SURFACE DENSITY OF RADIANT SOURCES MEASURED MICROSCOPY: CORRECTION FOR DIFFRACTION AND BY FOCUS OPTICAL LIMITATIONS by DAVID WILLIAM 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 THE REQUIREMENTS FOR THE DEGREE MASTER; OF OF SCIENCE in THE FACULTY OF GRADUATE DEPARTMENT OF STUDIES PHYSICS We accept this thesis as conforming to the reauired standard THE UNIVERSITY O F BRITISH COLUMBIA October 3rd 1986 © David William Knowles, 1986 OF In p r e s e n t i n g requirements this thesis f o r an of British it freely available in partial advanced degree at Columbia, understood for that Library s h a l l make for reference and study. I f o r extensive copying of h i s or be her copying or f i n a n c i a l gain g r a n t e d by publication s h a l l not be E-6 (.3/81) of further this Columbia thesis head o f this my It is thesis a l l o w e d w i t h o u t my of The U n i v e r s i t y o f B r i t i s h 1956 Main M a l l V a n c o u v e r , Canada V6T 1Y3 the representatives. permission. Department University the f o r s c h o l a r l y p u r p o s e s may by the the I agree that agree t h a t p e r m i s s i o n department or f u l f i l m e n t of written ABSTRACT A new technique is introduced membrane bound components conversion of fluorescence the spatial optical for the on living cells inuitro. intensity to response of the diffraction and focus limitations of the A theoretical fluorescently (the determination and involved microphotometer to for the inherent the of (WGA) onto W G A/red The fluorescence adsorbed account modelling of labelled ligand cell interaction microphotometer the intensified membrane conversion red cell concentrations concentration on video is a imaging was technique surface. of bulk was and fluorescenated concentration based digitizing used Individual surface evaluated laser images with a resolution of 0.25Mm. bulk the the adsorption of a fluorescence various of system. with to density technique provides a simple number density combination on surface undertaken to examine erythrocyte). WGA This the and experimental study was microphometer. The of to cells W G A to and with biological cell a fluorescence determine incubation that the isolated and the time. fluorescence microscope equipment characterize were a in produces adsorption of incubated in dependence of The equilibrium g results gave binding ratio a microscopic of one association constant W G A molecule per of 2.95x10 liters/mole, a molecular glycophorin molecule on the red cell surface 5 and the number of glycophorin molecules per human red blood cell as ii (6.5±0.3)xl0 . TABLE OF CONTENTS Abstract ii List of Figures v List of Symbols vii Acknowledgements viii I. Introduction: Fluorescence Microphotometry and Biological Systems A . Fluorescence Imaging B. Image Analysis C. A Model System 1. Membrane Structure and the Red Blood Cell D. Application of the Fluorescence Intensity to Number Density Technique II. Fourier Analysis and Physical Optics A . The Fourier Transform B . The Discrete Fourier Transform C. Fourier Optics D . The Optical Transfer Function 1 1 2 3 3 Conversion 5 8 8 11 11 14 III. The Fluorescence Microphotometer A . Introduction .". B. Photometer Hardware ; 1. The Source of Radiation 2. The Optics and Microscope 3. Video Camera and Video Signal Multiplexing 4. The Microprocessor 5. The Hardware Interface C. Photometer Software 1. Z80 Assembler Routines D. Static Photometer Response 1. Introduction 2. Method:- Linearity, Invarience and Camera Gain 3. Results 4. Discussion and Conclusion 17 17 18 18 18 20 21 23 25 25 34 34 36 37 40 IV. Conversion of Fluorescence Intensity to Number Density:A . Introduction 1. Fluorescence Intensity to Number Density Conversion B. The Molecular Surface Density Calibration Experiment 1. Experimental Procedure C. The Theoretical Analysis Method 1. The Transfer Function 2. Multiplane Analysis including Focus Aberration 3. Discrete Numerical Analysis 4. The Theoretical Experiment D. Results E . Discussion 1. Frequency Domain Resolution 44 44 45 45 45 47 47 48 50 51 52 59 61 iii 2. A Calculation of the Optical Collection Depth F. A Single Composite Transfer Function 1. A i m 2. Introduction 3. Method 4. Results 5. Disscussion 6. Conclusion V. Specific Molecular Adsorption to Cell Surfaces A . Introduction 1. The Molecular Interaction 2. The Scatchard Plot B. Experimental Preparation 1. Chemical List 2. Pipette Preparation 3. Cell Preparation C. The Experimental Procedure 1. Data Collection D. Data Analysis 1. Sphere Surface Projection 2. The Application of Simple Discrete Fourier Optics E. The Effect of the Fluorescent Label on the Wheat Germ F. Kinetic and Equilibrium Behaviour of Red Cell/WGA Adsorption G. Results H. Discussion 64 67 67 67 68 69 70 71 76 76 76 77 79 79 80 81 81 83 84 86 89 92 93 93 95 Appendix 100 List of References 105 iv LIST OF FIGURES Number Title Page 1 The 321 Video Analyser Slow Scan Output 2 The Hardware Interface Schedule 24 3 Flow Chart of Data Acquisition/Display Software 26 4 A D A Voltage to 31 5 The S S V S Lead Edge Synchronization 33 6 Laser 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 11 Theoretical Image and Object Projection 12 Bit Binary Conversion and Incandescent Intensity of a Pipette Fluctuations Crossection Crossection 22 53 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 66 16 Frequency Spectra of the Theoretical Object Pipette Crossection 17 Frequency Verses Cylinderical Object Height Spectra 72 of the Theoretical Image Pipette Crossection 73 18 Multi Isofocal Analysis Composite Transfer Function 74 19 Incoherent 75 20 The Projection of an Aspirated Red Cell into 2 Dimensions Showing the Intensity Crossection 85 Spherical Surface 88 21 Transfer Function at 2/im Crossection v Out of Focus 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 LIST OF SYMBOLS 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 = ^ Dinnensionless Frequency c f Optical Transfer Cutoff f(x) Derivative of f(x) p(x) Surface Density A(x) ( - 1 - x ; -1<X<1 0 Sinc(x) ; otherwise = (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. I N T R O D U C T I O N ; 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 R Y A N D BIOLOGICAL 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 response by binding influence. These recognition and antibodies. Ligands, specifically interactions fusion to control through most receptor a host of which proteins of morphogensis, are on proteins, the catalyse target physiological functions development and cell cells from they gamete function of vital systems, growth, repair from injury and disease and the essential cellular metabolic processes. of The characterization of such ligand/cell interactions is thus 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 study on the single experimental interaction, number living fluorescence Arndt-Jovin et al.,1985]. scale, density invitro. microphotometer macromolecular fluorescently cells equipment The system The new is capable labelled molecules been designed and and distribution of membrane [Koppel,1979, and has is a Peters laser bound based, microprocessor et al.,1981; McGregor developement of assembled measuring is its the et calibration number to proteins driven, al.,1984; on a density of 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. IMAGE The ANALYSIS physics adsorbed on fluorescence a cell. of a subsequent pipette quantification of the technique is introduced known concentration fluorescence cross-section proportional inherent A the intensity to number density. It encapsulation the of this problem is to in the problem projected is the an The size of the probe fluorescence experiment cross-sectional the object in in a have a relation conversion micropipette of an a intensity the and transverse cylinder (figure to of which involves the intensity would volume of density of ligand simple is a new technique of fluorescent analysis. such for surface profile 10). resolution One of the system. Red blood cells for example, have an approximate average diameter of 5 y m and the 4jum *.f object can a band be separated The effect, due to the diffraction and determine has pass which attenuates spatial frequencies above Thus the resolution of the S3'Stem, which is the minimum distance that two points 0.25 ^ m . by photometer surface focus density and still be seen as distinct in the image, is nature of physical optics, is an image compromised limitations [Agard,1984] that distribution. However, by cannot using the be used theory directly to 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 for by a simple optical correction factor. t F r o m the model presented in chapter 4. accounted Introduction: Fluorescence Microphotometry and Biological Systems / 3 C. A M O D E L S Y S T E M Red blood cells and wheat interaction. This system to characterize the Ketis&Grant,1982; WGA as a interaction to wheat germ were used as a al.,1982; Grant&peters,1984], the distribution model of ligand/cell been [Lovrien&Anderson,1980; characterize surface[Evans&Leung,1984; from agglutinin is widely studied. Much work has Ketis et probe germ carried out simply Anderson&Lovrien,1981; and other of protein studies on the Snoek,1985]. Wheat germ agglutinin is a protein and is one of many such proteins which are use the red cell extracted termed lectins. Lectins have the ability to agglutinate red cells. The aggultination of red cells in the presence of [Sharon 1977]. sugar wheat germ This and further agglutinin is shows that that wheat inhibited by wheat germ germ the agglutinin agglutinin binds bound protein glycophorin since glycophorin contains 1. Membrane Structure and the Red sugar N-acetylglucosamine binds specifically specifically to the to this membrane N-acetylglucosamine. 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 individually in the components to in small quantities blood plasma the red Israelachvili,Marcelja&Horn,1980] molecules together and spectrin. by The thus a simple finger isolation is not a cell amphiphilic whole non-covalent from structure prick. They also exist problem. There are three membrane, lipid is molecules, a condensed intermolecular forces [Singer&Nicholson,1972; amphiphilic state protein of matter held [Israelachvili,1985; Introduction: Fluorescence Microphotometry and Biological Systems / 4 Israelachvili&Ninham,1977], the packing of which determine the minimum configurational energy the Owicki&McConnell,1979]. lipid The red and cells protein are molecules never-the-less and [Marcelja,1976; able to withstand an average of 120 days of circulation within the cardiovascular system. The first component, amphiphilic surfactant physically separates the environments in composition and osmolarity. molecules, exterior These form a structure and interior to the molecules are cell, cholesterol which which differ and lipids, comprise a hydrophilic head group and a hydrophobic fatty acid tail. Membranes formed largely of phospholipids and cholesterol. The phospholipids have group joined to two fatty acid chains and a phosphate group. The the condensed matter is a double layer of lipid are a glycerol phosphate group is connected to a head group such as ethanolamine, choline or serine. The of and molecules with structure 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 plane of the membrane but are highly incompressible in the third dimension. Lipids are associated with the the membrane lipids in a form a two dimensional fluid highly asymmetrical fashion in the [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 can be fixed via their association proteins traverse the with the membrane membrane and their position cytoskeleton. Surface proteins Introduction: Fluorescence are associated that with surface. one Proteins on membrane to interaction [Tanford,1973] the the side other of the one membrane surface surface. since Microphotometry and Biological Systems / 5 This the are barrier. While the specific functions are of the above cell lipid the that the can is into known as environment reactive to work required to drag structural extend cell/environment interaction. selective able thus move partition freely about through the the hydrophilic region of portion of the membrane integrity is determined creates a by the large lipids, carried out by the proteins. The proteins of the external bilayer bilayer basic not and sort of motion is opposed by the hydrophobic protein through the hydrophobic central energy alone the the with, The glycocalx which environment glycocalx, interacts surface cell and since it this and 100A . the the cell type mediates layer This 1 is becomes characterizes monitors some the region portion of the ambassador of and is a highly but the cell/environment biochemistry. The third structure cytoskeleton. as The cytoskeleton spectrin. It spherical, supports biconcave which is essential membrane peculiar the shape. when the is highly to some is made cells, the of long entangled APPLICATION DENSITY A CONVERSION simple set germ and creates the This an shape allows and resists THE area the particular, is the excess possibility of a non surface to volume microcirculation. ratio Since the dilatation [Evans&Hochmuth,1977] the 1986]. FLUORESCENCE INTENSITY TO NUMBER TECHNIQUE of experiments agglutinin to in filamentous proteins known red cell is deformed in the cohesive OF cell red cell membrane cell would rupture due to such deformation [Evans D. red was surface conducted of the to characterize human the red blood cell. adsorption of Red blood cells wheat were Introduction: Fluorescence Microphotometry and Biological Systems / 6 individually isolated and incubated WGA. in various concentrations of fluorescently labelled 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 WGA surface density of WGA and is a function of the bulk 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 g WGA 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±0.2xl0 M m " . 2 The average red cell surface area is 1 3 0 ± 1 0 M m and thus there is ( 6 . 5 ± 0 . 3 ) x l 0 These results compare favourably 5 with 2 glycophorin molecules per red cell. 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 3-5x10 5 copies of glycophorin per red cell. II. F O U R I E R A N A L Y S I S A. T H E F O U R I E R AND PHYSICAL OPTICS TRANSFORM 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 which frequencies transform Baron de Fourier represent and the equations inverse are frequency Fourier transform the transformations space. The Fourier construct together, object. reconstructs that The inverse function •(x) are given by analysis provides a 7 r f Equation x between physical takes a physical space object physical object. of the plane waves The result transform takes frequence. this Once on each way of predicting a frequency response is determined of its of the system, the frequency 2.2 space and and computes which, when is the frequency all of the output we simply transform frequencies transform the frequencies Determining the system its own but recording the output to a point source is of a spectrum spectra system which is characteristic characteristic then give the predicted output. problem 2.1 Equation l 2 , r f x function physical space, Fourier a will have analytical 2 and waves space. input. A system function l the physical space object by computing the superposition of plane defined in frequency act " e f transform added space, a / d f .*(f ) . e which take in units of inverse Fourier of dx.*(x) . ( * ( f ) )= 1 the frequencies, the of determining 2.1 and 2.2. *(x)=Ff of and the process a given input is known as Fourier analysis. The Fourier * ( f )=Ff(*(x) )=f These (1768-1830), done the object with back response very the given the of the input into frequency frequency response into physical space to to all frequencies simply input. A true point source by is an experimentally is represented by Fourier Analysis and Physical Optics / all frequencies Fourier the each analysis system unique absolute is a to is a acting individually. through This frequency are two important and linear. unique output is simultaneously the the property equals must system the hold which of is function properties therefore the then output reconvolved of or the several of the stimuli deconvolves effectively must that for of time of each analysis which are and The system property independent outputs Fourier the is the superposition. sum of the because response and space which defines how Invariance individual frequency components the space, component. apply there there in function in frequency must be invariant input function into its time output position. Linearity stimuli acting of its amplitude attenuates each frequency Fourier have; constant transform the system For at 10 an input sent one at into the a output function. There The is one type of the other point concerning the dimension in physical and frequency of input function depends entirely physical space might be time, three on the system space. being studied. The units dimensional space or a combination these. Strictly for the purpose of ease of Fourier analysis, and to avoid edge of 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 over Similarly components into an temporal input frequencj function of r real with dimension one over components space distance. is with dimension of transformed into one spatial time. frequencj' Fourier Analysis and Physical Optics / B. T H E D I S C R E T E F O U R I E R For fast computer aided TRANSFORM numerical transform [Higgins,1976] theoretical input function, and the data points computation one which acts upon an array which represent 11 the Fourier amplitude of data. transform and defines the a discrete Fourier The data represents produces phase an array of the the of complex plane waves of increasing frequency. The physical array physical space of N where points is assumed and A x T = N.Ax is to represent the one complete incremental physical period, T, in space distance. Hence the incremental frequency space distance is; Af=(T)~ =(N.Ax)~ 1 and Imaging OPTICS Systems:- A n imaging system, optical elements arranged so as an long the image. another So the system the system the 1. as is thought of as aberrations, in the most general sense, to collect light from an object optical elements is invariant in time, superposition geometric The 2.3 is in units of inverse distance. C. F O U R I E R to Equation 1 are stationary is a and use with system of it to create respect and depending on its geometric to one aberrations, spatially invariant although never perfectly so. Also due principle of electromagnetic radiation, but again the system is thought of as linear. resolution of an optical system is determined by three the wavelength of light, parameters: depending on Fourier Analysis and Physical Optics / 12 2. the numerical aperture 3. and the degree of geometric An imaging system from the object, aberration. is said to be diffraction limited if a diverging spherical wave, is mapped into a spherical wave which converges to the same relative position on the image. The diffraction limitation of an imaging system because the object is being investigated which is characterised by an electromagnetic by its wavelength. A n y ultra probe structure arises of finite size with characteristic dimension less than this finite size will not be resolved in the image. The diffraction limited system numerical The corresponds aperture equals Abbe the refractive resolution. (1840-1905) to unity. Abbe numerical aperture optical of [Hecht&Zajac,1974]. index of the medium adjacent to the recognised in air the numerical aperture that the resolution varied system. This is less than or directly wavelength of the light and inversety as the numerical aperture. the The concept lens multiplied by the sine of the half angle of the maximum cone of light collected by the lens. For an objective equal thoeretical was introduced by Ernst numerical aperture objective to the maximum with The importance of is in its relation to the minimum physical aperture aperture is a window through which the the system of the 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 which decreases the resolution of the image. Geometric aberrations stray from perfectly their geometric path. A system with aberrations 1. cause the light to does not produce spherical converging wave from a diverging spherical input wave less resolution than the diffraction limit. Two examples of geometric imperfections in the curvature of the lens, aperture a and has aberrations are: 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 of to the system information and about distort the the object. However, all way in which an imaging system distorts its image can attained from the system's the image relative point spread function. A n imaging system's function is it's spatially dynamic response imaging system model it. The created all effect the resolution with Fourier analysis point spread function is an amplitude and phase It holds all the information about to be point spread function which completely characterizes and is used in conjunction from a point source. the the mathematically map of the image 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 point spread functions positioned at each source object is represented frequencies frequency space creates a function which shows exactly component the spatial space frequency thus all array. frequency each and by point in the independent known as the optical transfer the imaging system for an the aberration unity in within function is the free, the at constant point spread how the initial object shape. a true point amplitude function in into system attenuates This function is function and in frequency space mimics the action of hence diffraction limited system, system. aperture the Fraunhofer 2.5) and the Mathematically the function.(Equation of the of Further, in creating an image from its object. The point spread function illumination wavelength aperture transformation linear superposition of and zero shape if and one otherwise, diffraction size defines equation pattern of the is governed of the a pupil 2.4, by minimum physical function then lens completely the which is point spread aperture or pupil Fourier Analysis and Physical Optics / inside the lens otherwise A(x)=[ i h(x)=M.f dx.A(\d-x).e aperture Equation 2.4 Equation 2.5 -i27TXX 0 D. T H E OPTICAL TRANSFER 14 FUNCTION The relation of the optical transfer function to the point spread function depends whether the light collected from the object is spatially coherent or on 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 spatially varies randomly in a statistical manner the light unison, and therefore must electromagnetic are components. incoherent be a system For image superimposable Thus superimposed components. impulse responses in the therefore the object is incoherent. For coherent illumination the various impulse responses in the the from by coherent is linear plane by illumination vary in statistically system in intensity. is of the linear One defines of amplitude the c The incoherent dx.h(x).e - i 27rf x the independent intensity in from vary in the and object, the fashions, and electromagnetic phase coherent transfer as the Fourier transform of the point spread function. (Equation H (f)=/ plane addition of amplitude and phase of incoherent addition image and an function 2.6) Equation 2.6 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) Hj(f)= J f ddXx x 'hhU()x ) ' 2 - | ' _ - i 2 7 r f x P E q u a t i o n 2.7 e / dx.Jh(x): 2 x 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 E q u a t i o n 2.8 H(-f)=H (f) E q u a t i o n 2.9 f !H(f)|<!H(0)! Two examples extensively (equation of optical in the following 2.11) transfer theoretical functions work is for a circular lens aperture square lens aperture E q u a t i o n 2.10 [Goodman, 1968] are for incoherent and the second with the simple aberration of focus error. which are systems. (equation used The first 2.12) for a Fourier H(p)= f |[cos" p-p/(1-p )] 1 2 Analysis and Physical Optics / 16 ;p<1 ;Otherwise H ( p ) = A ( p ) s i n c [ ^ p ( l - | p ! )] Equation 2.11 Equation 2.12 III. T H E A. FLUORESCENCE MICROPHOTOMETER INTRODUCTION The fluorescence excite microphotometer fluorescence is an instrument emission. The photometer that uses laser irradiation to uses a microscope and processes images with the aid of video equipment and a microprocessor. The instrument is capable measuring and producing a two dimensional map of low levels of 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 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 then expanded glass. The through by beam dichroic system, wavelength pumps the decays and fluorescence emitts emission sj'stem which through the imaging. The video camera The is amperes. collimating the expanded a software is sent up using the fluorescent photons is of collected impermeable light to with less to off a the objective objective as by energy the the and objective shorter imaging system piece of plane the by equipment 17 hence and laser an consists manual gain controls supporting video analysis scattered is shutter controlled and rotating, of the condenser. frosted microscope The lasing centers on the object into an excited state which dichroic is split and focused electronic The laser beam wavelength. eyepeice of a wavelength. passes through the in real The for visual shutter and is, in effect, creates, longer a The dichroic light passing and electronic controlled, intensified sensitive time, a photometer. one dimensional 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 plotter. enhancement The using the graphics first stage video terminal and for permanent of analysis is principles of physical optics. calibration Particular copies on a followed analytic by image 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 attenuates optical element is beam intensity, a is shutter TTL manufactured driven and has by Uniblitz. It completely a response time milliseconds. The beam is then expanded to a size which fills the entrance of 10 aperture of the microscope. The beam expander consists of a piano convex lens with a focal length of 2.5 scattered as centimeters which is placed one focal distance away and collects light from a rotating, sand blasted sheet of glass. The frosted glass acts a two dimensional array of irradiating point sources randomises the spatial coherence The inverted microscope, distance, the 40X, objective dichroic systems. continual rotation up with a across the beam. manufactured by lens and its and the Leitz, is set Leitz Ploem Pac which short houses working up to four 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 of longer wavelength due to conservation of energy. emission is always It is collected by the and passes through the dichroic which completely attenuates the laser emission. The fluorescence objective shorter wavelength beam is then split and sent through 25X eyepeices which project a real image for visual and electronic monitoring. Preceeding the video camera complete entrance pupil attenuation of is the another Uniblitz fluorescence vidicon tube of the video camera. electronic image and shutter protects which the controls highly the sensitive The Fluorescence Microphotometer / 20 3. V i d e o C a m e r a a n d V i d e o S i g n a l M u l t i p l e x i n g The two Intensicon dimensional mapping of object fluorescence 8, low light level, monochrone intensity video is camera. The manufactured by Lenzar Optics Corporation, Florida U . S . A . . Its intensified vidicon tube monitored camera an was sensing device is an and was custom designed with manual intensifier gains. The gain settings by are manually adjusted in intervals of 0.01 and video 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 Inc., Colorado U . S . A . . The individual picture elements functions preformed by the 1. The the 321 321 Video Analyser manufactured by Colorado Video processes television signals so that the brightness may be read. For our application there are two of essential 321: multiplexes a video signal. The horizontal and markers are verticle seen as a position marker on to horizontal and verticle line on the video picture and their position is adjusted by controls on the front of the 2. The 321 reflects instrument. produces the a brightness Slow of Scan the video picture output signal (SSVS) elements under the which horizontal position marker. The S S V S is a verticle array of picture elements which are updated continuously at the video scan rate. Thus the S S V S is a series of square per scan are wave voltage pulses, one line, and is terminated by a verticle sink pulse. The 5 times 64^sec, have the video signal thus an output range the between 239 SSVS 0 and 13 square SSVS output levels wave pulses, volts. The each being sink pulse falls to a The Fluorescence negative level of -0.8 The SSVS the is is also volts for a duration of 1.37msec. (Figure multiplexed onto the left side of the sent to a Microphotometer / 21 video picture. The video monitor for video signal and is displayed vertically on multiplexed interlaced composite visual assessment analog to digital converter board in the 1) and the SSVS is sent Mixer maufactured by to Vista Electronics, California Video Digital U.S.A.. This device multiplexes up to eight analog inputs, a twelve hour clock and a video frame onto the video signal. A l l this video picture 401 The information can be and is displayed in alphanumeric is sent to a three quarter inch videocassette 4. The the microprocessor. The camera's video output signal is read in parallel by a model 401 Voltage video signal selectively character count positioned within form. The output of the the recorder manufactured by Sony. Microprocessor digitization, storage, analysis manufactured by Cromenco Inc., a Z80 central computer has and display is controlled by California U . S . A . . The computer a microprocessor is designed around processing unit and talks to its peripherals along an S100 a 4 megahertz internal clock thus each bus. clock cycle is one quarter The of a microsecond. The basic killobytes application peripherals of memory was a include and a D.E.C. dual eight Cromenco Twin VT240 inch intelligent graphics floppy disk drivers. Added Universal Asynchronous Receiver (TUART) and an I/O Technology A / D / A Converter Board. The T U A R T , by Cromenco, provides two channels of duplex serial data exchange, terminal, for 64 specific Transmitter manufactured two channels of The Fluorescence Microphotometer / 22 The 321 Video Analyser Slow S c a n 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 is manufactured by independent sections binary I/O Technology, Valencia California U.S.A. and board has two of operation. One section converts analog voltages into a digital, representation and the other converts a digital number voltage. Only the A / D section is presently used and consists into an analog 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 boards. The talks to the experimental output of the ports. Pins 12, laser The J2 via the A D A and TUART A D A board is configured in differential input mode and channel 0 and 1 of its C A Connector Port are connected the equipment 321 video analyser. The 24 and 14 of the J3 and camera shutters TUART 13, DC output and Slow Scan board has 25 via a T T L driven relay, and the start/stop of a and 14 video two parallel input/output parallel output port are connected by means parallel output port pins to the T T L driven control the shutter and control power videocassette supply. recorder, of the real time clock of the 401 Digital Voltage Mixer. The A D A C A connector via a 25 which port and the T U A R T J2 parallel output port are interfaced pin blue ribbon cable which runs into the back of the blue interface redirects the connections, via 75S2 coaxial cable, hardware interfacing schedule is seen in figure 2. to the various devices. box The The Fluorescence Microphotometer / 24 The Hardware Interface Schedule 12 Laser Shutter Drive 0 24 TUART J3 Laser Shutter Parallel Output Port 14 GND Camera Shutter On" V / A Camera Shutter 13 25 TUART ttl relay Videocassette Recorder TUT J2 Parallel Outpu,t Port 14 GND 401 Blue Multiplexer interface Clock Box 16 ADA C A Connector Port 8 15 7 DC Output SSVS GND 321 Video Analyser FIGURE 2 The hardware interface shedule shows the physical connections microprocessor ports and the devices the microprocessor controls. between the The Fluorescence Microphotometer / 25 C. P H O T O M E T E R SOFTWARE There are three areas of software data control:- acquisition, dispay and analysis. The data acquisition software essential part of the is written in microphotometer. section, synchronizes with and reads relevent information about Fortran and consists of a package. This software the assembler This software, the video variety Z80 and is discussed interlaced composite image. The of routines displays fluorescence display which a transparent in the but following video signal extracting software combine to data, in Textronics is make 4010 written a in graphics mode, on the graphics page of the D . E . C . console or in hard copy on the Textronics plotter. The acquisition and package which consists of one display runs software and. controls short laser this time the fluorescence the graphics The analysis software, match the pulse been a specific which organized type of fluorescently and concatenated experiment. stimulates The the into one experiment object. During image is digitized, written to a disk file and displayed on terminal. Figure 3 shows the flow of this acquisition/diplay software. written in Fortran, uses the techniques spatial form of the characteristics has photometer of Fourier optics output by modelling the optical to transfer 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 A s s e m b l e r The data Routines 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 FLOW DATA C H A R T ACQUISITION MENUE READ / DISPLAY DATA EX IT 1 • • • 1 • • • 2 . .. 3 2 ENTER FILENAME R L E NAME READ SOFTWARE 3 ENTER FILE 26 OF SSVS PLOT OPEN Fluorescence Microphotometer / & PLOT DATA ENTER # OF VIDEO SPACE BAR T O INITIATE EXPERIMENT OPEN CAMERA UNPAUSE OPEN Fl E L D S THE LASER CALL SHUTTER VCR SHUTTER SSAS CLOSE BOTH SHUTTERS PAUSE THE VCR WRITE DATA PLOT THE TO THE COLLECTED DISK FILE CURRENT 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 displa3 ed on the graphics monitor. r 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 read and write supplied before in building a software by the ascii to and from the system the operating system call. system These PUTCHAR and G E T C H A R leave callers the system in assembler which environment terminal. These and require system pass calls their unaffected. is having the ability to certain are registers into on stack routine PRINT routines are to be configured incorpoated parameters The basic the routines and in doing so writes a complete message to the console. The message is set up in memory and must be terminated by hexadecimal zero. The next step real numbers was the definition and the ability to handle can be represented in binary using a fixed real numbers. number Signed of bits. The routines written are to handle signed, 32 bit, fixed point real numbers. The value of such which a number is defined by the addition of the value is the binarj' contents of the bit times associated with each bit N is the bit position and 2^ 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 001E C000 30.75 Two 32 bit numbers is passed to each of the four 32 bit Binary Hexadecimal Decimal 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 D I V which is passed two 32 bit parameters variables are and uses two local 32 bit variables to compute the division. The four the and F L represent QUOTIENT, DIVISOR, the FRAME and the ANSWER. the high and low order sixteen bits of the quotient QH, QL and the low order sixteen bits of the frame respectively. The flow of the divide routine is given below and consists of subtractions, that one computes a long hand decimal division except that D I V works with 32 bit binary comparisions and data shifting in the representations. A = 32 /*bit count*/ ANSWER=0.0 F R A M E = 0.0 FL = QH DIV1: Shift Left Q L into F R A M E SUBtract the DIVISOR and F R A M E IfCDIVISOR > FRAME) Shift Left 0 into A N S W E R DIV2: Else Shift Left 1 into A N S W E R FRAME DIV3: = F R A M E - DIVISOR A = A-1 If(A = 0) jump to DIV1 Exit same way The Fluorescence Microphotometer / 29 Routines G E T R and P U T R an the real number input/output routines. G E T R ascii string from console input and converts PUTR converts a real console. GETR is a negative sign and a dumped PUTR on the is each 16 division a input and the real an ascii routine period. A n y incorrect string and prints accepting input causes routine waits for the 32 bit number. It an error number characters, message to be successively the to a be resubmitted. after converted into ascii and, when printed in reverse, is fraction of the binary numeric it on bits by decimal ten until the dividend is zero. The remainders It decimal multiplication format into it into a real binary number and most are by free number reads divides the decimal equivalent. mantissa, binary console passed significant pop are then successively ten converted until to, the multiplies the mantissa and printed is in, routines which move a 32 least significant zero. ascii real number. The routines L O A D represent The and 16 overflow represents and S A V E are 32 bits, after the the the each decimal bit push and bit number from a memory location to the top of stack and visa versa respectively. The next the TUART called set must J2WORD of routines control various device functions by altering the J2 and J3 initialize the parallel output ports. J2 and and J 3 W O R D which will J3 control The routine status contain the current status of from which word and these declare status of these are variables two output ports. Routine SLEEP 10msec times and is the videocassette passed a 16 number passed. bit number and creates a real time pause S L E E P is used because devices like the recorder (VCR) require a transient of shutter time to carry out their various actions. Routine VCR is passed the J2WORD and will recorder by changing the status of bit 0 of the J2 pause/unpause port. the videocassette The Fluorescence Microphotometer / 30 Routine C L O C K is passed the J 2 W O R D and start/stops changing the status of bit 1 of the J2 Routines LASER and camera and C A M E R A shutter are the 401 real time clock by port. passed the by changing the status J3WORD and open/close the laser of bit 2 and 3 respectively of the J3 port. The major data routine samples acquisition the routine is SSAS, Slow Scan Average Storage. analog Video Analyser slow scan output via channel This 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 read from the word. The conversion is completed in 12/xsec and the digital result is 16 bit data word. The most significant 4 bits of the data the A D A channel number and when the conversion is complete. Thus the data is only representation negative 12 of bits the long analog and is voltage an read, approximate (see negative Figure 4) two's complement because the positive voltages It is indicate converted two's complement only approximate are represented by numbers that are too small by one. That is, where -5 volts can be correctly represented 7FF hexidecimal, + 5 volts should be represented by 801 and not 800 by hexidecimal. This is simply because 801H + 7FFH = 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 the missmatch 0.002 volts. approximation becomes of 1 in the insignificant due to positive voltages on the 12 the scaling involved since bit scale represents only The Fluorescence Microphotometer / 31 ADA VOLTAGE 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 The 321 Video Analyser slow scan output consists Microphotometer / 32 of two interlaced fields which 1 th make up a frame. negative creates sink an Each frame pulse array is -g Q followed by of 255, 16 sec 239 bit, long. Each field consists positive, elements 64/usec, into square which it of a wave averages 1.37msec pulses. SSAS alternate slow scan fields. The number of fields to be averaged is passed to S S A S as a parameter on top of stack. There are several areas that needed careful attention to acheive synchronization and timing. When S S A S is called it first polls the until the next to take the the most then the 12 bit number from the A / D conversion and examine 12 bit number represented a addition of the other voltage less than positive going edge which starts the test on a -0.617 12 volts bit number is read. thus The the polling four was not zero polling polls the sink pulse for lead data edge is found when a voltage above this field. volts. This same in video If the time next and speed, was the top 5 bits. -0.617 loop starts at local label SSAS3.T The loop starting SSAS2 the slow scan output sink pulse is found. The actual test, for convenience significant bit was zero and the precise loop is This loop does 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 (Figure 5) conversion Then, at X +26.75Msec sometime once the X-26.75<xsec , X , between conversion is field. the interval elements Thus are tsee appendix and X is tested. set, At 26.75Msec this time the lead edge. elapses the as the conversion at is set. It is this conversion which becomes the first array element and from which the timing is set the read at 0 and 26.75Msec passed the 26.75 for the recording of the remaining picture elements picture elements, which are to the 53.5jisec sampled between, into 64jxsec wide, are pulse. and not on, their This guarantees transition edges. sampled that The the in between picture main data The Fluorescence Microphotometer / 33 THE SSVS LEAD EDGE SYNCHRONIZATION X+ 26-75yus V V 64 L I S LEAD EDGE ssvs SINK POLSE 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 acquisition loop starts at S S A S l . It samples 255 Microphotometer / 34 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 with redundent acquisition loop has two paths statements excutes so each and each has in exactly 256 been carefully padded clock cycles which is 64Msec. A t the end of each data acquisition, at the loop starting S S A S 5 1 , the array of picture average and speed the 1, 2, elements is leaves divided each by element the in number 12 of fields bit negative read. two's This computes complement form. the For 16 bit number is divided by binary logical shift which allows division by 4, 8 and 16. For this reason SSAS can read only these numbers of data fields. D. STATIC P H O T O M E T E R R E S P O N S E 1. Introduction In this system's is to view, section the static photometer response is determined to ensure that the output is linear and invariant with respect to intensity input. The method illuminate with and analyse monochromatic photometer output light, of uniform intensity as a absolute displacement, within the field of view. function of across the illumination field intensity of and 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 sorts of lens and has an optical transfer function which must include all 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 optical transfer function alone. 6 one The Fluorescence 2. Method:- L i n e a r i t y , Invarience These calibration photometer was a measurements and Camera involve known controllable uniform Gain finding digital output and light intensity the functional relationship input. Required for such source of replacing the dichroic system with a beam Microphotometer / 36 illumination. This between measurement was achieved by splitting mirror, placing a front silvered mirror at the microscope objective plane and using various degrees of neutral density filters, inserted shutter aperture approximate shutters before the camera to control light intensity. The camera is stopped down to produce a circular bright field image with dimension of a open, shutter, produces video picture image a red blood cell. This uniform circle and results of in a square set up, with laser illumination which is wave slow scan the on and centered both in the video signal which is read and stored by the microprocessor for analysis. The calibration BKGND.Z80. software, The written in program uses the Z80 assembler, routine SSAS slow scan fields and averages, the picture elements The subsequent stored under to read a requested the number of the picture elements The routine is used to zero and calibrate the photometer. of in Its 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 and name in the spatial interval requested. output is a spatial and temporal average the region of interest. first is monitoring the intensity every thirty seconds This was done initially using the incandescent band pass filter. It soon became clear that over a camera period of half an hour. microscope light source with a narrow incandescent intensity fluctuations were intolerable for system calibration. The photometer output is a digitized voltage which is a function of light intensity, The Fluorescence camera by Microphotometer / 37 intensifier gain and camera video gain. Functional relationships were built up holding two function of the of the third. variables The invariance photometer output, within the Invariance requires that constant field this and of the measuring system of view, over deviation be zero. a is output given by spatial For response the the to a deviation in and temporal system as be average. linear the photometer output voltage will depend linearly on the input intensity. 3. Results Over the the field of view of the background noise, a photometer, constant output implies spatial invariance. Photometer weeks. and to within is produced from period characteristic experiment, output laser intensity. beam of instabilities However, period and thus the photometer intensity fluctuations over a output combinations of voltage/intensity setting. intensities The voltage INT and output laser voltage but is fairly linear Over commonly intensity of constant input. This manufacturer the time related stablizes to after terms 30 minutes and a course of an fluctuations in the warm up an initial compares them beam with the intensity for source. measured A G C gain is and what the equipment. more period was dependence a is invariant in time. Figure 6 shows the laser fluctuations of the incandescent Photometer new are resolution limited by output levels wander slightly over a period of This is attributed to the video camera settling the shown in a the range in figure decreases in the as function 7 nonlinearly range 5 of to relative 7. The and is independent as intensity of of the decreases producing output voltages third of the rail voltage and the maximum output, rail, voltage. shape the gain at low between one The Fluorescence LASER AND INTENSITY Microphotometer / 3 8 INCANDESCENT 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 OUTPUT VOLTAGE Fluorescence Microphotometer / 3 9 VERSES INTENSITY 5 7 VOLTAGE 4• X x X X X X 2 3 4 6 RELATIVE 8 9 10 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 The intensifier gain (INT) sets the the photometer output voltage dependence of output voltage The gain video in an intensifier tube exponential on intensifier amplifies (AGC) video camera the voltage. like fashion. Figure gain signal Microphotometer / 40 settings from at the various intensifier 8 affects shows the settings. AGC tube produces an empty amplification. It produces a monotonic but erratic output voltage as shown in figure 9. The AGC It and increase gain is unity for settings thus in the less than 1. 4. Discussion and Conclusion Raw photometer problem the output process is number data not strictly Figure 7, linear. To circumvent was best fitted using a sum of a spline function. This function is used to convert one in data display and analysis. The scaled data the scaling point and the becomes this the advantageous it rescaling fits the origin. Due to the since raw line nature decreases the of lower a greater proportional amount. This increases the signal to noise ratio. The rescaling photometer AGC dependence, maximum intensity/voltage nonlinearity voltages but output into a scaled output which is linear with intensity. The through the the invariant voltage/intensity polynomials known as photometer is is thought of as part output is linearised with gain control are used of the data intensity. The to relate measured collection voltage intensities process and thus dependence on INT and at different gain control settings. The system linearitj' output. response. was provides Further found a to be calibration system invariant curve calibration The dynamic spatial response and, between involves after minor corrections, constant the uniform input determination of linear. and the of the system is modelled in chapter The related dynamic 4 and The INTENSIFIER GAIN Fluorescence ( INT) Microphotometer / 41 RESPONSE 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 / AGC SETTING FIGURE 9 The video gain results in an empty magnification of the monotonic but erratic increase in the output voltage video signal. It prodi 42 The Fluorescence Microphotometer / 43 discussed in chapter 5. 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. INTRODUCTION This chapter describes of surface analysis bound of the resolution of the a simple technique for the conversion of fluorescence molecules experimental to their data optical system number requires density the to determine [Knowles&Evans,1986]. theoretical the intensity modelling of the correction due to optical The spatial transfer limitations. The theoretical and experimental results effecting the theoretical were explained in terms optical collection depth. The calculation giving the relevent intensity prameters collected from of the were a parameters established cylinder of by a isotropic radiators as a function of cylinder height in the direction of the optical axis. Finally the feasibility of modelling the transfer system's function was determined. The focus aberration with a single composite success of this would simplify the theoretical analysis of the experimental data. The experimental/theoretical linear dependence the between optical system correction factor technique fluorescence confirmed the was that focus aberrations gave dependent surprisingly simple indicating a intensity and number density. The experimental on the results results optical transfer model of and showed how the optical cutoff. Finally it is shown 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 N u m b e r 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 problem of finding a suitable fluorescence standard an origional and the technique was needed. B. THE MOLECULAR SURFACE 1. E x p e r i m e n t a l Procedure DENSITY CALIBRATION The aim of these experiments was to encapsulate EXPERIMENT 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. pipette, at a given diameter, Experimental intensity cross-sections through the 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 procedure repeated intensity profile across the pipette for several different internal diameters. was The taken and 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 surface density concentration. would be the local However due to the pipette diameter multiplied by finite collection depth of the projected the objective, solution 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 fluorescein represent was conducted isothiocyanate, using FITC/WGA. physiological surface wheat The densities of germ agglutinin concentrations used glycophorin in the conjugated were red with calculated cell to membrane 5 which range volume at from 3-5 10 molecules :l: maximum diameter over per unit red surface cell [Lovrien&Anderson,1980]. area within the pipette The 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 WGA 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 To analyse and verify ANALYSIS METHOD 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 adequately. There is good reason the real system quite 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 T r a n s f e r Function 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 viewed particularly simple solution is the optical transfer function of a system with incoherent aperture of side L. The equation monochromatic light, of wavelength X, transfer function, in the one dimensional through a square case, is given by 2.12. 2. Multiplane Analysis including Focus Aberration The multiplane analysis involves the subdivision of the object into isofocal sections of uniform thickness which sections are analysed plane. The is small enough to neglect the edge shape. Individual taking into account their varying displacement from the focal image is produced by summing the individually analysed isofocal sections of the object. The 2. A analysis process for a single isofocal section is that presented in chapter 5 real space object function, in this case the shape of the isofocal section, is Fourier transformed into frequency components which can the and optical transfer function (OTF) with the then be operated on appropriate focus aberration. by 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 thickness circle is divided into an odd number of rectangular isofocal sections. Their is a cross-sectional fraction of a dimension at wavelength and the given their length displacement from is proportional to the the circle center. diameter is hence the number of sections times their thickness, equation 4.1, odd number was and The an 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 Equation I. = 2 . v / ( R - ( k - j ) ) 2 ( 2 \x\<l/2 1 s l a b , (x) = e ( 0 object or theoretically isofocal sections,equation Equation 4.2 Equation 4.3 Otherwise K The 4.1 ideal profile is given by the summation of all the n 4.4. 2R Object(x) = — . Z slab,(x) n k=1 n Equation 4.4 K th The out-of-focus displacement of the k section is given by the number of sections away thickness. from the focal given in wavelengths plane so the times their The out-of-focus displacement is maximum pathlength of focus error W, of the optical transfer function, is given by equation 4.5. W = (k-j).t.X Equation 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 |h(x)| with the modulus squared of their respective point spread functions (equation 4.6). That is, each isofocal section is transformed 2 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) = Image(x) = 2 s l a b . (x) . ! h ( x ) j k=1 n r°°df . e k= 1 —CD L n E q u a t i o n 4.6 2 k 2 i r i fx . [ /°°dx. s l a b , ( x ) . e — oo 2 l t i fx ] .H(|—) 1^ K E q u a t i o n 4.7 3. Discrete Numerical Analysis Equations incoherent, 4.4 and 4.7 represent a mathematical model of the image response of an 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 Tukey [Cooley & Tukey is an algorithm re-introduced in 1964 by Cooley and 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 F F T 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 N where N is the number of data points. 2 The one dimensional analysis was performed in arrays of various sizes from 128 to 4096 data points theoretical which sets experiments the are spatial frequency carried out resolution. by The the fundamental 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, the resulting image. FOC analyses is a each real separately array of N POLYST and contains the theoretical image. S L N O thickness of the isofocal sections and the pipette and sums points which and S L T H diameter them up to create is returned by are the number and is determined by their product. C U T O F F is the O T F frequency cutoff in units of A f and R A D and H are the radius and central height of the object function which is centered of the array. Thus P O L Y S T takes an object function, equation 4.4, image function, equation 4.7, taking into account in the middle and creates an the optical transfer function, with focus aberration, of the imaging system (figure 11). 4. The Theoretical Experiment The next stage was to determine dictated by the model. The of a transverse diameter 4.7, Linear diameter central Intensity at of intensity on pipette the dimensional array. Map, which frequency intensity on cutoff, and returns the image It was successively a simple matter calls POLYST of writting with paremeter, the optical frequency cutoff. diameter. The program is analysis the pipette function, equation a program, increasing cutoff and graphically illustrating the pipette diameter theoretical pipette projection. It has two relevant input parameters, constant pipette dependence computer routine P O L Y S T does and the optical frequency in a one the pipette dependence called with of one 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. The RESULTS fundamental experimental result is the pipette of given diameter which containes fluorescence intensity profile through a fluorescenated W G A . Typical experimental data is shown in figure 10. In this data lies information about the resolution of the system the and the profile relationship between predicted sensitivity of the photometer output, in the physiological range of surface high. It in good agreement is interesting to note with that that The theoretically was was intensity and pipette diameter. the light scattered within the shape and of the densities, 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 In corollary the Fourier 10). fundamental theoretical experiment was the optical analysis of the pipette cross-section. isofocal sectioning and 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 determines object the data results optical transfer function gives the in a best fit cutoff for the optical correction theoretical system. factor, The pipette image function which corresponding theoretical 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 PIPETTE C R O S S E C T I O N A DIMENSION F I G U R E 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 THEORETICAL OF IMAGE A AND PIPETTE OBJECT PROJECTION CROSSECTION RELATIVE INTENSITY CROSSECTIONAL DIMENSION F I G U R E 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 explain domain the resolution. It also prompted another theoretical experiment to effects contributing to intensity/diameter linearity. This validification and explaination will diameter are transfer cutoff be delt linearly of with in the dependent. the system. disscussion. The The linearity linearity The intensity constant constant, and the pipette on the optical with optical depends L, decreases frequence cutoff as seen in figure 13. The conversion of fluorescence by three linear intensity to molecular density is hence simply obtained relationships. Firstly, relative fluorescence pipette diameter by the experimental linearity constant : ^e x ^ p = ~e ^ x pM v intensity by accounts aberration, equation factor correction optical transfer volume and factor that for the intensity loss is 4.8 scaled due to focus 4.9. Surface The which pipette to 4.8. E q^u a t i o n D v intensity collected from the optical correction related , given by equation Secondly, the experimental fluorescence an is is cutoff. from one It a = ^xp'Z over the represents surface Equation linearity constant the where difference the in projected and is intensity surface a 4.9 function of collected density from from the a 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 I N T E R N A L P I P E T T E DIAMETER INTERNAL P I P E T T E DIAMETER (JU m ) F I G U R E 12 Theoretically and experimentally obtained data showing a linear dependence between the fluorescence intensity collected from F I T C / W G A 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 LINEARITY CONSTANT Intensity VERSES to Number Density:- / TRANFER 57 CUTOFF LINEARITY I 0-5 0 CONSTANT J- _ - - - * " * —<— 5 10 15 TRANSFER 20 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 F I T C A V G A and that collected from the F I T C A V G A 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:- / volume and the molecular density at the surface are equal. Thirdly, W G A concentration the pipette diameter number density, equation multiplied by the theoretical and thus relative from analysis figure fluorescence cutoff frequency, gave 13, the the intense the surface optical correction that equals the experimental intensity projected collected exp E q u a t i o n 4.10 best fit transfer means M Thus the 4.10. n = D.[WGA] The is 58 = the function cutoff factor, linearity 1/L=1.39. constant, linearity constant, equation 4.0±0.1um The at the scaling 1 of predicted 4.11. E q u a t i o n 4.11 L from fluorescent density, n, multiplied by M as molecules adsorbed / ( L . [ W G A ] ) , equation to a surface is the 4.12. GXp Surface surtace M — = L .[ W G * A ] n E q u a t i o n 4.12 Conversion of Fluorescence Intensity to Number Density:- / 59 E. DISCUSSION The experimental intensity profiles of the pipette at different diameters were of high signal to noise ratio. The adsorption of WGA of albumin to glass is inhibited by the presence in solution because this blood plasma protein coats blood surfaces such incompatable 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 transfer dictates. cutoff approaches It rises increases the quickly from zero theoretical limit towards but, at the a theoretical certain asymtotically. The limit frequency, of 1 flattens dynamic range of as the off and the transfer cutoff is between 0 and 10 ^ m This is a function of the illumination wavelength and model stating that is a practical result of the system with any diffraction limited optical focus aberration using visible radiation for illumination, will completely attenuate spatial frequencies linearity constant collected by the with of the order of unit inverse microns. The decrease in transfer optical system cutoff represents due to focus intensity is arbitrarily scaled in a ratio linearity constant of L = l 1. A 1:1 the increasing loss of information aberration. The relative fluorescence with the pipette diameter and thus a represents one of two situations. unit linearity constant, represents a system of when viewing infinite a transfer three cutoff dimensional object, and hence infinite resolution and depth of field. However 2. 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 any transfer diffraction limited cutoff, which was produced from the model, one sees that 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. WO-J) p eff = f 1 2 ;w>x/2 ;W<X/2 E q u a t i o n 4.13 p . is a function of W, the out-of-focus displacement. Note that for W<X/2 the F( 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 equation 4.14. p Note that (p ^ Q ^ ^^ c ' s greater eff c Af than the elemental frequency spacing, f E q u a t i o n 4.14 >> 1 the number of array elements, in frequency space, between the DC component and the effective cutoff. In practical represented terms, by 60 isofocal section has consider array the the analysis elements of a 20jum diameter of an N element array. shortest effective cutoff and thus pipette which is The most out-of-focus determines the required frequency domain resolution. This isofocal section is lOum or 20X out of focus thus; W = 20X = 0.00629 Ax - i - o A m -1 Let the frequency cutoff, f , equal 4um which is that of the actual system. Then Conversion of Fluorescence the condition to such a be situation satisfied, N = 128 would function since analysis was done in arrays represents given by equation result in a it falls to zero in less than the Intensity to Number Density:- / 63 4.14, poor is that 0.00839.N> > 1. representation two elemental of the frequency In transfer spacings. The of N = 4096 which, even in this worst case situation, dynamic behaviour of the transfer function with sufficient frequency resolution. The resolution of the and some Fourier characteristic transformation length within which of the the object function depends fluctuations of the on Af 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 array reguardless of the pipette's elements elemental distances, increased the frequency analysis. Ax and elemental The Af, for frequency concern section different that the sized pipettes. increasing size. This independent intensity on keeps of pipette pipette conclusion is that N = 4096. Ax As the variation anomolous effect on the results. To maintain a constant the size of the transverse represented by 60 actual size. This resulted in a decreased, was was in pipette might the different diameter resolution Af of of the have an elemental frequency spacing section, within the array, is varied according to its actual constant and since the array size. both cases the dependence diameter In was linear with the size same scaling of this sort does not effect the was of fixed, relative linearity results Af was theoretical constant. when working The at Conversion of Fluorescence Intensity to Number Density:- / 64 2. A C a l c u l a t i o n of the O p t i c a l C o l l e c t i o n D e p t h The explanation of the intensity/diameter linearity lies in the geometry of problem and is related to the optical collection depth which must vary with diameter. A theoretical problem was set up and executed collection depth of the microscope objective. The the pipette which would determine problem involved the the isofocal sectioning and analysis of the one dimensional crossectional projection of the intensity of a cylinder of light. The cylinder has a variable collected axial from length a narrow dimensional rectangular The rectangle (figure 14). cylinder a radius tangential to the optical axis and This would perpendicular projection is the determine to the the amount focal plane. of light The one ideal intensity map of a cylinderical object. is divided into isofocal sections of constant width which are analysed individually to take into account their out-of-focus displacement. This analysis can thought of as similiar to the pipette crossection be analysis except, in this case only a narrow strip through the center of the crossection is sampled. The results reaches focus. a The reached of the analysis maximum distance is the as are the object size from the collection depth. The particularly in the case in figure increases focal plane depth increases with an increase and presented of at 15. show perpendicularly which the important They point to that to the intensity plane maximum intensity note is that the is of first collection in object size parallel to the plane of focus. Thus, the pipette crossection, the central contributions from the off axis defocused portions of the isofocal intensity has sections. There are two effects: 1. The intensity maximum maximum as collected the intensity from section is an width reached, isofocal increases. section The increases increases width, with at the to which some the out-of-focus Conversion of Fluorescence THE PROJECTION OF A INTO SHOWING THE 2 Intensity to Number Density:- / CYLINDERICAL 65 OBJECT DIMENSIONS INTENSITY CROSSECTION 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 VERSES Intensity CYLINDERICAL to Number Density:- / OBJECT 66 HEIGHT F I G U R E 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 the only contributing effect is the reaches rectangular a maximum crossectional out-of-focus analysis as the displacement above isofocal sections of constant width second one mentioned which is why the height two effects increases are increases. are with pipette seen However in and compete diameter, so does intensity the because the thus pipette although width of the isofocal sections. The result is intensity/diameter linearity. F. A SINGLE COMPOSITE TRANSFER FUNCTION 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 about the origin. of the object. including focus function is a real function of spatial frequency which is symetric It models an imaging system by attenuating In the error, the displacement. Thus object be divided optical transfer must different to case of optical a diffraction transfer model the image into isofocal function. The limited function is incoherent dependent resolution of a sections each result of this the spatial frequencies imaging on the system, out-of-focus three dimensional object, of which multi is section multiplied analysis by is the a the Conversion of Fluorescence transformation aberration, of the object function, taking into account into an image function. The question is, obtained from a single transfer analysis Intensity to Number Density:- / 68 the effect of focus ' can such a transformation be function'? If so, much time would be saved in data 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 transform of straight the forward. A n optical transfer image function function as given by equation divided by the function, H(f), is Fourier transform of the Fourier the object Equation 4.15 4.15. f °°dx. Image ( x ) . e ~ 2 7 r i f x H(f) = /°°dx.Object ( x ) . e ~ 2 , r l f x — oo In the equations case of the 4.4 and pipette 4.7, in crossection the object and image functions terms the isofocal and of existance of a composite transfer function, H com p» sectioning are analysis. defined, If the is assumed then the image is the inverse Fourier transform of the composite transfer function multiplied by the Fourier transform of the object, equation Image(x) = f°°df . e — oo 2 7 r l fx 4.16. . [H COuip . r°°dx .Ob j e c t ( x ) . e 2 i r i f x —oo Equation Equating the two forms of the image function (equations 4.7 ] 4.16 and 4.16), and noting Conversion of Fluorescence that 2R/n is a constant and can and the sumation equation 4.7, over then the k can Intensity to Number Density:- / be brought outside both integrals brought composite inside the transfer is of the form defined by equation integral, over function is given by 2 i r i f x frequency equation by space, in 4.17 which Equation 4.17 P solution to its 4.16 ] m The in equation 4.15. 2 [ H ( f ) . / " d x . s l a b , (x) . e " H „ = JizJ If? _ ° n » -2irifx I f dx.slab.(x).e k=i -a, k C 69 equation conformation 4.17 with the function given in equations 2.8, is derived numerically three 2.9 properties and and of an its validity is incoherent determined optical transfer more complete the projected 2.10. 4. Results A stepwise approach understanding of crossectional equations taking the the pipette 4.4 to and Fourier the final result to equation solution functions 4.7. of the The frequency transform and was taken 4.17. object and to ensure Figure 11 a shows corresponding image defined spectra of these two functions is obtained by figures 16 and 17 are plots of the verses frequency of the sinusoidal functions. The composite optical transfer obtained by the division frequency spectrum The result transfer is seen of the of the in by frequency spectrum of the amplitude function is object function into the image. figure 18. It has some function with some anomolous behaviour. features characteristic of an optical 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 relative to the object. This causes division by zero frequency 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 and equals the composite transfer function in the interval between zero the effective cutoff frequency and was zero at frequencies above the effective cutoff. Conversion of Fluorescence Intensity to Number Density:- / 71 6. C o n c l u s i o n 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 a bandpass but is shifted several different transfer in the frequency domain. The analysis which by involves 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. IMAGE I' Ij FREQUENCY SPECTRA SPATIAL FREQUENCY ) 2 3 4 i i • F I G U R E 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. Jpll k I (Jd m Conversion of Fluorescence Intensity to Number Density:- / 74 MULTI ISOFOCAL ANALYSES COMPOSITE T R A N S F E R FUNCTION AMPLITUDE F I G U R E 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:- / INCOHERENT AT 2 u m TRANSFER 75 FUNCTION OUT-OF-FOCUS 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 T O C E L L S U R F A C E S A. INTRODUCTION This in section is concerned the living living biological system. systems physiology. binding is membrane One such of from area cross Grant&Peters,1984; erythrocyte with fluorescently oligosaccharides transmembrane is This bridging of with molecule of essential which govern was interactions interactions much mediated [Bell, 1978; of the by the carried wheat out gem isothiocyanate Such in cells specific Parsegian&Gingell,1980; on the was an agglutinating protein The N-acetylglucosamine. and their group adhesion study fluorescein glycoprotein, cell molecules [Evans&Leung,1984]. labelled broad interactions of interest Evans, 1985]. germ fluorescently surface bridging and the cross wheat One very labelled molecules agglutinin and sugars binds are extracted (WGA) was specifically present glycophorin. The aim is to determine human on to the the kinetic and equilibrium behaviour of red cell/WGA adsorption. 1. The Molecular Interaction Lectins, cells, first comes named from heamagglutins because tha Latin of their legere which means to ability to agglutinate pick or choose red blood [Sharon, 1977]. Extracted mainly from plants, lectins are proteins that bind with various degrees of specificity to sugar Wheat germ, binds molecules. very [Lovrien&Anderson, 1980] cell membrane similar specifically which is a glycoprotein, in nature to germ agglutinin (WGA), to residue the sugar in the tertiary glycophorin. The mechanism enzyme-substrate binding 76 where extracted from wheat N-acetylglucosamine structure of lectin the tertiary of the sugar outer binding structure is of the Specific Molecular Adsorption to Cell Surfaces / enzymatic protein molecules. The is capable affinity of lectin and for approximately 3 -1 10 M receptors membranes in of weakly sugar lectins ranges binding to other, binding for appropriate which from bind 10 to to often smaller, substrate monosaccharides glycolipid 10 M " 77 and is glycoprotein [Grant&Peters,1984]. 6 Irreversibile binding occurs for affinity constants greater than 4*10 1 M [Grant&Peters,1984]. 2. The Scatchard Plot Ligand is process, lectin a term used describe biological molecule example enzyme sugar binding. A l l biological phenomena Consider substrate, hormone and depend on involved in receptor or a binding in this ligand interactions case of one another. a macromolecule, [Cantor&Schimmel,1980]. have the with i of its one and any for kind or this to M , which Assume same microscopic that association sites bound to lectins macrostate weight, J2 the n sites sites constant for have the binding of distinct of a ligand no mutual interaction k. Let M . represent L . There are M . . The number sites is the statistical has many ways microstates of binding a L and all macromolecule which represent i ligands onto n ., and is given by equation 5.1. n,i n S2„ • = -, r-H—rr n,i (n-i) ! . l! 1 The important equilibrium condition is the Equation M number of moles of ligand, v, 5.1 bound per Specific Molecular Adsorption to Cell Surfaces / 78 mole of macromolecule and is given by equation 5.2 .2 i . [ M . ] v= - = ° i = Macroscopic association macromolecule 0 constants, interaction _ (equation Equation 5.2 1 K., are involved 5.3) and vary in each process depending on i, the of ligand 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 <=> [M.] 1 [M. , ] [ L ] K.= I - I E q u a t i o n 5.3 n = Q . P_ii • , k Equation 5.4 n,i-1 These equations can be solved for v in terms of the microscopic assocaition constant k and the ligand concentration v Rearranging this [ L ] . (Equation 5.5) = n[L]«k 1+[L]•k equation gives a linear plot, named after E q u a t i o n 5.5 Scatchard, verses v with a slope of -k and an intercept n»k. (Equation 5.6) of v/ [ L] Specific Molecular Adsorption to Cell Surfaces / 79 " =n«k [L] The Scatchard binding of plot ligands gives to the a two - v k parameters, macromolecule. often because other or than Boldt, that lectin binding is a there is more k and Non linear binding assumptions do not hold, because Equation one the class n, plots that characterize indicate that binding sites interact of site. linear function of receptor It is reported, concentration. the 5.6 simple simple with each Surolia & This is not the case when looking at lectin mediated agglutination of cells which is produced by cell surface cross bridging. them once they are surface density holding two receptor is cells The ligands will bind to individual cells brought into contact. Cell agglutination occurs sufficient together. to This produce is almost the a amount of and when the crossbridging threshold effect crossbridge since receptor capable below a of certain density cell aggultiation will not occur. B. EXPERIMENTAL PREPARATION 1. Chemical List FITC/WGA:Fluorescein fluorescenated volumes conjugate molar at plant lectin concentrations was ratio Isothiocyanate stored was at supplied fluorescent label present. and is around -20°C conjugated supplied, in a 1000 Mg/ml, by Wheat anatysis report. Agglutinin physiological saline Miles and information regarding in their Germ Scientific. protein buffer The is in 2ml FITCAVGA concentration The claim that there a and is no free Specific Molecular Adsorption to Cell Surfaces / Phosphate Saline: P B S Buffered distilled water was made in a 2 litre volume of 80 deionized, with: 1.3064g of potassium phosphate 7.154g of sodium phosphate ( K H PO .), (Na HPO" ) 2 4 and 14.192g of sodium chloride (NaCl). The phosphates are supplied by M C B Manufacturing Chemicals I N C . and the chloride by Fisher Scientific Company. The resulting osmolarity [Waymouth,1970] an p H of 290mOsm PBS and 7.4pH has a sodium physiological respectively. Human Serum Albumin: H S A is a blood plasma protein which when added to suspending buffer cell at a concentration morphology. It is chloride with 0.1% of 0.5 supplied in a 30 sodium ozide as a the gram percent helps maintain normal red gram per cent solution of 0.85% sodium preservative. 2. Pipette Preparation Red blood cells are diameters ranging diameter, glass mechanically from tubing. solenoid driven pipette at the microforge be required 0.5 The to manipulated with micropipettes of internal 3 M m . The from tubing puller. The diameter with is heated are and a microforge, made drawn glass needles are into electrically heated. The hot glass bead needle tip to fracture. The pipettes are is 1mm, needle designed in the manipulated into internal points viewed microscopically by and laboratory. consists of a small glass bead mounted on fine tungsten anneals to, the glass surface of the pipette. the pipettes entrance a cut The wire which can contact with, and Once cool, a slight manipulation causes then filled with PBS by boiling them Specific Molecular Adsorption to Cell Surfaces / 81 under vacuum in solution. 3. C e l l Preparation 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 course of an experiment, solutions were made up in the order of 10 throught the 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 Preparation the day PROCEDURE 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. chamber A double 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 w ith T 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 transverse 150 Mm. diamond tip section pencil. of the It pipette is helpful and it is if the fracture useful with is clean entrance across diameters the around These requirements are quickly checked by viewing the pipette in air with the microscope. A t this point the double chamber the transfer into the chamber stage is inserted at the objective and cell aspiration pipettes neumatic are micromanipulators. The focal plane and mounted into the chuck which transfer and red cell pipette mounts enter the 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 During this time the pressure the controlling manometer PBS/HSA in the pipettes glass at the bottom of the is zeroed by adjusting the height of stands and watching for zero flow at the pipette is, in a controlled manner, chamber. drawn up the sewer pipette entrance. 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. An 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 cell firmly held spherical red cell to which and pipette midplane of the are manuvered into the chamber W G A will transfer subsequently pipette to avoid bumping the chamber which is adsorb. The red in the walls. Now, the vertical 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 pipette, incubated in the pipette and brought back transfer pipette manuvered between to which the red cell is quickly removed from the transfer W G A for a predetermined time, returned to the transfer to the red cell side. The cell is again taken out of is bottom then of cell and objective. removed the chamber A t this stage from the which field represents visualization is equipment for a measurement of the fluorescence of view. the The shortest transferred to the cell is distance the video intensity profile across the cell. 1. Data Collection The cell is first visualized with a white light source which is filtered to reduce intensity and create a narrow band above the irradiant fluorescent greatly 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 important not to bump, even the floor. The white light is completely The data collection program, previously loaded into memory, is it is attenuated. now given a data filename and the number of video fields to be skipped and then read. On receiving the start execution command the opened. Three seconds elapse cassette recorder which allows the is unpaused and camera shutter recorder sufficient start up time but critically allows shutter opening vibrations, which are picked up by the cell pipette, to dissipate. The shutter video signal's laser vertical video fields. Shutters file on monitor. magnetic The is then opened, the synchronization pulse and software skips then synchronizes with reads the the appropriate are now closed, the V C R is paused, the data is written into a disk and is software then plotted onto returns it's the control 4010 graphics menu and page is of the ready for D.E.C. another Specific Molecular Adsorption to Cell Surfaces / 84 measurement. D. D A T A The ANALYSIS 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 dimensional of the cell. object is being Effectively, projected onto a two dimensional the vidicon surface of the camera. Figure red cell onto manipulated the information two dimensions. Any plane on the three which is infact 20 shows the projection of the aspirated vertical slice of the grid can be digitized, 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 surface of a spherical membrane verses the other. This interaction and data has information the imaging displacement stored response bound to the from one side of the cell to in it both about the membrane/WGA of the photometer. The interaction parameter of direct interest is the surface density of W G A membrane/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 increasing amount of surface area of P whereas, due to the cell curvature, an 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 i f this central part of the transverse Specific Molecular Adsorption to Cell Surfaces / 8 5 THE PROJECTION RED SHOWING CELL THE OF AN INTO 2 ASPIRATED DIMENSIONS INTENSITY CROSSECTION 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 response could be taken out. It was the broadening effect of the photometer 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 density. The approach was adsorbed surface 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 theoretical output the imaging represents effect of the photometer the photometer output. The and the transformed 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 section through covered the middle of the sphere. Consider a sphere, of radius r uniformly with fluorescent molecules area. Figure 21 along a transverse at an adsorbed surface density of n shows a cross-section of the sphere. Molecules per unit 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, unit displacement f(x), is given by equation Let dx be the 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 f(x) p Now in the ( x ) 5.7. 5.8. = j/(r -x ) 2 Equation 2 2.n^,dl = Equation 5.9) is given by the Pythagorean relation. The final form of dl results from the simple differential relation given in equation dl 5.10. •[(dfU)) +d x] = 2 2 = / [ ( f ( x ) ) - H ].dx Equation 2 df(x)=f(x).dx linear 5.8 limit of dx approaching zero, which it does by definition in differential calculus, dl (equation Then 5.7 substitution density. equation 5.12, equation 5.7. of This by equation is p(x) Equation 5.9 into coverted substitution = , the the geometry of , r 0 2 equation into " v/(r -x ) 2 5.9 2 5.8 projected of ; -r<x<r gives linear this a general density specific form of problem a 5.10 of the sphere, given Equation by 5.12 Specific Molecular Adsorption to Cell Surfaces / 88 F I G U R E 21 In the calculation of the spherical surface projection element dl is projected onto the element dx and results by equation 5.12. the cross-sectional surface in a surface density given 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). The assumption now r N = J" d x . p ( x ) = 2irrn -r Equation made is that p(x) scales linearly with fluorescent emission 5.13 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 The A p p l i c a t i o n of Simple Discrete F o u r i e r Optics 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 imaging system. For a system space to mimic the effect of the 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 spherical cell. The analysis is done numerically and from hence the surface of a discretely microprocessor of the photometer. The first job is to construct a one by the 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 was the average function value over the interval Ax A v (x x 2) - - (x+—2) • x intensity This was done profile in the range Ax, effectively because at x, is simply the area under the 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) = c •r -] 2 2 = c.r.sin (-) V(r -x ) /.dx // x S r ; -r<x<r Equation The 5.14 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 intensity profile which can be modified in such a way imaging system. Optical diffraction limited system theory states that the of the as to model the effect of the optical transfer function for a viewing through a circular aperture, of diameter 1, with Specific Molecular Adsorption to Cell Surfaces / 91 incoherent monochromatic illumination of wavelength 2.11. This frequency is a real function of frequency which X is given by H(p), equation attenuates components of the object function. There is zero the amplitude of 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 ) = 0. The optical transfer o function, H(f), is simply multiplied by the frequency spectrum of the object function, I (f), 0 and the inverse transform of this gives the image function I.(x) (equation 5.15). I . ( x ) = /°°df . H ( f ) . I ( f ) . e l 2 7 r f x 0 1 Equation 5.15 —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 which directly relates to the adsorbed W G A concentration. determined and some indication of the photometer these parameters E. T H E EFFECT To see with represents OF T H E molecular chemical stress FLUORESCENT which is a Never-the-less and this the cell radius is the final stage in a single cell experiment. isothiocyanate weight. Also frequency cutoff is given. Attaining LABEL the distribution of W G A on the surface fluorescein intensity of the cell the with WHEAT GERM of the cell, the W G A is fluorescent conjugation the ON THE presence probe process of of considerably puts the conjugated the probe smaller WGA could through change conformation and binding specificity. It is hoped that the conjugation process its 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 solutions at unlabelled protein, the situation the plot protein favours the concentration to either the intensity intensity preferential binding effects. at the of red cells varying sugar incubated labelled verses is a or in different ratios of labelled and residues on the cell [Sharon, 1977;Lovrien&Anderson, 1980]. favoured protein will fluorescence of analysis specifically glycophorin preferentially Since involves the W G A binds protein, competitive other. same protein. membrane process the procedure unlabelled If WGA red the binding then in bind to the partial exclusion of measure the protein ratio of will amount quickly of a the labelled establish any Specific Molecular Adsorption to Cell Surfaces / 93 F. KINETIC AND EQUILIBRIUM BEHAVIOUR OF RED CELL/WGA ADSORPTION The aim of these experiments is to characterise the kinetic behaviour of the adsorption of W G A onto the red cell surface. glycocalyx is the environment. The region above the lipid bilayer which glycocalyx is made up of hydrophillic is and equilibrium The cell membarne exposed to the portions of the cell's membrane proteins. The glycocalyx is thought to extend ~ 1 0 0 A 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 necessary to concentration. determine the the adsorption of W G A on the red cell membrane it is equilibrium Experimentally this is amount bound achieved by, at as each a function of bulk 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 WGA bulk concentrations between 0.01/xg/ml and 5fig/ml [Evans&Leung,1884]. G. The RESULTS first result (figure 12) shows that the fluorescent label has no effect on the binding constant associated with the reaction between W G A 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 / 9 4 COMPETITIVE FITC/WGA O 0-25 ADSORPTION AND 0-5 OF WGA 0-75 ^ (VlTC/ W G A ] QFITC/WGA + 10 W G A ^ F I G U R E 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 W G A and the cell surface. Specific Molecular Adsorption to Cell Surfaces / 95 WGA 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 . At 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 indicates the that plot of the the simple assumptions glycophorin are indicates isotherm is shown in not completely a binding constant figure It is not linear which of identical, non interacting binding sites on sound. However the of 2.95* 1 0 liters/mole 8 molecules bound per glycophorin as 25. linear and gives the part of the number curve of W G A 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. the label and the This says labelling that, process to within the have no resolution of the effect on WGA/red photometer, cell surface adsorption. The kinetic data gives the chemical equilibrium. It cells were incubated time taken to reach, was important, singular!)' to at ensure the that and the adsorbed concentration low W G A bulk concentrations, the bulk concentration at, that remained Specific Molecular Adsorption to Cell Surfaces / ADSORPTION THE SURFACE OF KINETICS HUMAN WGA 4+ 3 50 1 / V ONTO ERYTHROCYTE O DENSITY XlO 96 X A n yUm~ 2 | oi o-oi + _ -O — — -Q 2 i> - - ' % A f D-O50 FIGURE 23 T I M E ( min ) 100 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 W G A . Specific Molecular Adsorption to Cell Surfaces / WGA / RED CELL ADSORPTION 97 ISOTHERM SURFACE CONCENTRATION IO 3 + 50yam - 2 -H 2- 1o WGA The adsorption isotherm characterizes the red cell surface. It shows the concentration of W G A . CONCENTRATION (JULQ/\T\\ ) F I G U R E 24 the equilibrium interaction between W G A and adsorbed concentration as a function of bulk Specific Molecular Adsorption to Cell Surfaces / WGA / RED CELL SCATCHARD 98 PLOT F I G U R E 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. Specific Molecular Adsorption to Cell Surfaces / 99 constant. 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 surface density of binding constant of macromolecule as at saturation 3 5.0±0.2xl0 The the from such an isotherm, and the Glycophorin has one protein to plot, 2.95x10 liters/mole only binds cell at 3 6000AMU gives equilibrium number a of the ligands per many sites for W G A binding but the W G A molecule binds to of red 2 Mm . Scatchard g n = 0.93. WGA and any probably one data indicates glycophorin molecule. W G A is inhibits the binding of second that a large 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 number of These results cell surface area glycophorin molecules compare [Adair&Kornfeld,1974; is on the favourably Snoek,1985; 130±10Mm f human with red those [Evans&Fung,1972], blood cell cited Lovrien&Anderson,1980]. is in By the (6.5±0.3)xl0 . the a then literature radio label 5 technique, Snoek cell that and concluded that there was there was specific binding 5x10 of glycophorin molecules on the one mole glycophorin. t F r o m routine red cell measurements made in the laboratory of W GA 7 per mole red of APPENDIX Slow Scan Interlaced Video Signal Synchronization and Acquisition Software EXT EXT EXT EXT DUMP PUTCHAR SCALE PUTR HICW: LOCW: EQU EQU 0C1H OCOH ; M S B OF A / D C T R L W O R D ;LSB OF A/D C T R L WORD CHI: GOl: EQU EQU 21H 0A1H NUM: WIN: EQU DB 255D 0 ;ADA DIFF MODE C H A N . l ;ADA DIFF MODE CHAN.l A N D CONVERSION START ENTRY SSAS > SLOW SCAN A V E R A G E STORAGE. 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 be 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. HIGH R E G , N U M TO BE READ LD EG: L O W R E G , N U M TO S K I P P LD PUSH R E G P A I R (RP) LD R P , A D D R E S S O F 600 B Y T E S PUSH RP CALL SSAS END OF E X A M P L E SSAS: PUSH PUSH PUSH PUSH PUSH AF BC DE HL IX LD PUSH ADD IX,0000H IX IX, SP LD OUT LD OUT A,00H HICW,A A,CH1 LOCW,A LD H,(IX+0FH) ;SAVE ENVIRONMENT ;LINE COUNT CALLERS PARAMETER :SET A D A C H A N N E L 100 1 / SSAS4: SSAS6: SSAS36: SSAS35: SSAS30: LD L,(IX + 0EH) LD LD (IX + 0 0 H ) , N U M A,00H LD INC LD INC DEC JP (HL),A HL (HL),A HL (IX + 00H) NZ,SSAS4 LD A,(IX+11H) CP JP CP JP CP JP CP JP CP JP LD LD LD 16D Z,SSAS6 08D Z,SSAS6 04D Z,SSAS6 02D Z,SSAS6 01D Z,SSAS6 A,16D (IX+11H),A (WIN),A XOR ADD JP LD DEC XOR OR OR JP A A , ( I X + 10H) Z,SSAS30 HL,2380D HL A H L NZ,SSAS35 DEC JP (IX+10H) NZ,SSAS36 LD LD LD OUT RR RR RR RR RR RR H,(IX + OFH) L,(IX + 0EH) A,G01 LOCW,A A A A A A A LD (IX + 0 0 H ) , N U M ;HL = ADDRESS BYTES ;COUNT=NUM INITIALIZE VOLTS 101 OF 600 WITH ZERO ;TEST THAT THE # WINDOWS ;IS O N E O F 1,2,4,8,16. ;SKIP W I N D O W S L O O P ;IF(WIN = 0) J M P SSAS30 2380x28cc= 16.6msec ;LOOP cycles SSAS35 ;START CONVERSION ;WAIT 12 Msec IS 28 OF / SSAS3: IN A,HICW AND LD LD OUT IN AND LD LD SLA RLA BIT OFH D,A A,G01 LOCW,A A,LOCW 80H E,A A,D E 4,A ;READ CONVERSION ;START 102 PREVIOUS CONVERSION SETS Z TO ZERO #>0 J M P IF Z B I T = 0 IF NZ,SSAS3 JP AND OFH ; J M P IF - . 6 V O L T < A / D # < 0 JP Z,SSAS3 ;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: IN A,HICW LD D,A LD A,G01 OUT LOCW,A ;START CONVERSION IN A,LOCW LD E,A LD A,D SLA E RLA BIT 4,A ;SETS Z TO Z E R O IF #>0 JP NZ,SSAS5 ; J M P IF Z BIT = 0 AND OFH JP Z,SSAS2 ;WHILE(VOLT<-.6)READ ANOTHER ;This causes the first data element to be read, at S S A S 1 ;at a time between 26 and 52/xsec into the first slow scan voltage SSAS5: NOP RR RR RR RR RR RR RR RR RR RR RR RR RR RR A A A A A A A A A A A A A A ;NEED 126cc AD AD / 103 SSAS1: S S A S 19: SSAS21: RR RR RR RR RR A A A A A IN LD IN LD LD OUT A,HICW D,A A,LOCW E,A A,GOl LOCW,A LD A,D AND JP 08H Z,SSAS19 LD AND LD JP LD AND LD LD NOP INC LD ADD LD DEC LD ADC LD INC INC A,D OFH D,A SSAS21 A,D OFH D,A A , (WIN) HL A,E A,(HL) (HL),A HL A,D A,(HL) (HL),A HL HL ;THIS IS T O A L L O W 64jtisec ;TO T H E N E X T C O N V E R S I O N ;READ A D DATA ;START CONVERSION ANOTHER ; C O N V E R S I O N F R O M 12 BIT TO 16BIT ;2'S C O M P L I M E N T N U M B E R ;23cc ;32cc ;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 DEC (IX + 00H) JP NZ,SSAS1 33cc End of Slow Scan Loop. Each path is 256cc= 64^sec SSAS40: LD RR A,255D B ;THIS L O O P IS T O E N S U R E / S S A S 50: SSAS51: SSAS52: RR B RR B RR RR DEC JP B B A NZ.SSAS40 DEC JP (IX+11H) NZ,SSAS30 LD LD LD LD (IX + O H ) , N U M H,(IX + 0FH) L,(IX + 0EH) A , (WIN) SRL JP SRL INC RR DEC JP INC INC DEC JP A Z,SSAS52 (HL) HL (HL) HL S S A S 51 HL HL (IX + 00H) NZ,SSAS50 LD LD LD LD POP H,(IX + 0DH) L,(IX + 0CH) (IX+11H),H (IX+10H),L IX POP IX POP POP POP POP INC INC INC INC RET HL DE BC AF SP SP SP SP 104 ;THAT ONLY EVERY OTHER V I D E O F I E L D IS R E A D ;THIS LOOP IS 255x54 CLOCK CYCLES ; A P P R O X . 3.5msec ;DEC T H E WINDOE J M P IF N O T Z E R O COUNT ;HL = STORAGE ADDR. ;THIS L O O P C O M P U T E S AVERAGE THE ;COPY D O W N R E T U R N ADDR. ;R E M O V E COUNT PARAMETER ;RESTORE CALLERS ENVIRONMENT ;RETURN ROUTINE TO CALLING 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 A n n . 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 Molecular Cross-Bridges Biophys.J. 48:175-183 Evans E . 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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 Fields Biophys. J . 50:339-348 Hecht-Zajac, Optics Changes Induced by Applied Electric 1974 Addison & Wesley Publishing Co. Higgins R . J . , 1976 Fast Fourier Transform: A n Introduction with some Mini Computer 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 Experiments ? 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 . 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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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Title | Surface density of radiant sources measured by optical microscopy : correction for diffraction and focus limitations |
Creator |
Knowles, David William |
Publisher | University of British Columbia |
Date Issued | 1986 |
Description | 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). WG 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 0.25μm. The fluorescence conversion technique was used to characterize the adsorption of WGA on to the red cell surface. Individual cells were isolated and incubated in various bulk concentrations of fluorescenated WGA to determine the dependence of adsorbed concentration on bulk concentration and incubation time. The equilibrium results gave a microscopic association constant of 2.95x10⁸ liters/mole, a molecular binding ratio of one WGA molecule per glycophorin molecule on the red cell surface and the number of glycophorin molecules per human red blood cell as (6.5±0.3)x10⁵. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2010-06-20 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0085240 |
URI | http://hdl.handle.net/2429/25904 |
Degree |
Master of Science - MSc |
Program |
Physics |
Affiliation |
Science, Faculty of Physics and Astronomy, Department of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
Aggregated Source Repository | DSpace |
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