isolation is not a problem. There are three components to the red cell membrane, [Singer&Nicholson,1972; Israelachvili,Marcelja&Horn,1980] amphiphilic lipid molecules, amphiphilic protein molecules and spectrin. The whole structure is a condensed state of matter held together by non-covalent intermolecular forces [Israelachvili,1985; Introduction: Fluorescence Microphotometry and Biological Systems / 4 Israelachvili&Ninham,1977], which determine the minimum configurational energy and the packing of the lipid and protein molecules [Marcelja,1976; Owicki&McConnell,1979]. The red cells are never-the-less able to withstand an average of 120 days of circulation within the cardiovascular system. The first component, amphiphilic surfactant molecules, form a structure which physically separates the environments exterior and interior to the cell, which differ in composition and osmolarity. These molecules are cholesterol and lipids, and comprise a hydrophilic head group and a hydrophobic fatty acid tail. Membranes are formed largely of phospholipids and cholesterol. The phospholipids have a glycerol group joined to two fatty acid chains and a phosphate group. The phosphate group is connected to a head group such as ethanolamine, choline or serine. The structure of the condensed matter is a double layer of lipid molecules with the tails internalized towards the center of the bilayer, and the head groups forming the two surfaces of the membrane [Singer&Nicholson,1972]. This structure is a liquid crystal [Evans&Hochmuth,1977] in which the lipids form a two dimensional fluid in the plane of the membrane but are highly incompressible in the third dimension. Lipids are associated with the membrane in a highly asymmetrical fashion [Capaldi,1974]. In the red cell most lipids that terminate in a choline group are on the outer layer while lipids with terminal primarj' amino groups are on the inner half. Lipids with oligosaccharides, glycolipids, are found only on the outer half of the red cell membrane. The second membrane component is the array of amphiphilic protein molecules which are essentially in solution, and have varying degrees of motional freedom, within the fluid membrane. Intra-membrane proteins traverse the membrane and their position can be fixed via their association with the membrane cytoskeleton. Surface proteins Introduction: Fluorescence Microphotometry and Biological Systems / 5 are associated with one side of the membrane alone and thus move freely about that surface. Proteins on one surface are not able to partition through the membrane to the other surface. This sort of motion is opposed by the hydrophobic interaction [Tanford,1973] since the work required to drag the hydrophilic region of the protein through the hydrophobic central portion of the membrane creates a large energy barrier. While the basic structural integrity is determined by the lipids, the specific functions are carried out by the proteins. The proteins of the external layer of the lipid bilayer can extend into the cell environment some 100A1. This region above the bilayer is known as the glycocalx, and since this is the portion of the cell that the environment interacts with, it becomes the ambassador of cell/environment interaction. The glycocalx characterizes cell type and is a highly but selective reactive surface which monitors and mediates the cell/environment biochemistry. The third structure peculiar to some cells, the red cell in particular, is the cytoskeleton. The cytoskeleton is made of long entangled filamentous proteins known as spectrin. It supports the red cell membrane and creates the possibility of a non spherical, biconcave shape. This shape allows an excess surface to volume ratio which is essential when the red cell is deformed in the microcirculation. Since the membrane is highly cohesive and resists area dilatation [Evans&Hochmuth,1977] the cell would rupture due to such deformation [Evans 1986]. D . A P P L I C A T I O N O F T H E F L U O R E S C E N C E I N T E N S I T Y T O N U M B E R D E N S I T Y C O N V E R S I O N T E C H N I Q U E A simple set of experiments was conducted to characterize the adsorption of wheat germ agglutinin to the surface of the human red blood cell. Red blood cells were Introduction: Fluorescence Microphotometry and Biological Systems / 6 individually isolated and incubated in various concentrations of fluorescently labelled WGA. The resulting fluorescence intensity map is of WGA adsorded onto the cell surface and is proportional to the projected surface area of the cell (Figure 20). The whole intensity profile is theoretically modelled to determine the cell diameter and the normal fluorescence intensity. The normal fluorescence intensity can be directly related to the molecular surface density of WGA and is a function of the bulk WGA concentration and the incubation time. This experimental and theoretical technique is used to characterize the kinetics of the WGA/red cell inetraction. The kinetic data indicates the time and surface concentration at which equilibrium is reached and results in an interaction isotherm and a Scatchard plot. The Scatchard plot predicts the microscopic association constant and the number of molecules of WGA bound per glycophorin molecule on the membrane surface. The results are: the microscopic association constant of the interaction between WGA g and membrane bound glycophorin is 2.95x10 liters/mole. at equilibrium saturation there is 0.93 molecules of WGA bound per molecule of glycophorin on the red cell. the density of glycophorin molecules on the human red blood cell is 5 . 0 ± 0 . 2 x l 0 M m " 2 . The average red cell surface area is 1 3 0 ± 1 0 M m 2 and thus there is ( 6 . 5 ± 0 . 3 ) x l 0 5 glycophorin molecules per red cell. These results compare favourably with thoes cited in the literature [Adair&Kornfeld, 1974; Anderson&Lovrien,1981]. Snoek, 1985, concluded that there was 5x10 5 glycophorin molecules on the red cell and that there was a specific binding of one mole of WGA per mole of glycophorin. Lovrien and Anderson, 1981, state a Introduction: Fluorescence Microphotometry and Biological Systems / 7 value of 3-5x105 copies of glycophorin per red cell. II. F O U R I E R A N A L Y S I S A N D P H Y S I C A L OPTICS A . T H E F O U R I E R T R A N S F O R M The Fourier transform has become an essential tool in the study and determination of the response characteristics of linear invarient systems. Define a system as being a 'black' box which creates an output for a given input. For example: 1. A telephone system where vocal sound waves are the input and mechanically stimulated sound waves are the output. 2. An optical system where diverging light from the object is the input and the light converging to an image plane is the output. The success of a system in maintaining correct output- for its corresponding input is determined by its static and dynamic response. The static response is the response of the system to a monotonic input. For a system to be characterizable and thus applicable it will produce the same output, independent of time and absolute position, for a given input. This is the property of invariance. The dynamic response is the response of the system to sudden changes in input. One could theoretically test the dynamic response by studying the output produced from a purely sinusoidal input and varying its frequency. Zero frequency is the special case of static response, and it is understandable that there will be a certain critical frequency above which the system is too slow to respond and produces some sort of mean output. The whole concept of Fourier analysis has to do with this frequency response. In fact any input can be constructed from the superposition of sinusoidal (plane) waves of various amplitude and frequency. This theorem was devised by a French physicist 8 Fourier Analysis and Physical Optics / 9 Jean Baptiste Joseph Baron de Fourier (1768-1830), and the process of determining which frequencies represent a given input is known as Fourier analysis. The Fourier transform and the inverse Fourier transform of a function •(x) are given by equations 2.1 and 2.2. * ( f )=Ff(*(x) )=f d x . * ( x ) . e " l 2 7 r f x E q u a t i o n 2.1 *(x ) = F f 1 (*(f ) )= / f d f . * ( f ) . e l 2 , r f x E q u a t i o n 2.2 These are the transformations which take a function between physical space and frequency space. The Fourier transform takes a physical space object and computes the frequencies, in units of inverse physical space, of the plane waves which, when added together, construct that physical object. The result is the frequency spectrum of the object. The inverse Fourier transform takes the frequency spectra and reconstructs the physical space object by computing the superposition of plane waves defined in frequency space. Fourier analysis provides a way of predicting the output of a system given the input. A system will have a frequency response which is characteristic of the input frequence. Once this is determined we simply transform the object into frequency space, act on each of its characteristic frequencies with the frequency response function of the system, then transform the frequencies back into physical space to give the predicted output. Determining the system response to all frequencies is an analytical problem all of its own but is done very simply by experimentally recording the output to a point source input. A true point source is represented by Fourier Analysis and Physical Optics / 10 all frequencies at constant amplitude in the frequency space, and therefore the Fourier transform of its output is a function in frequency space which defines how the system attenuates each frequency component. For Fourier analysis to apply there are two important properties the system must have; the system must be invariant and linear. Invariance is the property that for each unique input there is a unique output which is independent of time or the absolute position. Linearity is the property of superposition. The output of several stimuli acting simultaneously equals the sum of the outputs of each of the stimuli acting individually. This must hold because Fourier analysis deconvolves an input function into its individual frequency components which are effectively sent one at a time through the system response function and then reconvolved into the output function. There is one other point concerning the dimension in physical and frequency space. The type of input function depends entirely on the system being studied. The units of the physical space might be time, three dimensional space or a combination of these. Strictly for the purpose of ease of Fourier analysis, and to avoid edge effects, the input function is assumed to be one period of an infinite array of identical such input functions. The frequency is given by one over the period and hence has dimensions of inverse physical space. Thus an input function which varies in time is transformed into temporal frequencjr components with dimension of one over time. Similarly an input function of real space is transformed into spatial frequencj' components with dimension one over distance. Fourier Analysis and Physical Optics / 11 B. T H E D I S C R E T E F O U R I E R T R A N S F O R M For fast computer aided numerical computation one defines a discrete Fourier transform [Higgins,1976] which acts upon an array of data. The data represents the theoretical input function, and the Fourier transform produces an array of complex data points which represent the amplitude and the phase of the plane waves of increasing frequency. The physical array of N points is assumed to represent one complete period, T, in physical space where T = N.Ax and Ax is the incremental physical space distance. Hence the incremental frequency space distance is; A f = ( T ) ~ 1 = ( N . A x ) ~ 1 E q u a t i o n 2 . 3 and is in units of inverse distance. C. F O U R I E R OPT ICS Imaging Systems:- An imaging system, in the most general sense, is a system of optical elements arranged so as to collect light from an object and use it to create an image. So long as the optical elements are stationary with respect to one another the system is invariant in time, and depending on its geometric aberrations, the system is thought of as spatially invariant although never perfectly so. Also due to the superposition principle of electromagnetic radiation, but again depending on geometric aberrations, the system is thought of as linear. The resolution of an optical system is determined by three parameters: 1. the wavelength of light, Fourier Analysis and Physical Optics / 12 2. the numerical aperture 3. and the degree of geometric aberration. A n imaging system is said to be diffraction limited if a diverging spherical wave, from the object, is mapped into a spherical wave which converges to the same relative position on the image. The diffraction limitation of an imaging system arises because the object is being investigated by an electromagnetic probe of finite size which is characterised by its wavelength. Any ultra structure with characteristic dimension less than this finite size will not be resolved in the image. The diffraction limited system corresponds to the maximum thoeretical resolution. The concept of numerical aperture was introduced by Ernst Abbe (1840-1905) [Hecht&Zajac,1974]. The numerical aperture equals the refractive index of the medium adjacent to the objective lens multiplied by the sine of the half angle of the maximum cone of light collected by the lens. For an objective in air the numerical aperture is less than or equal to unity. Abbe recognised that the resolution varied directly with the wavelength of the light and inversety as the numerical aperture. The importance of the numerical aperture is in its relation to the minimum physical aperture of the optical system. This aperture is a window through which the system collects information about the object. Clearly, unless the object was sitting inside the window, which is physically imposible, only part of the information radiating from the object can be collected. It is this loss of object information due to numerical aperture which decreases the resolution of the image. Geometric aberrations cause the light to stray from their geometric path. A system with aberrations does not produce a perfectly spherical converging wave from a diverging spherical input wave and has less resolution than the diffraction limit. Two examples of geometric aberrations are: 1. imperfections in the curvature of the lens, known as spherical aberrations, and 2. the slight variation in optical focal length as a function of wavelength, Fourier Analysis and Physical Optics / 13 known as chromatic aberration. The wavelength, numerical aperture and geometric aberrations all effect the resolution of the system and distort the image relative to the object. However, all the information about the way in which an imaging system distorts its image can be attained from the system's point spread function. A n imaging system's point spread function is it's spatially dynamic response function which completely characterizes the imaging system and is used in conjunction with Fourier analysis to mathematically model it. The point spread function is an amplitude and phase map of the image created from a point source. It holds all the information about an invariant linear system because any object can be made up by an array of appropriately positioned point sources. The image created from such an object is the linear superposition of point spread functions positioned at each point in the array. Further, a true point source object is represented by all spatial frequencies at constant amplitude in frequency space and thus the transformation of the point spread function into frequency space creates a function which shows exactly how the system attenuates each frequency component independent of the initial object shape. This function is known as the optical transfer function and in frequency space mimics the action of the imaging system in creating an image from its object. The point spread function for an aberration free, hence diffraction limited system, is governed completely by the illumination wavelength and the shape and size of the minimum physical aperture in the system. Mathematically if one defines a pupil function which is unity within the aperture and zero otherwise, equation 2.4, then the point spread function is the Fraunhofer diffraction pattern of the lens aperture or pupil function.(Equation 2.5) A ( x ) = [ i Fourier Analysis and Physical Optics / 14 i n s i d e t h e l e n s a p e r t u r e o t h e r w i s e E q u a t i o n 2.4 h ( x ) = M . f 0 d x . A ( \ d - x ) . e -i27TXX E q u a t i o n 2.5 D. T H E O P T I C A L T R A N S F E R F U N C T I O N The relation of the optical transfer function to the point spread function depends on whether the light collected from the object is spatially coherent or incoherent. Spatially coherent light is produced when the phase of the light from each point on the object is fixed in relation to the other points. Whereas if the phase from each object point varies randomly in a statistical manner the light from the object is spatially incoherent. For coherent illumination the various impulse responses in the image plane vary in unison, and therefore must be superimposed by addition of amplitude and phase of the electromagnetic components. For incoherent illumination from the object, the impulse responses in the image plane vary in statistically independent fashions, and therefore are superimposable by addition of the intensity of the electromagnetic components. Thus a coherent system is linear in amplitude and phase and an incoherent system is linear in intensity. One defines the coherent transfer function as the Fourier transform of the point spread function. (Equation 2.6) H c ( f ) = / d x . h ( x ) . e - i 27rf x E q u a t i o n 2.6 The incoherent transfer function is the Fourier transform of the modulus squared of Fourier Analysis and Physical Optics / 15 the point spread function. This must be appropriately normalized so that the transfer function operating on an object function results in a unitary operation which leaves the spatial dimension of the object invariant.(Equation 2.7) f dx 'h(x) ' 2 P _ i 2 7 r f x H j ( f ) = J x d X - | h U ) ' - e / xdx.Jh(x): 2 E q u a t i o n 2.7 The three general properties of an incoherent optical transfer function are: (Equations 2.8,2.9,2.10) 1. the function at zero frequency is unity 2. the function is hermitian 3. the function is never greater than it's zero frequency component H(0)=1 H ( - f ) = H f ( f ) ! H ( f ) | < ! H ( 0 ) ! E q u a t i o n 2.8 E q u a t i o n 2.9 E q u a t i o n 2.10 Two examples of optical transfer functions [Goodman, 1968] which are used extensively in the following theoretical work are for incoherent systems. The first (equation 2.11) is for a circular lens aperture and the second (equation 2.12) for a square lens aperture with the simple aberration of focus error. Fourier H(p)= f | [ c o s " 1 p - p / ( 1 - p 2 ) ] Analysis and Physical Optics / 16 ;p<1 ;Otherwise Equation 2 . 11 H ( p ) = A ( p ) s i n c [ ^ p ( l - | p ! )] Equation 2 . 1 2 III. T H E F L U O R E S C E N C E M I C R O P H O T O M E T E R A. I N T R O D U C T I O N The fluorescence microphotometer is an instrument that uses laser irradiation to excite fluorescence emission. The photometer uses a microscope and processes images with the aid of video equipment and a microprocessor. The instrument is capable of measuring and producing a two dimensional map of low levels of fluorescence emission from microscopic objects. This chapter has three sections: 1. an explaination and layout of the photometer hardware, 2. an outline of the photometer software 3. and a check for photometer invarience and linearity The photometer's source of illumination is an argon ion laser which is water cooled and runs a head current of 40 amperes. The laser beam is shutter controlled and then expanded by collimating the light scattered off a piece of rotating, frosted glass. The expanded beam is sent up to the objective plane of the microscope through a dichroic system, using the objective as the condenser. The lasing wavelength pumps the fluorescent centers on the object into an excited state which decays and emitts photons of less energy and hence longer wavelength. The fluorescence emission is collected by the objective and passes through the dichroic sj'stem which is impermeable to the shorter laser wavelength. The light passing through the dichroic is split and focused by an eyepeice for visual and electronic imaging. The electronic imaging system consists of a shutter controlled, intensified video camera with manual gain controls and is, in effect, a sensitive photometer. The supporting video analysis equipment creates, in real time, a one dimensional 17 The Fluorescence Microphotometer / 18 array of video picture elements which are monitored on an oscilloscope and digitized by an analog to digital converter for storage, analysis and display by the microprocessor. The interlaced composite video data is stored in the 64 killobytes of main memory and then transferred, for long term storage, to magnetic floppy disks. Data is displayed on a graphics video terminal and for permanent copies on a graphics plotter. The first stage of analysis is calibration followed by image enhancement using the principles of physical optics. Particular analytic techniques depend on the type of experiment being done. B. PHOTOMETER HARDWARE 1. The Source of Radiation The illuminating radiation is generated by an Inova-90 series 4 laser which was manufactured by Coherent, California U.S.A.. The laser is continuous wave and has tunable emission across a spectrum from ultra violet through visible to infrared. It provides a constant source of monochromatic illumination tunable to the absorption frequency of the fluorescent material being excited. For the experiments conducted the laser was tuned to 460 nanometers at an output power of 300 milliwatts. 2. The Optics and Microscope All the optical equipment is mounted on an optical flat bench manufactured by Newport Research Co.(NRC). The optical bench sits on three quarter inch plate steel which is supported by four, height-adjustable legs and the whole set up is on a solid wooden table. The Fluorescence Microphotometer / 19 The first optical element is a shutter manufactured by Uniblitz. It completely attenuates beam intensity, is T T L driven and has a response time of 10 milliseconds. The beam is then expanded to a size which fills the entrance aperture of the microscope. The beam expander consists of a piano convex lens with a focal length of 2.5 centimeters which is placed one focal distance away and collects the scattered light from a rotating, sand blasted sheet of glass. The frosted glass acts as a two dimensional array of irradiating point sources and its continual rotation randomises the spatial coherence across the beam. The inverted microscope, manufactured by Leitz, is set up with a short working distance, 40X, objective lens and the Leitz Ploem Pac which houses up to four dichroic systems. The expanded beam enters the microscope through the Ploem Pac diaphragm. It passes through the dichroic which directs it up to the objective plane using the objective as the condenser. The stimulated fluorescence emission is always of longer wavelength due to conservation of energy. It is collected by the objective and passes through the dichroic which completely attenuates the shorter wavelength laser emission. The fluorescence beam is then split and sent through 25X eyepeices which project a real image for visual and electronic monitoring. Preceeding the video camera entrance pupil is another Uniblitz electronic shutter which controls the complete attenuation of the fluorescence image and protects the highly sensitive vidicon tube of the video camera. The Fluorescence Microphotometer / 20 3. V i d e o C a m e r a and Video S i g n a l M u l t i p l e x i n g The two dimensional mapping of object fluorescence intensity is monitored by an Intensicon 8, low light level, monochrone video camera. The camera was manufactured by Lenzar Optics Corporation, Florida U . S . A . . Its sensing device is an intensified vidicon tube and was custom designed with manual intensifier and video gains. The gain settings are manually adjusted in intervals of 0.01 from 0 through 10. The output is a composite, interlaced video signal with a black to white peak to peak voltage of 2.6 volts and negative triggering horizontal and verticle sycronization pulses. This signal is read by a model 321 Video Analyser manufactured by Colorado Video Inc., Colorado U . S . A . . The 321 processes television signals so that the brightness of individual picture elements may be read. For our application there are two essential functions preformed by the 321: 1. The 321 multiplexes a horizontal and verticle position marker on to the video signal. The markers are seen as a horizontal and verticle line on the video picture and their position is adjusted by controls on the front of the instrument. 2. The 321 produces a Slow Scan video output signal (SSVS) which reflects the brightness of the picture elements under the horizontal position marker. The SSVS is a verticle array of picture elements which are updated continuously at the video scan rate. Thus the SSVS is a series of square wave voltage pulses, one per scan line, and is terminated by a verticle sink pulse. The SSVS output levels are 5 times the video signal thus the 239 SSVS square wave pulses, each being 64^sec, have an output range between 0 and 13 volts. The sink pulse falls to a The Fluorescence Microphotometer / 21 negative level of -0.8 volts for a duration of 1.37msec. (Figure 1) The SSVS is also multiplexed onto the video signal and is displayed vertically on the left side of the video picture. The multiplexed interlaced composite video signal is sent to a video monitor for visual assessment and the SSVS is sent to the analog to digital converter board in the microprocessor. The camera's video output signal is read in parallel by a model 401 Video Digital Voltage Mixer maufactured by Vista Electronics, California U . S . A . . This device multiplexes up to eight analog inputs, a twelve hour clock and a video frame count onto the video signal. A l l this information can be selectively positioned within the video picture and is displayed in alphanumeric character form. The output of the 401 is sent to a three quarter inch videocassette recorder manufactured by Sony. 4. The Microprocessor The digitization, storage, analysis and display is controlled by a microprocessor manufactured by Cromenco Inc., California U . S . A . . The computer is designed around a Z80 central processing unit and talks to its peripherals along an S100 bus. The computer has a 4 megahertz internal clock thus each clock cycle is one quarter of a microsecond. The basic peripherals include a D . E . C . VT240 intelligent graphics terminal, 64 killobytes of memory and dual eight inch floppy disk drivers. Added for specific application was a Cromenco Twin Universal Asynchronous Receiver Transmitter (TUART) and an I/O Technology A / D / A Converter Board. The T U A R T , manufactured by Cromenco, provides two channels of duplex serial data exchange, two channels of The Fluorescence Microphotometer / 22 The 321 Video Analyser Slow Scan Output 6 4 ^usec Volts -0-8 I -37ms FIGURE 1 The output of the 321 Video Analyser is a slow scan interlaced video signal. It represents the brightness of picture elements under a verticle slice of the video image and consists of a negative vertical synchronization pulse followed by 239 voltage pulses. The Fluorescence Microphotometer / 23 eight bit parallel data exchange and ten interval timers. The A / D / A converter board is manufactured by I/O Technology, Valencia California U . S . A . and has two independent sections of operation. One section converts analog voltages into a digital, binary representation and the other converts a digital number into an analog voltage. Only the A / D section is presently used and consists of eight analog inputs converting analog to digital data with a resolution of 12 bits in a conversion time of 12 Msec. 5. The Hardware Interface The microprocessor talks to the experimental equipment via the A D A and T U A R T boards. The A D A board is configured in differential input mode and channel 0 and 1 of its C A Connector Port are connected to the DC output and Slow Scan video output of the 321 video analyser. The T U A R T board has two parallel input/output ports. Pins 12, 24 and 14 of the J3 parallel output port are connected and control the laser and camera shutters by means of a T T L driven shutter power supply. The J2 parallel output port pins 13, 25 and 14 control the videocassette recorder, via a T T L driven relay, and the start/stop of the real time clock of the 401 Digital Voltage Mixer. The A D A C A connector port and the T U A R T J2 parallel output port are interfaced via a 25 pin blue ribbon cable which runs into the back of the blue interface box which redirects the connections, via 75S2 coaxial cable, to the various devices. The hardware interfacing schedule is seen in figure 2. The Fluorescence Microphotometer / 24 The Hardware Interface Schedule 12 2 4 T U A R T J 3 Parallel Output Port 14 GND T U A R T 13 2 5 J 2 Para l le l Outpu,t P o r t 14 GND 16 8 A D A C A 15 C o n n e c t o r 7 Port Laser Shutter Drive Camera Shutter On" V / A tt l relay T U T B l u e i n t e r f a c e Box 0 Laser Shutter Camera Shutter V i d e o c a s s e t t e Recorder 401 Multiplexer C l o c k D C O u t p u t SSVS G N D 3 2 1 V ideo Analyser F I G U R E 2 The hardware interface shedule shows the physical connections between the microprocessor ports and the devices the microprocessor controls. The Fluorescence Microphotometer / 25 C. P H O T O M E T E R S O F T W A R E There are three areas of software data control:- acquisition, dispay and analysis. The data acquisition software is written in Z80 assembler and is a transparent but essential part of the microphotometer. This software, discussed in the following section, synchronizes with and reads the interlaced composite video signal extracting relevent information about the video image. The display software is written in Fortran and consists of a variety of routines which combine to make a graphics package. This software displays fluorescence data, in Textronics 4010 mode, on the graphics page of the D . E . C . console or in hard copy on the Textronics plotter. The acquisition and display software has been organized and concatenated into one package which runs and. controls a specific type of experiment. The experiment consists of one short laser pulse which fluorescently stimulates the object. During this time the fluorescence image is digitized, written to a disk file and displayed on the graphics terminal. Figure 3 shows the flow of this acquisition/diplay software. The analysis software, written in Fortran, uses the techniques of Fourier optics to match the spatial form of the photometer output by modelling the optical transfer characteristics of the system. A majority of this software was run on the University mainframe which offers substantial computing power and reduces the computing time by several orders of magnitude. The analysis software also varied depending on the individual experiment and the required information. 1. Z80 Assembler Rout ines The data acquisition software is written in Z80 assembler for flexibility, precise timing and speed. Each routine is written to handle a specific task and the result is a software system which has been organized into several libraries. Parameters are The Fluorescence Microphotometer / 26 F L O W C H A R T O F D A T A A C Q U I S I T I O N / D I S P L A Y S O F T W A R E M E N U E READ SSVS • • • 1 PLOT DATA • • • 2 E X I T . . . 3 1 2 3 E N T E R FILENAME E N T E R R L E NAME OPEN F I L E R E A D & PLOT D A T A E N T E R # O F V I D E O Fl E L D S S P A C E BAR T O I N I T I A T E E X P E R I M E N T OPEN C A M E R A S H U T T E R UNPAUSE T H E V C R OPEN L A S E R S H U T T E R C A L L S S A S C L O S E B O T H S H U T T E R S P A U S E T H E V C R W R I T E T H E C O L L E C T E D DATA TO D I S K F I L E P L O T T H E C U R R E N T DATA FIGURE 3 The recording and display of the crossectional fluorescence intensity is software controlled. The program initiates a short laser pulse which fluorescently stimulates the object. During this time the fluorescence image is digitized, written to a disk file and displa3red on the graphics monitor. The Fluorescence Microphotometer / 27 passed strictly on the stack and it is the responsibility of each routine to save and restore the callers environment. The first step in building a software system in assembler is having the ability to read and write ascii to and from the system terminal. These basic routines are supplied by the operating system and require certain registers to be configured before the system call. These system calls are incorpoated into the routines P U T C H A R and G E T C H A R which pass their parameters on stack and in doing so leave the callers environment unaffected. The routine PRINT writes a complete message to the console. The message is set up in memory and must be terminated by hexadecimal zero. The next step was the definition and the ability to handle real numbers. Signed real numbers can be represented in binary using a fixed number of bits. The routines written are to handle signed, 32 bit, fixed point real numbers. The value of such a number is defined by the addition of the value associated with each bit which is the binarj' contents of the bit times 2 ^ N is the bit position and ranges from 0, the least significant bit, to 31 the most significant bit. Thus, for example, the three representations below are equivalent in numeric value. 0000 0000 0001 1110 1100 0000 0000 0000 32 bit Binary 001E C000 Hexadecimal 30.75 Decimal Two 32 bit numbers is passed to each of the four mathematical routines A D D , S U B t r a c t , M U L t i p l y and DIVide. The 32 bit answer is returned on the top of The Fluorescence Microphotometer / 28 stack. The most complicated and most interesting routine was DIV which is passed two 32 bit parameters and uses two local 32 bit variables to compute the division. The four variables are the Q U O T I E N T , DIVISOR, the F R A M E and the A N S W E R . Q H , Q L and F L represent the high and low order sixteen bits of the quotient and the low order sixteen bits of the frame respectively. The flow of the divide routine is given below and consists of subtractions, comparisions and data shifting in the same way that one computes a long hand decimal division except that DIV works with 32 bit binary representations. A = 32 /*bit count*/ A N S W E R = 0 . 0 F R A M E = 0.0 F L = Q H DIV1 : Shift Left Q L into F R A M E SUBtract the DIVISOR and F R A M E IfCDIVISOR > F R A M E ) Shift Left 0 into A N S W E R DIV2: Else Shift Left 1 into A N S W E R F R A M E = F R A M E - DIVISOR DIV3 : A = A-1 If(A = 0) jump to DIV1 Exit The Fluorescence Microphotometer / 29 Routines G E T R and P U T R are the real number input/output routines. G E T R reads an ascii string from console input and converts it into a real binary number and P U T R converts a real binary number into an ascii string and prints it on the console. G E T R is a free format input routine accepting numeric characters, a negative sign and a period. Any incorrect input causes an error message to be dumped on the console and the routine waits for the number to be resubmitted. P U T R is passed a real binary 32 bit number. It successively divides the most significant 16 bits by decimal ten until the dividend is zero. The remainders after each division are converted into ascii and, when printed in reverse, represent the decimal equivalent. It then successively multiplies the least significant 16 bits, the mantissa, by decimal ten until the mantissa is zero. The overflow after each multiplication is converted to, and printed in, ascii and represents the decimal fraction of the real number. The routines L O A D and S A V E are 32 bit push and pop routines which move a 32 bit number from a memory location to the top of stack and visa versa respectively. The next set of routines control various device functions by altering the status of the T U A R T J2 and J3 parallel output ports. The routine from which these are called must initialize the J2 and J3 control status word and declare variables J2WORD and J 3 W O R D which will contain the current status of these two output ports. Routine S L E E P is passed a 16 bit number and creates a real time pause of 10msec times the number passed. S L E E P is used because devices like the shutter and videocassette recorder (VCR) require a transient time to carry out their various actions. Routine V C R is passed the J 2 W O R D and will pause/unpause the videocassette recorder by changing the status of bit 0 of the J2 port. The Fluorescence Microphotometer / 30 Routine C L O C K is passed the J 2 W O R D and start/stops the 401 real time clock by changing the status of bit 1 of the J2 port. Routines L A S E R and C A M E R A are passed the J3WORD and open/close the laser and camera shutter by changing the status of bit 2 and 3 respectively of the J3 port. The major data acquisition routine is SSAS, Slow Scan Average Storage. This routine samples the analog Video Analyser slow scan output via channel 1 of the A D A board. A n analog to digital conversion is initiated by setting bit 7 in the A D A control status word. The conversion is completed in 12/xsec and the digital result is read from the 16 bit data word. The most significant 4 bits of the data indicate the A D A channel number and when the conversion is complete. Thus the converted data is only 12 bits long and is an approximate negative two's complement representation of the analog voltage read, (see Figure 4) It is only approximate negative two's complement because the positive voltages are represented by numbers that are too small by one. That is, where -5 volts can be correctly represented by 7FF hexidecimal, +5 volts should be represented by 801 and not 800 hexidecimal. This is simply because 801H + 7 F F H = 0, in fact 000H - 800H = 800H and further, F F F cannot be used to represent zero since 000H - F F F H = 1. This conversion mechanism is a function and a minor logic error of the A D A board. However the approximation becomes insignificant due to the scaling involved since the missmatch of 1 in the positive voltages on the 12 bit scale represents only 0.002 volts. The Fluorescence Microphotometer / 31 ADA V O L T A G E TO 12 BIT BINARY CONVERSION FIGURE 4 The analog video output is digitized for subsequent image processing. The analog to digital conversion results in a 12 bit binary number which is an approximate negative two's compliment representation of the voltage read in. The Fluorescence Microphotometer / 32 The 321 Video Analyser slow scan output consists of two interlaced fields which 1 th make up a frame. Each frame is -g Q sec long. Each field consists of a 1.37msec negative sink pulse followed by 239 positive, 64/usec, square wave pulses. SSAS creates an array of 255, 16 bit, elements into which it averages alternate slow scan fields. The number of fields to be averaged is passed to SSAS as a parameter on top of stack. There are several areas that needed careful attention to acheive precise synchronization and timing. When SSAS is called it first polls the slow scan output until the next sink pulse is found. The actual test, for convenience and speed, was to take the 12 bit number from the A / D conversion and examine the top 5 bits. If the most significant bit was zero and the addition of the other four was not zero then the 12 bit number represented a voltage less than -0.617 volts. This polling loop starts at local label SSAS3.T The loop starting SSAS2 polls the sink pulse for the positive going edge which starts the next video field. This loop does the same test on a 12 bit number thus the lead data edge is found when a voltage above -0.617 volts is read. The polling time in this loop is 107 clock cycles which is 26.75/usec. Thus the A / D conversion that initiated the exit jump from the lead edge polling loop was set sometime , X , between 0 and 26.75Msec passed the lead edge. (Figure 5) Then, once the conversion at X is set, 26.75Msec elapses as the conversion at X-26.75<xsec is read and tested. At this time the conversion at X +26.75Msec is set. It is this conversion which becomes the first array element and from which the timing is set for the recording of the remaining picture elements in the field. Thus the picture elements, which are 64jxsec wide, are sampled between the interval 26.75 to 53.5jisec into the pulse. This guarantees that the picture elements are sampled between, and not on, their transition edges. The main data tsee appendix The Fluorescence Microphotometer / 33 T H E SSVS LEAD EDGE SYNCHRONIZATION s s v s SINK POLSE X+ 26-75yus V V 64 L I S LEAD EDGE X - 26-75JJLS FIGURE 5 In the acquisition of the Slow Scan Video Signal it was important that the analog to digital conversions were initiated within each data pulse and not on the transition edges. The Fluorescence Microphotometer / 34 acquisition loop starts at S S A S l . It samples 255 slow scan video elements at a regular interval of 64/xsec, per element, and adds them to the data array. For the purpose of addition the 12 bit negative two's complement numbers read from the A D A Data Word are converted into 16 bit negative two's complement. The conversion is achieved by adding F000 hexidecimal to numbers greater than or equal to 800 hexidecimal. This allows a maximum of sixteen 12 bit numbers to be added without overflow. The main data acquisition loop has two paths and each has been carefully padded with redundent statements so each excutes in exactly 256 clock cycles which is 64Msec. A t the end of each data acquisition, at the loop starting SSAS51, the array of picture elements is divided by the number of fields read. This computes the average and leaves each element in 12 bit negative two's complement form. For speed the 16 bit number is divided by binary logical shift which allows division by 1, 2, 4, 8 and 16. For this reason SSAS can read only these numbers of data fields. D . S T A T I C P H O T O M E T E R R E S P O N S E 1. Introduction In this section the static photometer response is determined to ensure that the system's output is linear and invariant with respect to intensity input. The method is to illuminate with monochromatic light, of uniform intensity across the field of view, and analyse photometer output as a function of illumination intensity and absolute displacement, within the field of view. The Fluorescence Microphotometer / 35 The photometer is a two dimensional imaging system which is not simply an optical system because it includes video and computer electronics to record, process and display the image. There are three extensive variables to the system. They are the input intensity, the intensifier gain and the video gain of the video camera. While the output is controlled by these, and one hopes in an invariant and linear way, all the information about the imaging quality of the system is given by the optical and electrical response functions of the optical, video and to a lesser extent computer systems. The first assumption is to combine these three systems into one and call it an imaging system. Its input is the diverging rays from the microscope object and its output is an array of picture elements which represents the intensity of the input at a certain relative position. The dynamic spatial calibration of the imaging system is completed when: 1. invariance is confirmed, 2. linearity is confirmed, 3. the linear functional relationship is determined 4. and the system transfer function is determined. Of course in practice the system is only invariant over a limited field of view, is never exactly linear and has an optical transfer function which must include all sorts of lens and focus aberrations. This results in a transfer function which becomes object size and object shape dependent and rather difficult to ascertain. In fact, chapter 5 shows that it is often impossible to represent a system by one optical transfer function alone. 6 The Fluorescence Microphotometer / 36 2. Method:- L i n e a r i t y , Invarience and Camera G a i n These calibration measurements involve finding the functional relationship between photometer digital output and light intensity input. Required for such measurement was a known controllable uniform source of illumination. This was achieved by replacing the dichroic system with a beam splitting mirror, placing a front silvered mirror at the microscope objective plane and using various degrees of neutral density filters, inserted before the camera shutter, to control light intensity. The camera shutter aperture is stopped down to produce a circular bright field image with the approximate dimension of a red blood cell. This set up, with laser on and both shutters open, produces a uniform circle of illumination which is centered in the video picture image and results in a square wave slow scan video signal which is read and stored by the microprocessor for analysis. The calibration software, written in Z80 assembler, is stored under the name B K G N D . Z 8 0 . The program uses the routine SSAS to read a requested number of slow scan fields and averages, the picture elements in the spatial interval requested. The subsequent output is a spatial and temporal average of the picture elements in the region of interest. The routine is used to zero and calibrate the photometer. Its first application was in determining the uniformitj' of the laser beam intensity. This was a matter of attenuating the beam intensity to a level acceptable by the camera and monitoring the intensity every thirty seconds over a period of half an hour. This was done initially using the incandescent microscope light source with a narrow band pass filter. It soon became clear that incandescent intensity fluctuations were intolerable for system calibration. The photometer output is a digitized voltage which is a function of light intensity, The Fluorescence Microphotometer / 37 camera intensifier gain and camera video gain. Functional relationships were built up by holding two of the variables constant and measuring output response as a function of the third. The invariance of the system is given by the deviation in photometer output, within the field of view, over a spatial and temporal average. Invariance requires that this deviation be zero. For the system to be linear the photometer output voltage will depend linearly on the input intensity. 3. Results Over the field of view of the photometer, and to within the resolution limited by the background noise, a constant output is produced from a constant input. This implies spatial invariance. Photometer output levels wander slightly over a period of weeks. This is attributed to the video camera and what the manufacturer terms a settling period characteristic of new equipment. Over the time course of an experiment, output instabilities are more commonly related to fluctuations in the laser beam intensity. However, laser intensity stablizes after an initial warm up period and thus the photometer is invariant in time. Figure 6 shows the laser beam intensity fluctuations over a period of 30 minutes and compares them with the fluctuations of the incandescent source. Photometer output voltage was measured as a function of relative intensity for combinations of INT and A G C gain in the range 5 to 7. The shape of the voltage/intensity dependence is shown in figure 7 and is independent of the gain setting. The output voltage decreases nonlinearly as intensity decreases at low intensities but is fairly linear in the range producing output voltages between one third of the rail voltage and the maximum output, rail , voltage. The Fluorescence Microphotometer / 3 8 LASER AND INCANDESCENT INTENSITY FLUCTUATIONS o - Incandescent FIGURE 6 The linearity and invariance calibration of the microphotometer required spatially and temporally uniform illumination. The intensity fluctuations of the laser and filtered incandescent light source were compared. The Fluorescence Microphotometer / 39 OUTPUT V O L T A G E VERSES INTENSITY 4 • VOLTAGE x X X X X X 2 3 4 5 6 7 8 9 10 RELATIVE INTENSITY FIGURE 7 Photometer linearity was tested by determining the relationship between photometer output and the input intensity. The shape of the curve was independent of the camera setting and indicated the need for slight rescaling of the raw data to linearize it with the input. The Fluorescence Microphotometer / 40 The intensifier gain (INT) sets the video camera intensifier tube voltage. It affects the photometer output voltage in an exponential like fashion. Figure 8 shows the dependence of output voltage on intensifier gain settings at various AGC settings. The video gain (AGC) amplifies the signal from the intensifier tube and thus produces an empty amplification. It produces a monotonic but erratic increase in the output voltage as shown in figure 9. The AGC gain is unity for settings less than 1. 4. Discussion and Conclusion Raw photometer output is invariant but not strictly linear. To circumvent this problem the voltage/intensity dependence, Figure 7, was best fitted using a sum of polynomials known as a spline function. This function is used to convert the raw photometer output into a scaled output which is linear with intensity. The rescaling process is number one in data display and analysis. The scaled data fits the line through the maximum intensity/voltage point and the origin. Due to the nature of the nonlinearity the scaling becomes advantageous since it decreases the lower voltages a greater proportional amount. This increases the signal to noise ratio. The data rescaling is thought of as part of the data collection process and thus photometer output is linearised with intensity. The voltage dependence on INT and AGC gain control are used to relate measured intensities at different gain control settings. The system was found to be invariant and, after minor corrections, linear. The linearitj' provides a calibration curve between constant uniform input and related output. Further system calibration involves the determination of the dynamic response. The dynamic spatial response of the system is modelled in chapter 4 and The Fluorescence Microphotometer / 41 INTENSIFIER GAIN ( INT) R E S P O N S E I NT SETTING FIGURE 8 The intensifier gain controls the voltage across the the video camera intensifier tube. It effects the output voltage in an exponential like fashion. The above functional relations are used to relate image intensities collected at different INT settings. The Fluorescence Microphotometer / 42 AGC SETTING FIGURE 9 The video gain results in an empty magnification of the video signal. It prodi monotonic but erratic increase in the output voltage discussed in chapter 5. The Fluorescence Microphotometer / 43 IV. C O N V E R S I O N OF F L U O R E S C E N C E INTENSITY TO N U M B E R DENSITY:-A Theoretical Analysis of the Spatial Resolution of a Diffraction Limited  Imaging System including a Single Aberration, Focus Error A. I N T R O D U C T I O N This chapter describes a simple technique for the conversion of fluorescence intensity of surface bound molecules to their number density [Knowles&Evans,1986]. The analysis of the experimental data requires the theoretical modelling of the spatial resolution of the optical system to determine the correction due to optical transfer limitations. The theoretical and experimental results were explained in terms of the parameters effecting the optical collection depth. The relevent prameters were established by a theoretical calculation giving the intensity collected from a cylinder of isotropic radiators as a function of cylinder height in the direction of the optical axis. Finally the feasibility of modelling the system's focus aberration with a single composite transfer function was determined. The success of this would simplify the theoretical analysis of the experimental data. The experimental/theoretical technique gave surprisingly simple results indicating a linear dependence between fluorescence intensity and number density. The model of the optical system confirmed the experimental results and showed how the optical correction factor was dependent on the optical transfer cutoff. Finally it is shown that focus aberrations can be modelled by a single transfer function but only in an approximate fashion. 44 Conversion of Fluorescence Intensity to Number Density:- / 45 1. Fluorescence Intensity to Number Density Conversion The output of the photometer is an intensity mapping of surface bound molecules. A method was needed of converting this fluorescence intensity to a number density. The assumption are that the fluorescent centers collectively act as isotropic radiators and that they do not mutually interact. Thus, fluorescence intensity is a linear function of the surface density of fluorescently active molecules and an experiment was needed to determine the conversion factor. Because of photobleaching and the problem of finding a suitable fluorescence standard an origional technique was needed. B. T H E M O L E C U L A R S U R F A C E D E N S I T Y C A L I B R A T I O N E X P E R I M E N T 1. Experimental Procedure The aim of these experiments was to encapsulate a fluorescent solution within a micropipette and experimentally and theoretically determine the relationship between fluorescence intensity, collected through the center of the pipette, and local pipette diameter. A theoretical model of the optical system was constructed to explain and analyse the experimental data. Experimental intensity cross-sections through the pipette, at a given diameter, were compared with theory. The best fit theoretical curve established the transfer cutoff of the system, the optical correction factor due to focus aberration, the pipette diameter and the intensity through the center of the pipette. The experiment consisted of a double chamber stage with a red cell pipette and a transfer pipette. A known labelled WGA concentration, in one chamber, was drawn Conversion of Fluorescence Intensity to Number Density:- / 46 into the cell pipette a distance of several hundred microns. The pipette was then corked by aspirating a red blood cell into the pipette entrance. The pipette was then transferred into the other chamber which was filled with a non fluorescent isotonic solution. The fluorescence intensity profile across the pipette was taken and the procedure repeated for several different internal diameters. The maximum diameter, limited by the field of view of the photometer, was 20/xm. The ideal result is a linear relationship between intensity and pipette diameter. This would be the case if the optical system had an infinite depth of field which would facilitate a true two dimensional projection of the pipette. In this case the projected surface density would be the local pipette diameter multiplied by the solution concentration. However due to the finite collection depth of the objective, resulting from focus aberration, it was predicted that fluorescence intensity would attain some maximum as pipette diameter increased. Other anomalies of concern were the adsorption of W G A onto the glass and the lens effect of the glass pipette walls. The experiment was conducted using wheat germ agglutinin conjugated with fluorescein isothiocyanate, F I T C / W G A . The concentrations used were calculated to represent physiological surface densities of glycophorin in the red cell membrane 5 which range from 3-5 : l :10 molecules per red cell [Lovrien&Anderson,1980]. The volume at maximum diameter over unit surface area within the pipette should 5 contain on the order of 10 molecules. Hence for a pipette of maximum diameter of 5 3 20/ini, 2*10 W G A molecules are needed in a volume of 20/im . The molecular weight of W G A at neutral p H is 3 6 0 0 0 A M U [Sharon, 1977; Lovrien&Anderson, 1980] giving a concentration of 600Mg/ml. Actual experiments, for ease of preparation and expense, were done using W G A concentrations of lOOjug/ml. Thus experiments consisted of the collection and analysis of the cross-sectional fluorescence intensity, of Conversion of Fluorescence Intensity to Number Density:- / 47 a solution of FITC/WGA encapsulated within a pipette, at a variety of internal diameters. C. T H E T H E O R E T I C A L A N A L Y S I S M E T H O D To analyse and verify the experimental data a theoretical model of the optical resolution was constructed. It involved Fourier optical analysis to produce an optical model which would account for the effect of out-of-focus planes of a three dimensional object. Up to this stage physical optics combined with Fourier analysis has been used to model experimental data shapes (chapter 5). The optical transfer function used was that describing an incoherent diffraction limited situation which by definition is aberration free and to this stage has modelled the real system quite adequately. There is good reason for this; modern optical systems, especially the high performance equipment built by Leitz, can produce images with resolution close to the diffraction limit. This is simply because the geometric aberrations of such systems are very small. The sole effect of aberrations is the introduction of phase distortion into the band pass. This has the effect of distorting the ideal spherical form of the wave fronts emanating from the systems exit pupil. One such aberration effecting even the best equipment is focus error. Resolution drops off quiekty as an object is moved out of focus which has a significant effect on the image resolution of a three dimensional object. 1. The Transfer Funct ion To model the out-of-focus contribution from a three dimensional object, the effect of focus aberration has to be included in the diffraction limited optical transfer function. Fortunately the mathematics to deal with focus aberration is easily constructed and Conversion of Fluorescence Intensity to Number Density:- / 48 solved. The particularly simple solution is the optical transfer function of a system viewed with incoherent monochromatic light, of wavelength X, through a square aperture of side L. The transfer function, in the one dimensional case, is given by equation 2.12. 2. Multiplane Analysis including Focus Aberration The multiplane analysis involves the subdivision of the object into isofocal sections of uniform thickness which is small enough to neglect the edge shape. Individual sections are analysed taking into account their varying displacement from the focal plane. The image is produced by summing the individually analysed isofocal sections of the object. The analysis process for a single isofocal section is that presented in chapter 5 and 2. A real space object function, in this case the shape of the isofocal section, is Fourier transformed into frequency components which can then be operated on by the optical transfer function (OTF) with the appropriate focus aberration. The resulting frequency componentes represent the image of the isofocal section which is obtained from the inverse Fourier transform taking the frequency components back into real space. The object in this case is the transverse section of a tapered cylindrical pipette, a circle. The circle is divided into an odd number of rectangular isofocal sections. Their thickness is a fraction of a wavelength and their length is proportional to the cross-sectional dimension at the given displacement from the circle center. The diameter is hence the number of sections times their thickness, equation 4.1, and an odd number was choosen so that the focal plane could be positioned through the Conversion of Fluorescence Intensity to Number Density:- / 49 th center of the circle. Let there be n sections of thickness t and width I. Let the j section define the position of the focal plane and define a rectangular function slab ,equation 4.3, which is unity over the section width / and zero otherwise. The width th of the k section, with central focal plane in pipette radius R, is given by equation 4.2. Diameter = n.t E q u a t i o n 4.1 I. = 2.v / ( R 2 - ( k - j ) 2 ) E q u a t i o n 4.2 ( 1 \x\<l/2 E q u a t i o n 4.3 s l a b , (x) = e K ( 0 O t h e r w i s e The object or theoretically ideal profile is given by the summation of all the n isofocal sections,equation 4.4. 2R n O b j e c t ( x ) = — . Z s l a b , ( x ) E q u a t i o n 4.4 n k=1 K th The out-of-focus displacement of the k section is given by the number of sections away from the focal plane times their thickness. The out-of-focus displacement is given in wavelengths so the maximum pathlength of focus error W, of the optical transfer function, is given by equation 4.5. W = ( k - j ) . t . X E q u a t i o n 4.5 Conversion of Fluorescence Intensity to Number Density:- / 50 Then the theoretical image is the sum of the individual isofocal sections of the object convolved with the modulus squared of their respective point spread functions | h ( x ) | 2 (equation 4.6). That is, each isofocal section is transformed into frequency space, multiplied by its respective optical transfer function, transformed back into real space and summed (equation 4.7). The multiplicative constant 2R/n is a scaling factor which takes into account the unit amplitude of the rectangular function slab(x). Image(x) = 2 s l a b . (x) . ! h ( x ) j 2 E q u a t i o n 4.6 n k=1 k Image(x) = L r°°df . e 2 i r i f x . [ /°°dx. s l a b , (x) . e 2 l t i f x ] .H(|—) n k= 1 —CD — oo K 1^ E q u a t i o n 4.7 3. Discrete Numerical Analysis Equations 4.4 and 4.7 represent a mathematical model of the image response of an incoherent, monochromatic, diffraction limited optical system with the inclusion of focus aberration. The solution is derived numerically with the aid of fast Fourier transforms (FFT) and substantial computing power. The fast Fourier transform is an algorithm re-introduced in 1964 by Cooley and Tukey [Cooley & Tukey 1965]. It was designed specifically to run on computers which, by nature of their digital logic, sample and manipulate discrete sets of data. Thus the FFT replaces the continuous Fourier integral by a sum over the integrand. The algorithm reduces the number of mathematical operations from the conventional Conversion of Fluorescence Intensity to Number Density:- / 51 N 2 to N l o g 2 N where N is the number of data points. The one dimensional analysis was performed in arrays of various sizes from 128 to 4096 data points which sets the spatial frequency resolution. The fundamental theoretical experiments are carried out by the Fortran routine P O L Y S T ( F O C , S L N O , S L T H , N , C U T O F F , R A D , H ) . P O L Y S T breaks up the circular pipette profile into isofocal sections, analyses each separately and sums them up to create the resulting image. FOC is a real array of N points which is returned by P O L Y S T and contains the theoretical image. S L N O and S L T H are the number and thickness of the isofocal sections and the pipette diameter is determined by their product. C U T O F F is the OTF frequency cutoff in units of Af and R A D and H are the radius and central height of the object function which is centered in the middle of the array. Thus P O L Y S T takes an object function, equation 4.4, and creates an image function, equation 4.7, taking into account the optical transfer function, with focus aberration, of the imaging system (figure 11). 4. The Theoretical Experiment The next stage was to determine the dependence of intensity on pipette diameter dictated by the model. The computer routine P O L Y S T does the theoretical analysis of a transverse pipette projection. It has two relevant input parameters, the pipette diameter and the optical frequency cutoff, and returns the image function, equation 4.7, in a one dimensional array. It was a simple matter of writting a program, Linear Intensity Map, which successively calls P O L Y S T with increasing pipette diameter at constant frequency cutoff and graphically illustrating the dependence of central pipette intensity on pipette diameter. The program is called with one paremeter, the optical frequency cutoff. Conversion of Fluorescence Intensity to Number Density:- / 52 Some time was spent on the validification of these theoretical results and a comprehensive discussion arose involving the optical resolution, in frequency space, of the discrete Fourier analysis. D. RESULTS The fundamental experimental result is the fluorescence intensity profile through a pipette of given diameter which containes fluorescenated W G A . Typical experimental data is shown in figure 10. In this data lies information about the resolution of the system and the relationship between intensity and pipette diameter. The shape of the profile was in good agreement with that theoretically predicted and the sensitivity of the photometer output, in the physiological range of surface densities, was high. It is interesting to note that the light scattered within the glass wall makes the wall visible at the edges of the cross-section and important to note that the small peaks at the external glass/solution boundry indicate some W G A adsorption at that interface (figure 10). In corollary the fundamental theoretical experiment was the isofocal sectioning and Fourier optical analysis of the pipette cross-section. This takes the projected object function into its theoretical image, figure 11. The variety of image shapes from one object is dependent soley on the optical transfer cutoff. The comparison of theoretical and experimental data results in a best fit theoretical image function which determines the optical transfer cutoff for the system. The corresponding theoretical object function gives the optical correction factor, pipette diameter and maximum central intensity. The surprising result was that both experimental and theoretical data gives a linear Conversion of Fluorescence Intensity to Number Density:- / 5 3 EXPERIMENTAL PROJECTION OF A PIPETTE CROSSECTION D I M E N S I O N FIGURE 10 Experimentally obtained data showing the fluorescence intensity collected through transverse section of a cylinderical pipette Filled with a solution of FITC/WGA. Conversion of Fluorescence Intensity to Number Density:- / 54 T H E O R E T I C A L I M A G E A N D O B J E C T P R O J E C T I O N O F A P I P E T T E C R O S S E C T I O N RELATIVE INTENSITY CROSSECTIONAL DIMENSION FIGURE 11 The modelling of the optical response of a system compromised by diffraction and focus limitations results in a multi-isofocal-section analysis technique. This figure shows the theoretical object and image projection of isotropic radiators encapsulated within a cylinderical pipette. The reduction in central intensity of the image function is due to focus aberration and the spread is due to the diffraction limitation. Conversion of Fluorescence Intensity to Number Density:- / 55 dependence between fluorescence intensity and pipette diameter, figure 12. Checking the validity of the unexpected theoretical result required some careful control of the frequency domain resolution. It also prompted another theoretical experiment to explain the effects contributing to intensity/diameter linearity. This validification and explaination will be delt with in the disscussion. The intensity and the pipette diameter are linearly dependent. The linearity constant depends on the optical transfer cutoff of the system. The linearity constant, L , decreases with optical frequence cutoff as seen in figure 13. The conversion of fluorescence intensity to molecular density is hence simply obtained by three linear relationships. Firstly, relative fluorescence intensity is related to pipette diameter by the experimental linearity constant , given by equation 4.8. : ^ v ^ = M ~ v ^ - D E q u a t i o n 4.8 exp exp ^ Secondly, the experimental fluorescence intensity collected from the pipette is scaled by an optical correction factor which accounts for the intensity loss due to focus aberration, equation 4.9. S u r f a c e = ^ x p ' Z E q u a t i o n 4.9 The correction factor is one over the linearity constant and is a function of the optical transfer cutoff. It represents the difference in intensity collected from a volume and that from a surface where the projected surface density from the Conversion of Fluorescence Intensity to Number Density:- / 56 THEORETICAL AND E X P E R I M E N T A L DEPENDENCE OF FLUORESCENCE INTENSITY . ON INTERNAL PIPETTE DIAMETER INTERNAL PIPETTE DIAMETER (JU m ) FIGURE 12 Theoretically and experimentally obtained data showing a linear dependence between the fluorescence intensity collected from FITC/WGA encapsulated in a pipette and the pipette diameter. The theory showed that this linear dependence was independent to a constant of the resolution of the system. The experimental data has a linearity constant of 0.722 which relates to a transfer cutoff for the optical system of 4 inverse microns Conversion of Fluorescence Intensity to Number Density:- / 57 L I N E A R I T Y C O N S T A N T V E R S E S T R A N F E R C U T O F F LINEARITY CONSTANT I J-0-5 " _ - - - * 0 * —<— 5 10 15 20 TRANSFER CUTOFF (yUm~') F I G U R E 13 The linear dependence of fluorescence intensity on pipette diameter varied with the optical transfer cutoff of the system. This linearity constant indicated the difference in fluorescence intensity collected from a volume of FITCAVGA and that collected from the FITCAVGA if it were condensed onto a two dimensional surface. The inverse of the linearity constant is the optical correction factor. Conversion of Fluorescence Intensity to Number Density:- / 58 volume and the molecular density at the surface are equal. Thirdly, the pipette diameter multiplied by the W G A concentration is the projected number density, equation 4.10. n = D.[WGA] E q u a t i o n 4.10 The theoretical analysis gave the best fit transfer function cutoff as 4 . 0 ± 0 . 1 u m 1 and thus from figure 13, the optical correction factor, 1/L=1.39. The scaling of relative fluorescence intense means that the linearity constant, at the predicted cutoff frequency, equals the experimental linearity constant, equation 4.11. M e x p = L E q u a t i o n 4.11 Thus the intensity collected from fluorescent molecules adsorbed to a surface is the surface density, n, multiplied by M / (L . [WGA]) , equation 4.12. GXp M Surface = — * n E q u a t i o n 4.12 s u r t a c e L . [ W G A ] Conversion of Fluorescence Intensity to Number Density:- / 59 E. D ISCUSS ION The experimental intensity profiles of the pipette at different diameters were of high signal to noise ratio. The adsorption of WGA to glass is inhibited by the presence of albumin in solution because this blood plasma protein coats blood incompatable surfaces such as glass. However some WGA/glass adsorption was present in the experiments. This had a minimum effect on WGA concentration within the pipette because the same pipette was refilled and used many times, an equilibrium was quickly established between the glass and WGA and the experimental small peaks, at that interface, indicate a low adsorption concentration of WGA. The lens effect produced by the thickness and curvature of the pipette glass is insignificant because, at worst, all it does is slightly alter the intensity profile towards the edges. This effect can be incorporated into the optical transfer function of the theoretical analysis and does not distort the measurement of pipette radius or the intensity at the pipette center. The intensity/diameter linearity was pleasently unexpected and called for explanation to remove any doubts in experimental technique. Intuitively it was expected that intensity reach some maximum as diameter increased. The idea being that an object viewed at some displacement from the focal plane appears blured and less intense. Thus for a solution of isotropic radiators there will be some critical distance from the focal plane beyound which light will not contribute to the image. The theoretical model produced pipette intensity profiles from the ideal circular projection which successfully matched the experimental data. The profiles showed a linear dependence of intensity on pipette diameter. The linearity constant is a function of the transfer cutoff and defines the fluorescence intensity loss due to the optical limitations. The inverse of the linearity constant is the optical correction factor which is used to scale the experimental data. The linearity constant behaves Conversion of Fluorescence Intensity to Number Density:- / 60 as intuition dictates. It rises quickly towards the theoretical limit of 1 as the transfer cutoff increases from zero but, at a certain frequency, flattens off and approaches the theoretical limit asymtotically. The dynamic range of the transfer cutoff is between 0 and 10 ^ m This is a function of the illumination wavelength and is a practical result of the model stating that any diffraction limited optical system with focus aberration using visible radiation for illumination, will completely attenuate spatial frequencies of the order of unit inverse microns. The decrease in linearity constant with transfer cutoff represents the increasing loss of information collected by the optical system due to focus aberration. The relative fluorescence intensity is arbitrarily scaled in a ratio 1:1 with the pipette diameter and thus a linearity constant of L = l represents one of two situations. 1. A unit linearity constant, when viewing a three dimensional object, represents a system of infinite transfer cutoff and hence infinite resolution and depth of field. 2. However it also represents the situation of collecting fluorescence intensity from a surface. In such a case there is no fluorescence loss due to focus aberration since all the surface can be placed in focus. Concequentally the inverse of the linearity constant is the optical correction factor which accounts for losses due to focus aberration. The theoretical model predicted an optical spatial frequency cutoff of 4 . 0 ± 0 . 1 Mm ^. Also from the graph of linearity constant verses transfer cutoff, which was produced from the model, one sees that any diffraction limited optical S3'stem which includes focus aberration, and uses illumination from the visible spectrum, has an optical transfer cutoff between 0 and 10/im \ These results of the model are justified by a simple calculation knowing that the spatial resolution of an optical system is approximately half the illumination wavelength. In our system the wavelength was 460 nanometer. Thus the maximum diffraction limited resolution is 0.23/xm and the inverse of this is a spatial frequency Conversion of Fluorescence Intensity to Number Density:- / 61 of 4.35 nm \ This is the highest spatial frequency, at 460nm, to which a diffration limited system will respond. Thus the model has predicted a transfer cutoff slightly less than the aberration free limit which is exactly where it should be! The model also agrees with experiments in predicting a linear dependence between pipette mid intensity and diameter. 1. Frequency Domain Resolution The validification of the theoretical intensity/diameter linearity involved insuring sufficient spatial frequency resolution. There were two areas of concern. 1. Did the discrete Fourier analysis provide sampling with enough frequency domain resolution? 2. Should the Fourier analysis be such that the frequency sampling be at a constant interval? The first question arose because of the discrete nature of the Fourier analysis. The Fourier transform of a real object function results in an amplitude function of frequency. The optical transfer function is also an amplitude function of frequency. It was necessary to define an effective optical transfer cutoff, which is the lowest frequency at which the transfer function is first zero. H(p), equation 2.12, is first zero when the argument of the sine is equated to pi, ir, and results in an effective cutoff given by equation 4.13. W O - J ) ;w>x/2 p e f f = f 2 E q u a t i o n 4.13 1 ;W<X/2 p F(. is a function of W, the out-of-focus displacement. Note that for W<X/2 the Conversion of Fluorescence Intensity to Number Density:- / 62 optical transfer function, H(p), becomes zero when p = l and hence the effective cutoff equals the actual cutoff. To test that the OTF is represented with adequate resolution is to ensure that the effective frequency cutoff is always greater than the elemental frequency spacing, equation 4.14. Note that (pQ^ ^c^^ ' s the number of array elements, in frequency space, between the DC component and the effective cutoff. In practical terms, consider the analysis of a 20jum diameter pipette which is represented by 60 array elements of an N element array. The most out-of-focus isofocal section has the shortest effective cutoff and thus determines the required frequency domain resolution. This isofocal section is lOum or 20X out of focus thus; p e f f f c >> 1 E q u a t i o n 4.14 Af W = 20X = 0 . 0 0 6 2 9 Ax - i - o A m - 1 Let the frequency cutoff, f , equal 4um which is that of the actual system. Then Conversion of Fluorescence Intensity to Number Density:- / 63 the condition to be satisfied, given by equation 4.14, is that 0.00839.N> > 1. In such a situation N = 128 would result in a poor representation of the transfer function since it falls to zero in less than two elemental frequency spacings. The analysis was done in arrays of N = 4096 which, even in this worst case situation, represents the dynamic behaviour of the transfer function with sufficient frequency resolution. The resolution of the Fourier transformation of the object function depends on Af and some characteristic length within which the fluctuations of the transform are small. The simplest way to test for sufficient frequency domain resolution is to plot the Fourier transform and check that Af is small enough to represent the form of the transform. The second problem was one of scaling. The Fourier analysis was done in arrays of 4096 elements and initally each transverse section was represented by 60 of the array elements reguardless of the pipette's actual size. This resulted in a different elemental distances, Ax and Af, for different sized pipettes. As pipette diameter increased the elemental frequency decreased, increasing the resolution of the frequency analysis. The concern was that the variation in Af might have an anomolous effect on the results. To maintain a constant elemental frequency spacing the size of the transverse section, within the array, is varied according to its actual size. This keeps Ax constant and since the array size was fixed, Af was independent of pipette size. In both cases the dependence of relative theoretical intensity on pipette diameter was linear with the same linearity constant. The conclusion is that scaling of this sort does not effect the results when working at N = 4096. Conversion of Fluorescence Intensity to Number Density:- / 64 2. A Calcula t ion of the Opt ica l Col lec t ion Depth The explanation of the intensity/diameter linearity lies in the geometry of the problem and is related to the optical collection depth which must vary with pipette diameter. A theoretical problem was set up and executed which would determine the collection depth of the microscope objective. The problem involved the isofocal sectioning and analysis of the one dimensional crossectional projection of the intensity of a cylinder of light. The cylinder has a radius tangential to the optical axis and a variable axial length (figure 14). This would determine the amount of light collected from a narrow cylinder perpendicular to the focal plane. The one dimensional rectangular projection is the ideal intensity map of a cylinderical object. The rectangle is divided into isofocal sections of constant width which are analysed individually to take into account their out-of-focus displacement. This analysis can be thought of as similiar to the pipette crossection analysis except, in this case only a narrow strip through the center of the crossection is sampled. The results of the analysis are presented in figure 15. They show that intensity reaches a maximum as the object size increases perpendicularly to the plane of focus. The distance from the focal plane at which the maximum intensity is first reached is the collection depth. The important point to note is that the collection depth increases with an increase in object size parallel to the plane of focus. Thus, and particularly in the case of the pipette crossection, the central intensity has contributions from the off axis defocused portions of the isofocal sections. There are two effects: 1. The intensity collected from an isofocal section increases to some maximum as the section width increases. The width, at which the maximum intensity is reached, increases with the out-of-focus Conversion of Fluorescence Intensity to Number Density:- / 65 T H E PROJECTION OF A CYLINDERICAL O B J E C T INTO 2 DIMENSIONS SHOWING T H E I N T E N S I T Y C R O S S E C T I O N FOCAL PLANE F I G U R E 14 In the calculation of the optical collection depth, a cylinder of isotropic radiators, with the cylinderical axis perpendicular to the plane of focus, was analysed using the multi-isofocal-section technique. The resulting crossectional projection produced a rectangular function of intensity on the crossectional displacement. Conversion of Fluorescence Intensity to Number Density:- / 66 INTENSITY V E R S E S CYLINDERICAL O B J E C T HEIGHT FIGURE 15 The optical collection depth was determined by modelling the fluorescence intensity collected from a cylinder of isotropic radiators as a function of cylinderical length, perpendicular to the focal plane. The distance from the focal plane at which the maximum intensity is first reached is the collection depth. The important point is that the collection depth increases as the object size increases in the plane of focus. Conversion of Fluorescence Intensity to Number Density:- / 67 displacement. 2. The maximum intensity collected from an isofocal section decreases as the out-of-focus displacement increases. In the above rectangular analysis the isofocal sections are of constant width thus the only contributing effect is the second one mentioned which is why the intensity reaches a maximum as rectangular height increases. However in the pipette crossectional analysis the above two effects are seen and compete because although out-of-focus displacement increases with pipette diameter, so does the width of the isofocal sections. The result is intensity/diameter linearity. F . A S I N G L E C O M P O S I T E T R A N S F E R F U N C T I O N 1. A i m The aim of this analysis is to determine whether the multi isofocal analysis of the pipette crossection can be modelled by a single composite transfer function. 2. Introduction An optical transfer function is a real function of spatial frequency which is symetric about the origin. It models an imaging system by attenuating the spatial frequencies of the object. In the case of a diffraction limited incoherent imaging system, including focus error, the optical transfer function is dependent on the out-of-focus displacement. Thus to model the image resolution of a three dimensional object, the object must be divided into isofocal sections each of which is multiplied by a different optical transfer function. The result of this multi section analysis is the Conversion of Fluorescence Intensity to Number Density:- / 68 transformation of the object function, taking into account the effect of focus aberration, into an image function. The question is, ' can such a transformation be obtained from a single transfer function'? If so, much time would be saved in data analysis because a typical multi section analysis involves fourty Fourier transforms where as a composite transfer function would reduce this to two. 3. Method The method is straight forward. A n optical transfer function, H(f), is the Fourier transform of the image function divided by the Fourier transform of the object function as given by equation 4.15. f °°dx. Image (x) . e ~ 2 7 r i f x H ( f ) = E q u a t i o n 4.15 /°°dx.Object (x) . e ~ 2 , r l f x — oo In the case of the pipette crossection the object and image functions are defined, equations 4.4 and 4.7, in terms of the isofocal sectioning and analysis. If the existance of a composite transfer function, H c o m p » is assumed then the image is the inverse Fourier transform of the composite transfer function multiplied by the Fourier transform of the object, equation 4.16. Image(x) = f°°df . e 2 7 r l f x . [ H . r°°dx .Ob j e c t (x) . e 2 i r i f x ] — oo COuip —oo E q u a t i o n 4.16 Equating the two forms of the image function (equations 4.7 and 4.16), and noting Conversion of Fluorescence Intensity to Number Density:- / 69 that 2R/n is a constant and can be brought outside both integrals in equation 4.16 and the sumation over k can brought inside the integral, over frequency space, in equation 4.7, then the composite transfer function is given by equation 4.17 which is of the form defined by equation 4.15. 2 [ H ( f ) . / " d x . s l a b , (x) . e " 2 i r i f x ] H m „ = JizJ If? _ E q u a t i o n 4.17 C ° P n » - 2 i r i f x I f d x . s l a b . ( x ) . e k=i -a, k The solution to equation 4.17 is derived numerically and its validity is determined by its conformation with the three properties of an incoherent optical transfer function given in equations 2.8, 2.9 and 2.10. 4. Results A stepwise approach to the final result was taken to ensure a more complete understanding of the solution to equation 4.17. Figure 11 shows the projected crossectional pipette functions of the object and corresponding image defined by equations 4.4 and 4.7. The frequency spectra of these two functions is obtained by taking the Fourier transform and figures 16 and 17 are plots of the amplitude verses frequency of the sinusoidal functions. The composite optical transfer function is obtained by the division of the frequency spectrum of the object function into the frequency spectrum of the image. The result is seen in figure 18. It has some features characteristic of an optical transfer function with some anomolous behaviour. Conversion of Fluorescence Intensity to Number Density:- / 70 5. Disscussion The composite transfer function conforms to two of the three requirements of an inchoherent OTF. Firstly, the function at zero frequency is unity and secondly, the function is real and symetric about the origin. The condition which is not fulfiled is that the function is less than or equal to unity. The singularities arise because the nodes of the frequency spectra of the image are shifted towards lower frequency relative to the object. This causes division by zero in the calculation of the composite transfer function. The multi isofocal analysis not only attenuates the amplitude of the frequency components of the object but also shifts the overall form of the frequency spectra to lower frequency. This shifting process cannot be achieved by a single real function of frequency space, and in this sense there cannot exist a composite transfer function which mimics the action of the multi isofocal analysis. However the basic shape, neglecting the singularities, is similar to the transfer function, H(p) equation 2.12, with W = 4.375X (Figure 19). This comparison shows that the composite transfer function is not completely invalid and that it conforms in a general sense to the shape that is expected. It also results in the effective cutoff of the isofocal analysis. To first approximation the isofocal analysis can be modelled by a transfer function which equals the composite transfer function in the interval between zero and the effective cutoff frequency and was zero at frequencies above the effective cutoff. 6. Conclusion Conversion of Fluorescence Intensity to Number Density:- / 71 The conclusion is that the multi section isofocal analysis of a three dimensional object produces an image with a frequency spectrum that is not only attenuated by a bandpass but is shifted in the frequency domain. The analysis which involves several different transfer functions can only be modelled in an approximate way by a single composite transfer function. FIGURE 16 The frequency spectra of the ideal transverse section through a cylinder is obtained by taking the Fourier transform of the object function (equation 4.4) and results in a complex function of amplitude and phase verses frequency. The above plot is of amplitude verses frequency. I M A G E F R E Q U E N C Y S P E C T R A I' SPATIAL FREQUENCY (Jd m ) I j I 2 3 4 Jpll k i i • FIGURE 17 The frequencj^ spectrum of the image function of the transverse section through a cylinder is similar to the object spectrum except the amplitudes of the frequencies above 4 inverse microns are completely attenuated. Also the nodes of the spectrum are shifted relative to those of the object spectrum. Conversion of Fluorescence Intensity to Number Density:- / 74 MULTI ISOFOCAL ANALYSES COMPOSITE T R A N S F E R FUNCTION AMPLITUDE FIGURE 18 The multi isofocal analysis involves the division of the 3 dimensional object into isofocal sections. Each section is analysed by a transfer function which is dependent on the out-of-focus displacement. The composite transfer function is the result of trying to represent the multi isofocal analysis by a single transfer function. It has some similiarities to an incoherent transfer function (figure 19) but does not account for the shifting of the frequency spectrum by the isofocal analysis. The shifting of the image spectrum results in the above singularities. Conversion of Fluorescence Intensity to Number Density:- / 75 INCOHERENT T R A N S F E R FUNCTION AT 2 u m O U T - O F - F O C U S F I G U R E 19 This is the incoherent transfer function (equation 2.12) with a focus aberration of 2 microns (W = 4.375 lambda). It is similiar in form to the composite transfer function in figure 18 if one neglects the singularities on the composite transfer function. V. SPECIFIC M O L E C U L A R ADSORPTION TO C E L L SURFACES A. INTRODUCTION This section is concerned with fluorescently labelled molecules and their interactions in the living biological system. One very broad group of essential interactions in living systems is membrane surface interactions which govern much of the cells physiology. One such area of interest is cell adhesion mediated by the specific binding of cross bridging molecules [Bell, 1978; Parsegian&Gingell,1980; Grant&Peters,1984; Evans, 1985]. This study was carried out on the human erythrocyte and the cross bridging molecule was an agglutinating protein extracted from wheat germ [Evans&Leung,1984]. The wheat gem agglutinin (WGA) was fluorescently labelled with fluorescein isothiocyanate and binds specifically to oligosaccharides of N-acetylglucosamine. Such sugars are present on the transmembrane glycoprotein, glycophorin. The aim is to determine the kinetic and equilibrium behaviour of red cell/WGA adsorption. 1. The Molecular Interaction Lectins, first named heamagglutins because of their ability to agglutinate red blood cells, comes from tha Latin legere which means to pick or choose [Sharon, 1977]. Extracted mainly from plants, lectins are proteins that bind with various degrees of specificity to sugar molecules. Wheat germ agglutinin (WGA), extracted from wheat germ, binds very specifically to the sugar N-acetylglucosamine [Lovrien&Anderson, 1980] which is a residue in the tertiary structure of the outer cell membrane glycoprotein, glycophorin. The mechanism of lectin sugar binding is similar in nature to enzyme-substrate binding where the tertiary structure of the 76 Specific Molecular Adsorption to Cell Surfaces / 77 enzymatic protein is capable of weakly binding to other, often smaller, substrate molecules. The affinity of lectin sugar binding for appropriate monosaccharides is 3 -1 approximately 10 M and for lectins which bind to glycolipid and glycoprotein receptors in membranes ranges from 10 to 10 M " [Grant&Peters,1984]. 6 1 Irreversibile binding occurs for affinity constants greater than 4*10 M [Grant&Peters,1984]. 2. The Scatchard Plot Ligand is a term used to describe any biological molecule involved in a binding process, for example enzyme and substrate, hormone and receptor or in this case lectin sugar binding. All biological phenomena depend on ligand interactions of one kind or another. Consider a macromolecule, M , which has n sites for the binding of a ligand L [Cantor&Schimmel,1980]. Assume that the sites have no mutual interaction and all have the same microscopic association constant k. Let M . represent a macromolecule with i of its sites bound to lectins L. There are many microstates which represent this one macrostate M . . The number of distinct ways of binding i ligands onto n sites is the statistical weight, J2 ., and is given by equation 5 .1. n , i n 1 S2„ • = -, r - H — r r E q u a t i o n 5.1 n , i ( n - i ) ! . l ! M The important equilibrium condition is the number of moles of ligand, v, bound per Specific Molecular Adsorption to Cell Surfaces / 78 mole of macromolecule and is given by equation 5.2 .2 i . [ M . ] v= - = ° _ E q u a t i o n 5.2 i = 0 1 Macroscopic association constants, K., are involved in each process of ligand macromolecule interaction (equation 5.3) and vary depending on i, the number of ligands previously bound. K. is related to macromolecule and ligand concentration and to the microscopic association constant, k, and statistcal weight of the macrostate of the macromolecule. (Equation 5.4) M ^ + L <=> E q u a t i o n 5.3 [M.] n . K.= 1 = P_ii k E q u a t i o n 5.4 [M. , ] [ L ] Q • , I - I n , i - 1 These equations can be solved for v in terms of the microscopic assocaition constant k and the ligand concentration [ L ] . (Equation 5.5) v = n[L]«k E q u a t i o n 5.5 1+[L]•k Rearranging this equation gives a linear plot, named after Scatchard, of v / [ L ] verses v with a slope of -k and an intercept n»k. (Equation 5.6) Specific Molecular Adsorption to Cell Surfaces / 79 " = n « k - v k E q u a t i o n 5 .6 [L] The Scatchard plot gives the two parameters, k and n, that characterize simple binding of ligands to a macromolecule. Non linear plots indicate that the simple binding assumptions do not hold, often because the binding sites interact with each other or because there is more than one class of site. It is reported, Surolia & Boldt, that lectin binding is a linear function of receptor concentration. This is not the case when looking at lectin mediated agglutination of cells which is produced by cell surface cross bridging. The ligands will bind to individual cells and crossbridge them once they are brought into contact. Cell agglutination occurs when the receptor surface density is sufficient to produce the amount of crossbridging capable of holding two cells together. This is almost a threshold effect since below a certain receptor density cell aggultiation will not occur. B. EXPERIMENTAL PREPARATION 1. Chemical List FITC/WGA:Fluorescein Isothiocyanate conjugated Wheat Germ Agglutinin is a fluorescenated plant lectin and is supplied, in a physiological saline buffer in 2ml volumes at concentrations around 1000 Mg/ml, by Miles Scientific. The FITCAVGA conjugate was stored at - 2 0 ° C and information regarding protein concentration and molar ratio was supplied in their anatysis report. The claim that there is no free fluorescent label present. Specific Molecular Adsorption to Cell Surfaces / 80 Phosphate Buffered Saline: P B S was made in a 2 litre volume of deionized, distilled water with: 1.3064g of potassium phosphate ( K H PO .), 7.154g of sodium phosphate (Na 2 HPO" 4 ) and 14.192g of sodium chloride (NaCl). The phosphates are supplied by M C B Manufacturing Chemicals INC. and the sodium chloride by Fisher Scientific Company. The resulting PBS has a physiological osmolarity [Waymouth,1970] an p H of 290mOsm and 7.4pH respectively. Human Serum Albumin: H S A is a blood plasma protein which when added to the suspending buffer at a concentration of 0.5 gram percent helps maintain normal red cell morphology. It is supplied in a 30 gram per cent solution of 0.85% sodium chloride with 0.1% sodium ozide as a preservative. 2. Pipette Preparation Red blood cells are mechanically manipulated with micropipettes of internal entrance diameters ranging from 0.5 to 3Mm. The pipettes are made from 1mm, internal diameter, glass tubing. The tubing is heated and drawn into needle points by a solenoid driven pipette puller. The glass needles are viewed microscopically and cut at the required diameter with a microforge, designed in the laboratory. The microforge consists of a small glass bead mounted on fine tungsten wire which can be electrically heated. The hot glass bead is manipulated into contact with, and anneals to, the glass surface of the pipette. Once cool, a slight manipulation causes the needle tip to fracture. The pipettes are then filled with PBS by boiling them under vacuum in solution. Specific Molecular Adsorption to Cell Surfaces / 81 3. Ce l l Preparat ion Whole blood was extracted from a lance traumatized, blood engorged finger tip. The epithelium of the finger was washed with ethanol and dried to kill surface bacteria. The blood was collected in a glass pipette and transferred into a slightly hypotonic solution, of PBS and HSA. This osmotically swells the red cells giving them a smaller surface area to volume ratio. Since too many red cells in the experimental chamber would impede visibility and only several tens are needed throught the course of an experiment, solutions were made up in the order of 10 red cells per millilitre of solution. The cells maintain normal morphology for many hours in such solution. C. T H E E X P E R I M E N T A L P R O C E D U R E Preparation the day before the experiments involves; making and filling the appropriate pipettes, mixing the solutions of PBS, HSA and WGA and readying the microscope station. On the day, the station is powered up and left for an hour to let the laser and video electronics warm and settle. The laser is retuned and set at 300mWatts and the background video signal is zeroed using BKGND.COM. A double chamber stage is prepared by cutting slabs of coverslips and suspending them in vacuum grease across the ends of glass slides. The slides have a 2cm gap between them and are held stationary by a wire construction. The chambers have an 3 approximate 20mm volume and the stage is so designed to keep the chambers close but physically isolated. Next the transfer pipette is drawn, cut and filled wTith oil. The oil is necessary because pressure control in the transfer pipette is essential Specific Molecular Adsorption to Cell Surfaces / 82 and oil is incompressible, defeats water/glass/air interfacial tension and is immisicible with the solutions in the chamber. The transfer pipette is cut by etch and fracture using a diamond tip pencil. It is helpful if the fracture is clean across the transverse section of the pipette and it is useful with entrance diameters around 150 Mm. These requirements are quickly checked by viewing the pipette in air with the microscope. A t this point the double chamber stage is inserted at the objective focal plane and the transfer and cell aspiration pipettes are mounted into the chuck which mounts into the neumatic micromanipulators. The transfer and red cell pipette enter the chamber from the left and right respectively and the tips of both are positioned in the right side chamber and within the field of view. The chambers are filled using standard Pasteur pipettes with solutions of red blood cells in P B S / H S A and W G A in P B S / H S A on the right and left respectively. The red cells, being slightly more dense than the PBS/HSA, sink and settle on the glass at the bottom of the chamber. During this time the pressure in the pipettes is zeroed by adjusting the height of the controlling manometer stands and watching for zero flow at the pipette entrance. P B S / H S A is, in a controlled manner, drawn up the sewer pipette several hundred microns and the flow is clamped. From this time, due to the concentrating effect of chamber evaporation, experiments can be run to a maximum time of 30 minutes. A n experiment consists of moving the cell pipette, with a slight negative pressure, to the chamber bottom, picking up a cell and aspirating it into the pipette to form a firmly held spherical red cell to which W G A will subsequently adsorb. The red cell and pipette are manuvered into the transfer pipette which is in the vertical midplane of the chamber to avoid bumping the chamber walls. Now, the chamber can be gently translated in the direction which takes the pipettes out of the red cell Specific Molecular Adsorption to Cell Surfaces / 83 solution into the W G A solution. The red cell is quickly removed from the transfer pipette, incubated in the W G A for a predetermined time, returned to the transfer pipette and brought back to the red cell side. The cell is again taken out of the transfer pipette which is then removed from the field of view. The cell is manuvered to the bottom of the chamber which represents the shortest distance between cell and objective. A t this stage visualization is transferred to the video equipment for a measurement of the fluorescence intensity profile across the cell. 1. Data Collection The cell is first visualized with a white light source which is filtered to greatly reduce intensity and create a narrow band above the irradiant fluorescent frequency. Under this illumination the cell is positioned in the middle of the video monitor, the image is focused and the video analyser slow scan vertical line positioned along the midplane of the cell. With everything set up for a fluorescence measurement it is important not to bump, even the floor. The white light is completely attenuated. The data collection program, previously loaded into memory, is now given a data filename and the number of video fields to be skipped and then read. On receiving the start execution command the cassette recorder is unpaused and camera shutter opened. Three seconds elapse which allows the recorder sufficient start up time but critically allows shutter opening vibrations, which are picked up by the cell pipette, to dissipate. The laser shutter is then opened, the software synchronizes with the video signal's vertical synchronization pulse and skips then reads the appropriate video fields. Shutters are now closed, the V C R is paused, the data is written into a file on magnetic disk and is plotted onto the 4010 graphics page of the D . E . C . monitor. The software then returns it's control menu and is ready for another Specific Molecular Adsorption to Cell Surfaces / 84 measurement. D. D A T A A N A L Y S I S The raw data is a one dimensional array of 255 elements each of which is a digitized voltage representing the intensity of picture elements in the vertical section through the midplane of the cell. Effectively, the information on the three dimensional object is being projected onto a two dimensional plane which is infact the vidicon surface of the camera. Figure 20 shows the projection of the aspirated red cell onto two dimensions. Any vertical slice of the grid can be digitized, manipulated and stored in real time. This vertical slice will be termed a transverse section of the cell and the two dimensional projection area labelled P. Since the video analyser output is non linear with intensity output, the raw data is first rescaled to linearize it with intensity. The resulting data, figure 20, produces a plot of relative intensity of the projection of fluorescent molecules bound to the surface of a spherical membrane verses displacement from one side of the cell to the other. This data has information stored in it both about the membrane/WGA interaction and the imaging response of the photometer. The membrane/WGA interaction parameter of direct interest is the surface density of WGA adsorbed onto the membrane. Theoretically this is given by the fluorescence intensity in the middle of the transverse section which corresponds to the minimum intensit}' between the peaks (figure 20). This is so because at this position unit surface area on the cell projects onto unit surface area of P whereas, due to the cell curvature, an increasing amount of surface area is projected onto unit surface area of P as the outer transverse edge of the cell is reached. However, due to the noise and optical response of the photometer, it was unclear if this central part of the transverse Specific Molecular Adsorption to Cell Surfaces / 85 T H E P R O J E C T I O N O F AN A S P I R A T E D RED C E L L INTO 2 DIMENSIONS SHOWING T H E I N T E N S I T Y C R O S S E C T I O N FIGURE 20 In the anatysis of WGA/red cell surface adsorption, red cells are aspirated into a micropipette and manuvered into a solution of FITC/WGA for a predetermined amount of time. The fluorescence profile through the center of the cell is related to the spherical surface projection and shown as a plot of intensity verses crossectional displacement X. Specific Molecular Adsorption to Cell Surfaces / 86 section gave the best result. Any point within the cell on the transverse section gives the adsorbed density of WGA so long as the cell geometry and the broadening effect of the photometer response could be taken out. It was at this stage that theoretical analysis was implemented to model the photometer's output response and to remove the geometry of the cell. This would give the purely intrinsic parameter of WGA adsorbed surface density. The approach was to theoretically predict the shape of a two dimensional projection of the surface of the sphere. This solves the geometry of the problem. Next, the ideal sphere projection can be transformed, using Fourier optical analysis, into the broadened shape characteristic of the photometer output. In effect the ideal sphere projection represents the input data or object of the photometer, the optical analysis represents the imaging effect of the photometer and the transformed theoretical output represents the photometer output. The shape of the theoretical image depends upon the radius and amplitude of the object and the optical analysis. By varying these parameters a best fit curve to experimental data can be produced and this, in effect, predicts the adsorbed surface density using all the experimental data by removing the dependence on the geometry of the cell and the optical response of the photometer. 1. Sphere Surface Projection This calculation gives the projected surface density of molecules along a transverse section through the middle of the sphere. Consider a sphere, of radius r uniformly covered with fluorescent molecules at an adsorbed surface density of n per unit area. Figure 21 shows a cross-section of the sphere. Molecules are projected from the sphere surface, f(x), onto the transverse section given by the coordinate vector Specific Molecular Adsorption to Cell Surfaces / 87 x. The sphere surface cross-section, f(x), is given by equation 5.7. Let dx be the unit displacement along x and dl the part of the curve that subtends dx, figure 21, then the linear projected density, p(x), is given by equation 5.8. f ( x ) = j / ( r 2 - x 2 ) E q u a t i o n 5.7 p ( x ) = 2.n^,dl E q u a t i o n 5.8 Now in the limit of dx approaching zero, which it does by definition in differential calculus, dl (equation 5.9) is given by the Pythagorean relation. The final form of dl results from the simple differential relation given in equation 5.10. d l = • [ ( d f U ) ) 2 + d 2 x ] = / [ ( f ( x ) ) 2 - H ].dx E q u a t i o n 5.9 d f ( x ) = f ( x ) . d x E q u a t i o n 5.10 Then substitution of equation 5.9 into equation 5.8 gives a general form of the linear density. This is coverted into the projected linear density of a sphere, equation 5.12, by substitution of the geometry of this specific problem given by equation 5.7. p(x) = 2 , " , r 0 ; -r<x<r E q u a t i o n 5.12 v / ( r 2 - x 2 ) Specific Molecular Adsorption to Cell Surfaces / 88 FIGURE 21 In the calculation of the spherical surface projection the cross-sectional surface element dl is projected onto the element dx and results in a surface density given by equation 5.12. Specific Molecular Adsorption to Cell Surfaces / 89 This equation can be simply checked since the number of particles, N, on the surface of the transverse section of the sphere is n times the circumference of the section. Thus N = 27rrn. N must also be given by the integral, over the range of x, of the surface density p(x) with respect to x. Substitution, changing to trigonometric variables and evaluating the integral results in the correct answer (equation 5.13). r N = J" d x . p ( x ) = 2irrn E q u a t i o n 5.13 - r The assumption now made is that p(x) scales linearly with fluorescent emission intensity from the surface bound molecules. That is the intensity profile across the transverse section, I(x), is given by a constant times the surface densitj'. With constant irradiance, produced by the laser, and a unique transition probability from the identical fluorescent centers, the above assumption is exact for isotropic fluorescent radiators. The fluorescein isothiocyanate can be considered on a statistical average basis and when including thermal motion, in the two dimensional bilayer fluid, the assumption of isotropy is a valid one. 2. The A p p l i c a t i o n of Simple Discrete F o u r i e r Optics The response of a system is a function of frequency. That is, since a system is never perfect there will always exist an input frequency to which the system is too slow to respond. This is a critical frequency above which the system gives an average response and below which the system response increases as the frequency decreases. Fourier analysis provides the techniques to transform between real and frequency space. The optical analysis gives the theory from which optical transfer Specific Molecular Adsorption to Cell Surfaces / 90 functions are constructed, and act in frequency space to mimic the effect of the imaging system. For a system to be applicable to such analysis it must be linear and invarient. These terms and Fourier optics in general are discussed in chapter 2. The analysis done here is the spatial frequency analysis of the theoretical image profile of the transverse section of fluorescent emission from the surface of a spherical cell. The analysis is done numerically and hence discretely by the microprocessor of the photometer. The first job is to construct a one dimensional array which is the discrete numeric representation of the intensity profile I(x). Due to the singularity in this function, as x approaches the radius r, the value ascribed to the array at position x was the average function value over the interval A v Ax (x 2 ) - x - (x+—2) • This was done effectively because the area under the intensity profile in the range Ax, at x, is simply the integral of the profile, equation 5.14, and the average function value in this interval is the area above Ax divided by Ax. A(x) = /.dx c • r - ] x // 2 2S = c . r . s i n (-) ; -r<x<r V(r -x ) r E q u a t i o n 5.14 The next stage is to calculate the amplitude, phase and frequency of plane waves which when superimposed reconstruct I(x). The decomposition of I(x) into frequency components is achieved by Fourier transform and is done on computer by a discrete fast Fourier transform routine (DFFT). This produces the frequency spectrum of the intensity profile which can be modified in such a way as to model the effect of the imaging system. Optical theory states that the optical transfer function for a diffraction limited system viewing through a circular aperture, of diameter 1, with Specific Molecular Adsorption to Cell Surfaces / 91 incoherent monochromatic illumination of wavelength X is given by H(p), equation 2.11. This is a real function of frequency which attenuates the amplitude of frequency components of the object function. There is zero attenuation at zero frequency (equation 2.8) and attenuation increases with frequency up to the cutoff, f 0. Above f 0 the amplitude attenuation is complete, H(f>f o) = 0. The optical transfer function, H(f), is simply multiplied by the frequency spectrum of the object function, I 0(f), and the inverse transform of this gives the image function I.(x) (equation 5.15). I . ( x ) = /°°df .H(f ) . I 0 ( f ) . e l 2 7 r f x E q u a t i o n 5.15 1 —oo These sorts of calculations lend themselves to numerical evaluation because their ease of computation on fast computing machines. Also, such calculations often have no exact analytical solution. Ofcourse the numerical solution is not exact either and some care and often heuristic evaluation is needed to produce the desired degree of accuracy in the final image function. One has to ensure that the incremental unit in frequency space, Af (equation 2.3), is small enough to include the important dynamic behaviour of the object function represented in frequency space. The nature of the frequency spectrum of the object is object shape dependent and only by trial does one get an idea of the best elemental frequency unit for the job. At this stage in the data analysis, experimental cell data is retrieved from disk files and plotted on the graphics monitor. From the plot, the cell positioning, radius and intensity are approximtely determined and used as the parameters for the calculation of a theoretical curve. The curve is then overlayed with the experimental data, the parameters are adjusted, and new theoretical curves produced until a best fit is Specific Molecular Adsorption to Cell Surfaces / 92 achieved. The best fit curve gives the unit normal fluorescence intensity of the cell which directly relates to the adsorbed W G A concentration. Also the cell radius is determined and some indication of the photometer frequency cutoff is given. Attaining these parameters represents the final stage in a single cell experiment. E. T H E E F F E C T OF T H E F L U O R E S C E N T L A B E L ON T H E W H E A T G E R M To see the distribution of W G A on the surface of the cell, the W G A is conjugated with fluorescein isothiocyanate which is a fluorescent probe of considerably smaller molecular weight. Never-the-less the conjugation process puts the W G A through chemical stress and this with the presence of the probe could change its conformation and binding specificity. It is hoped that the conjugation process and the presence of the label have no effect on the W G A protein. The aim is to test for a discrepancy between the binding constants of unlabelled and labelled W G A . The experimental procedure involves the analysis of red cells incubated in different solutions at the same protein concentration at varying ratios of labelled and unlabelled protein. W G A binds specifically to the sugar residues on the red cell membrane protein, glycophorin [Sharon, 1977;Lovrien&Anderson, 1980]. If the binding process preferentially favours either the labelled or unlabelled W G A then in a competitive situation the favoured protein will bind to the partial exclusion of the other. Since the fluorescence intensity is a measure of the amount of labelled protein, the plot of intensity verses protein ratio will quickly establish any preferential binding effects. Specific Molecular Adsorption to Cell Surfaces / 93 F. K I N E T I C A N D E Q U I L I B R I U M B E H A V I O U R O F R E D C E L L / W G A A D S O R P T I O N The aim of these experiments is to characterise the kinetic and equilibrium behaviour of the adsorption of W G A onto the red cell surface. The cell membarne glycocalyx is the region above the lipid bilayer which is exposed to the cell's environment. The glycocalyx is made up of hydrophillic portions of the membrane proteins. The glycocalyx is thought to extend ~100A out from the lipid bilayer and the individual proteins, many of which have sugar residues attached in terminal positions, are the trees in a densely populated external membrane forest. The canopy of this forest is a highly, but selective, reactive surface which reflects the personality of the cell type and monitors and mediates the cell/environment metabolic processes. To characterise the adsorption of W G A on the red cell membrane it is necessary to determine the equilibrium amount bound as a function of bulk concentration. Experimentally this is achieved by, at each concentration, collecting kinetic data which gives the time dependence of W G A adsorption and the equilibrium membrane surface concentration. Red cells were individually incubated in various concentrations of W G A . The dynamic range of equilibrium surface concentrations was measured for W G A bulk concentrations between 0.01/xg/ml and 5fig/ml [Evans&Leung,1884]. G . R E S U L T S The first result (figure 12) shows that the fluorescent label has no effect on the binding constant associated with the reaction between WGA and glycophorin. Figure 22 shows how intensity varies as the amount of labelled W G A decreases at constant Specific Molecular Adsorption to Cell Surfaces / 94 COMPETITIVE ADSORPTION OF FITC/WGA AND WGA ^ O 0-25 0-5 0-75 10 ( V l T C / W G A ] Q F I T C / W G A + W G A ^ FIGURE 22 To see the distribution of W G A on the red cell surface, the W G A is labelled with a fluorescent probe. Experimentally the competitive adsorption of labelled and unlabelled W G A resulted in a linear dependence between fluorescence intensity and the ratio of labelled to total W G A concentration. This indicates that the label has no effect on the adsorption interaction between the WGA and the cell surface. Specific Molecular Adsorption to Cell Surfaces / 95 W G A concentration. The linear nature of this dependence indicates that there is no preferential adsorption of either the F I T C / W G A or the W G A . A t equilibrium, the amount of W G A adsorbed on the red cell surface depends on the bulk W G A concentration. To establish the equilibrium condition at a given bulk concentration, kinetic data was collected, figure 23, which shows the amount and the rate at which W G A adsorbs to the red cell surface. From these kinetic curves one obtains the equilibrium amount bound as a function of bulk concentration. Such data is known as an isotherm and is seen in figure 24. The Scatchard plot of the isotherm is shown in figure 25. It is not linear which indicates that the simple assumptions of identical, non interacting binding sites on the glycophorin are not completely sound. However the linear part of the curve indicates a binding constant of 2.95* 10 8 liters/mole and gives the number of W G A molecules bound per glycophorin as 0.93. H. DISCUSSION The linearity of the competitive binding results indicate that the labelled and unlabelled W G A has the same binding constant in the interaction between it and the red blood cell surface. This says that, to within the resolution of the photometer, the label and the labelling process have no effect on WGA/red cell surface adsorption. The kinetic data gives the time taken to reach, and the adsorbed concentration at, chemical equilibrium. It was important, at the low W G A bulk concentrations, that cells were incubated singular!)' to ensure that the bulk concentration remained Specific Molecular Adsorption to Cell Surfaces / 96 ADSORPTION KINETICS OF WGA ONTO THE HUMAN ERYTHROCYTE SURFACE DENSITY XlO 3 1 50 yUm~2 O X | A oi n o-oi 4+ V / 2 i> + _ - O — — -Q - - ' % A f D-O-50 TIME ( min ) 100 FIGURE 23 This figure shows the time dependence of the absorption of W G A on to the red cell surface. The interesting dynamic behaviour occured in a range of bulk concentrations from 0.01 to 5 micrograms per milliliter of WGA. Specific Molecular Adsorption to Cell Surfaces / 97 WGA / RED CELL ADSORPTION ISOTHERM SURFACE CONCENTRATION I O 3 + 5 0 y a m - 2 -H 2 -1o WGA CONCENTRATION (JULQ/\T\\ ) FIGURE 24 The adsorption isotherm characterizes the equilibrium interaction between WGA and the red cell surface. It shows the adsorbed concentration as a function of bulk concentration of W G A . Specific Molecular Adsorption to Cell Surfaces / 98 W G A / R E D C E L L S C A T C H A R D P L O T FIGURE 25 The Scatchard plot indicates, in the case of simple interactions, the binding constant between ligand and macromolecule and the equilibrium number bound. The non linearity of this plot shows that the interaction between W G A and membrane bound glycophorin does not obey the simple assumptions of identical non interacting binding sites. However the linear section of the curve gives an acceptable binding constant and indicates that only one W G A molecule binds per glycophorin on the red cell surface. constant. Specific Molecular Adsorption to Cell Surfaces / 99 The binding isotherm represents the equilibrium characterisation of the chemical interaction which in this case involves the binding of ligands in solution onto a two dimensional array of multivalent macromolecules. The isotherm indicates the equilibrium amount of W G A adsorption from a given bulk concentration and shows that at saturation W G A binds to the red cell at a surface density of 3 2 5 .0±0 .2x l0 Mm . The Scatchard plot, from such an isotherm, gives the binding constant of g 2.95x10 liters/mole and the equilibrium number of ligands per macromolecule as n = 0.93. Glycophorin has many sites for W G A binding but the data indicates that only one W G A molecule binds to any one glycophorin molecule. W G A is a large protein of 3 6 0 0 0 A M U and probably inhibits the binding of second and third molecules by simple steric hinderence. Combining the results of one to one molecular binding of W G A to glycophorin and the number density of bound W G A and knowing 2 the average red cell surface area is 130±10Mm f [Evans&Fung,1972], then the number of glycophorin molecules on the human red blood cell is (6 .5±0.3)xl0 . These results compare favourably with those cited in the literature [Adair&Kornfeld,1974; Snoek,1985; Lovrien&Anderson,1980]. By a radio label 5 technique, Snoek concluded that there was 5x10 glycophorin molecules on the red cell and that there was specific binding of one mole of W 7GA per mole of glycophorin. tFrom routine red cell measurements made in the laboratory A P P E N D I X Slow Scan Interlaced Video Signal  Synchronization and Acquisition Software E X T D U M P E X T P U T C H A R E X T S C A L E E X T P U T R H I C W : E Q U 0C1H ;MSB OF A/D C T R L WORD L O C W : E Q U OCOH ;LSB OF A / D C T R L WORD C H I : E Q U 21H ; A D A D I F F M O D E C H A N . l G O l : E Q U 0 A 1 H ; A D A D I F F M O D E C H A N . l A N D C O N V E R S I O N START N U M : E Q U 255D W I N : DB 0 > E N T R Y SSAS S L O W S C A N A V E R A G E S T O R A G E . This routine reads slow scan windows (vertical slice) and results in a window of average pixels. The number of windows to be skipped, the number to averaged and the address of 600 bytes of storage are to be passed on stack. The number of windows to be averaged is restricted to 1, 2, 4, 8 or 16. H I G H R E G , N U M TO B E R E A D L O W R E G , N U M TO S K I P P R E G P A I R (RP) R P , A D D R E S S OF 600 B Y T E S RP SSAS be E G : L D L D P U S H L D P U S H C A L L E N D OF E X A M P L E SSAS: P U S H P U S H P U S H P U S H P U S H L D P U S H A D D L D OUT L D OUT A F BC D E H L IX IX,0000H IX IX, SP A , 0 0 H H I C W , A A , C H 1 L O C W , A ; S A V E E N V I R O N M E N T C A L L E R S ; L I N E C O U N T P A R A M E T E R :SET A D A C H A N N E L 1 L D H,( IX+0FH) 100 / 101 SSAS4: SSAS6: SSAS36: SSAS35: SSAS30: L D L,( IX + 0EH) ; H L = A D D R E S S OF B Y T E S L D (IX + 0 0 H ) , N U M ; C O U N T = N U M L D A , 0 0 H I N I T I A L I Z E W I T H V O L T S L D (HL),A INC H L L D (HL),A INC H L D E C (IX + 00H) J P NZ,SSAS4 L D A,(IX+11H) ;TEST T H A T T H E # WINDOWS CP 16D ;IS O N E O F 1,2,4,8,16. J P Z,SSAS6 CP 08D J P Z,SSAS6 CP 04D J P Z,SSAS6 CP 02D J P Z,SSAS6 CP 01D J P Z,SSAS6 L D A,16D L D (IX+11H),A L D (WIN),A X O R A ;SKIP W I N D O W S L O O P A D D A,(IX+ 10H) ;IF(WIN = 0) J M P SSAS30 J P Z,SSAS30 L D HL,2380D 2380x28cc= 16.6msec D E C H L X O R A OR H OR L J P NZ,SSAS35 ;LOOP SSAS35 IS 28 cycles D E C (IX+10H) J P NZ,SSAS36 L D H,(IX + OFH) L D L,(IX + 0EH) L D A , G 0 1 OUT L O C W , A ; START C O N V E R S I O N RR A RR A RR A RR A RR A RR A ;WAIT 12 Msec L D (IX + 0 0 H) ,N UM 600 ZERO OF / 102 S S A S 3 : IN A , H I C W A N D O F H L D D , A L D A , G 0 1 O U T L O C W , A I N A , L O C W A N D 80H L D E , A L D A , D S L A E R L A BIT 4,A J P NZ,SSAS3 A N D O F H J P Z,SSAS3 ; R E A D C O N V E R S I O N P R E V I O U S ;START C O N V E R S I O N SETS Z TO ZERO IF A D #>0 J M P IF Z BIT=0 ; J M P IF - .6VOLT<A/D#<0 ;At this stage we have a number less than -0.6 volts ;and hence are in the sync pulse of the slow scan video signal ;Now want to poll for the lead edge SSAS2: I N A , H I C W L D D , A L D A , G 0 1 O U T L O C W , A ;START C O N V E R S I O N IN A , L O C W L D E , A L D A , D S L A E R L A BIT 4,A ;SETS Z TO ZERO IF #>0 J P NZ,SSAS5 ; J M P IF Z BIT = 0 A N D O F H J P Z,SSAS2 ; W H I L E ( V O L T < - . 6 ) R E A D A N O T H E R ;This causes the first data element to be read, at SSAS1 ;at a time between 26 and 52/xsec into the first slow scan voltage SSAS5: N O P ; N E E D 126cc RR A RR A RR A RR A RR A RR A RR A RR A RR A RR A RR A RR A RR A RR A A D / 103 RR A RR A RR A RR A ;THIS IS TO A L L O W 64jtisec RR A ;TO T H E N E X T C O N V E R S I O N SSAS1: I N A , H I C W L D D , A I N A , L O C W L D E , A ; R E A D A D D A T A L D A , G O l O U T L O C W , A ; S T A R T A N O T H E R C O N V E R S I O N L D A , D ; C O N V E R S I O N F R O M 12 BIT TO 16BIT A N D 08H ;2'S C O M P L I M E N T N U M B E R J P Z,SSAS19 L D A , D A N D OFH L D D , A J P SSAS21 ;23cc SSAS 19: L D A , D A N D OFH L D D , A L D A , (WIN) N O P ;32cc SSAS21: INC H L L D A , E A D D A,(HL) L D (HL),A D E C H L L D A , D A D C A,(HL) L D (HL),A INC H L INC H L ;60cc RR A RR A RR A RR A RR A RR A RR A RR A ;64cc P A D D I N G D E C (IX + 00H) J P NZ,SSAS1 33cc End of Slow Scan Loop. Each path is 256cc= 64^sec L D A,255D SSAS40: RR B ;THIS L O O P IS TO E N S U R E / 104 RR B ; T H A T O N L Y E V E R Y O T H E R V I D E O F I E L D IS R E A D RR B ;THIS L O O P IS 255x54 C L O C K C Y C L E S RR B ; A P P R O X . 3.5msec RR B D E C A J P NZ.SSAS40 D E C (IX+11H) ;DEC T H E W I N D O E C O U N T J P NZ,SSAS30 J M P IF N O T ZERO L D (IX + O H ) , N U M L D H,(IX + 0FH) L D L,(IX + 0EH) ; H L = S T O R A G E A D D R . SSAS 50: L D A , (WIN) ;THIS L O O P C O M P U T E S T H E A V E R A G E SSAS51: S R L A J P Z,SSAS52 S R L (HL) INC H L RR (HL) D E C H L J P SSAS 51 SSAS52: INC H L INC H L D E C (IX + 00H) J P NZ,SSAS50 L D H,(IX + 0DH) L D L,(IX + 0CH) L D (IX+11H),H L D (IX+10H),L ;COPY D O W N R E T U R N A D D R . POP IX ; R E M O V E C O U N T P A R A M E T E R POP IX ;RESTORE C A L L E R S E N V I R O N M E N T POP H L POP D E P O P BC POP A F INC SP INC SP INC SP INC SP RET ; R E T U R N TO C A L L I N G R O U T I N E LIST OF REFERENCES Adair W . L . , Kornfeld S. 1974 J . Biol. Chem. 249:4696-4704 Agard D . A . , 1984 Optical Sectioning Microscopy: Cellular Architecture in Three Dimensions Ann. Rev. Biophys. Bioeng. 13:191-219 Anderson R . A . , Lovrien R., 1981 Erythrocyte Membrane 2: Recent Clinical and Experimental Advances A . Liss Inc. N . Y . Arndt-Jovin D. J . , Nicoud M.R. , Kaufman S.J., Jovin T . M . , 1985 Fluorescence Digital Imaging Microscopy in Cell Biology Science 230:247-256 Bell G.I., 1978 Models for the Specific Adhesion of Cells to Cells Science 200:618-627 Cantor&Schimmel, 1980 Biophysical Chemistry Part III: The Behaviour of Biological Macromolecules Freeman & Company Capaldi R .A . , 1974 A Dynamic Model of Cell Membranes Scientific American March:25-33 Choy Y . M . , Wong S.L. , Lee C .Y . , 1979 Bioc. Biop. Res. Commun. 91:401-415 Evans E . A . , 1985 Detailed Mechanics of Membrane-Membrane Adhesion and Separation I: Continum of Molecular Cross-Bridges Biophys.J. 48:175-183 Evans E . A . , 1985 Detailed Mechanics of Membrane-Membrane Adhesion and Separation II: Discrete, Kinetically Trapped Molecular Cross-Bridges Bioplrys.J. 48:184-192 Evans E . A . , 1986 Structure and Deformation Properties of Red Blood Cells: Concepts and Quantitative Methods Methods in Enzymology (In Press) Evans E . A . , Leung A . , 1984 Adhesivity and Rigitity of Erythrocyte Membrane in Relation to Wheat Germ Binding The Journal of Cell Biology 98:1201-1208 Evans E . A . , Hochmuth R . M . , 1977 105 / 106 A Solid-Liquid Composite Model of a Red Cell Membrane J . Membrane Biology 30:351-362 Evans E . A . , Fung Y . C . , 1972 Improved Measurements of the Erythrocyte Geometry Microvascular Research 4:335-347 Goodman J .W. , 1968 Introduction to Fourier Optics McGraw-Hil l Publishing Gordon J . L . , 1980 Mechanisms Regulating Platelet Adhesion British Soc. for Cell Biology Symposium 3: Cell Adhesion and Motility. Curtis A . S . G . & Pitt J .D . - ed. Cambridge University Press Grant C . W . M . , Peters M . W . , 1984 Lectin-Membrane Interactions: Information from Model Systems Biochimica et Biophysica Acta 779:403-422 Gross D . , Loew L . M . , Webb W.W. , 1986 Optical Imaging of Cell Membrane Potential Changes Induced by Applied Electric Fields Biophys. J . 50:339-348 Hecht-Zajac, 1974 Optics Addison & Wesley Publishing Co. Higgins R.J . , 1976 Fast Fourier Transform: A n Introduction with some Mini Computer Experiments American Journal of Physics 44:766-773 Huang H . W . ? 1973 Mobility and Diffusion in the Plane of Cell Membrane J . Theoretical Biol. 40:11-17 Israelachvili J . N . , 1985 Intermolecular and Surface Forces Academic Press Israelachvili J . N . , Marcelja S., Horn R .G. , 1980 Physical Principles of Membrane Organization Quart. Rev. of Biophysics 13:121-200 Israelachvili J . N . , Ninham B.W. , 1977 Intermolecular Forces - The Long and the Short of It J . Colloid Interface Science 58:14-25 Kapitza H . G . , McGregor G. , Jacobson K . A . , 1985 Direct Measurement of Lateral Transport in Membranes' using Time Resolved Spatial Photometry Proc. Natl . Acad. Sci. U . S . A . 28:4122-4126 / 107 Ketis N.V., Grant C.W.M., 1982 Control of High Affinity Lectin Binding to an Integral Membrane Glycoprotein in Lipid Bilayers Biochimica et Biophysica Acta 685:347-354 Knowles D.W., Evans E.A., 1986 A Simple Method for In-Situ Conversion of Fluorescence Intensity to Number Density with Correction for Microscope Transfer Limitations Biophy. J. (to be submitted) Koppel D.E., 1979 Fluorescence Redistribution after Photobleaching: A New Multipoint Analysis of Membrane Translational Dynamics Biophys. J. 28:281-292 Lovrien R.E., Anderson R.A., 1980 Stoichiometry of Wheat Germ Agglutinin as a Morphology Controlling Agent and as a Morphology Protective Agent for the Human Erythrocyte J. Cell Biology 85:534-548 Marcelja S., 1976 Lipid-Mediated Protein Interaction in Membranes Biochimica et Biophysica Acta 455:1-7 McGregor G.N., Kapitza H.G., Jacobson K.A., 1984 Laser Based Fluorescence Microscopy of Living Cells Laser Focus/Electro Optics ???:85-93 Needham D., Evans E.A., 1986 Structural and Mechanical Properties of Giant Lipid (DMPC) Vesicle Bilayers from 20° Below to 10° Above the Liquid Crystal-Crystalline Phase Transition at 24 °C Biophysics J. (to be submitted) Owichi J.C, McConnell H.M., 1979 Theory of Protein-Lipid and Protein-Protein Interactions in Bilayer Membranes Proc. Natl. Acad. Sci. U.S.A. 76:4750-4754 Parsegian V.A., Gingell D. 1980 Red Blood Cell Adhesion III: Analysis of Forces J. Cell Science 41:151-158 Peters R., Briinger A., Schulten K., 1981 Continuous Fluorescence Microphotolsis: A Sensitive Method for Study of Diffusion Processes in Single Cells Proc. Natl. Acad. Sci. U.S.A. 78:962-966 Perry, Gilbert, 1979 J. Cell Science 39:257-272 Sharon N. 1977 Lectins Scientific American 236:108-119 / 108 Singer S.J., Nicholson G .L . , 1972 The Fluid Mosaic Model of the Structure of Cell Membranes Science 175:720-731 Snoek R., 1985 Spin Labeling and Analysis of Erythrocyte Surfaces Ph.D. Thesis University of British Columbia Tanford C , 1973 The Hydrophobic Effect John Wiley & Sons N . Y . Waymouth C , 1970 Osmolality of Mammalian Blood and of Media for Culture of Mammalian Cells Vitro 6:109-127 Vaz W . L . C . , Kapitza H . G . , Stumpel J . , Sackmann E. , Jovin T . M . , 1981 Translational Mobility of Glycophorin in Bilayer Membranes Dimyristoylphosphatidylcholine Biochemistry 20:1392 

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