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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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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 . A . , 1985 Detailed Mechanics of Membrane-Membrane Kinetically Trapped Molecular Cross-Bridges Bioplrys.J. 48:184-192 Evans E . A . , 1986 Structure and Deformation Properties Methods  Adhesion and Separation  Adhesion  I: Continum of  and Separation  of Red Blood Cells: Concepts  II:  Discrete,  and Quantitative  Methods in Enzymology (In Press) Evans E . A . , Leung A . , 1984 Adhesivity and Rigitity of Erythrocyte Membrane in Relation to Wheat Germ Binding The Journal of Cell Biology 98:1201-1208 Evans E . A . , Hochmuth R . M . , 1977 105  / 106 A Solid-Liquid Composite Model of a Red Cell J . Membrane Biology 30:351-362 Evans E . A . , Fung Y . C . , 1972 Improved Measurements of the Erythrocyte Microvascular Research 4:335-347  Membrane  Geometry  Goodman J . W . , 1968 Introduction to Fourier Optics McGraw-Hill Publishing Gordon J . L . , 1980 Mechanisms Regulating Platelet Adhesion British Soc. for Cell Biology Symposium 3: Cell Adhesion and Motility. Curtis A . S . G . & Pitt J . D . - ed. Cambridge University Press Grant C . W . M . , Peters M . W . , 1984 Lectin-Membrane Interactions: Information from Model Systems Biochimica et Biophysica Acta 779:403-422 Gross D . , Loew L . M . , Webb W . W . , 1986 Optical Imaging of Cell Membrane Potential 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 . Colloid Interface Science 58:14-25 Kapitza H . G . , McGregor G . , Jacobson K . A . , 1985 Direct Measurement of Lateral Transport in Membranes' using Time Resolved Photometry Proc. Natl. Acad. Sci. U . S . A . 28:4122-4126  Spatial  / Ketis N.V., Grant C.W.M., 1982 Control of High Affinity Lectin Binding Lipid Bilayers  to an  107  Integral Membrane Glycoprotein  in  Biochimica et Biophysica Acta 685:347-354 Knowles D.W., Evans E.A., 1986 A Simple Method for In-Situ Conversion of Fluorescence Intensity to Number Density with Correction for Microscope Transfer Limitations Biophy. J. (to be submitted) Koppel D.E., 1979 Fluorescence Redistribution after Photobleaching: A New Multipoint Analysis of Membrane Translational Dynamics Biophys. J. 28:281-292 Lovrien R.E., Anderson R.A., 1980 Stoichiometry of Wheat Germ Agglutinin as a Morphology Controlling Agent and a Morphology Protective Agent for the Human Erythrocyte J. Cell Biology 85:534-548  as  Marcelja S., 1976 Lipid-Mediated Protein Interaction in Membranes Biochimica et Biophysica Acta 455:1-7 McGregor G.N., Kapitza H.G., Jacobson K.A., 1984 Laser Based Fluorescence Microscopy of Living Cells Laser Focus/Electro Optics ???:85-93 Needham D., Evans E.A., 1986 Structural and Mechanical Properties of Giant Lipid (DMPC) Vesicle Bilayers from 20° Below to 10° Above the Liquid Crystal-Crystalline Phase Transition at 24 °C Biophysics J. (to be submitted) Owichi J.C, McConnell H.M., 1979 Theory of Protein-Lipid and Protein-Protein Interactions in Bilayer Membranes Proc. Natl. Acad. Sci. U.S.A. 76:4750-4754 Parsegian V.A., Gingell D. 1980 Red Blood Cell Adhesion III: Analysis of Forces J. Cell Science 41:151-158 Peters R., Briinger A., Schulten K., 1981 Continuous Fluorescence Microphotolsis: A Processes in Single Cells Proc. Natl. Acad. Sci. U.S.A. 78:962-966 Perry, Gilbert, 1979 J. Cell Science 39:257-272 Sharon N. 1977 Lectins Scientific American 236:108-119  Sensitive Method for Study of Diffusion  / 108 Singer S.J., Nicholson G . L . , 1972 The Fluid Mosaic Model of the Structure of Cell Science 175:720-731  Membranes  Snoek R., 1985 Spin Labeling and Analysis of Erythrocyte Surfaces P h . D . Thesis University of British Columbia Tanford C , 1973 The Hydrophobic Effect John Wiley & Sons N . Y . Waymouth C , 1970 Osmolality of Mammalian Blood and of Media for Culture of Mammalian Cells Vitro 6:109-127 Vaz W . L . C . , Kapitza H . G . , Stumpel J . , Sackmann E . , Jovin T . M . , 1981 Translational Mobility of Glycophorin in Bilayer Membranes Dimyristoylphosphatidylcholine Biochemistry 20:1392  

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