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Quantitative Imaging . Using imaging to analyze molecular events in living cells. Ann Cowan. FUNCTION OF MICROSCOPY. Function of any microscopy is NOT simply to magnify! Function of the microscope is to RESOLVE fine detail. Magnification makes objects bigger. Magnification.

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Quantitative imaging l.jpg
Quantitative Imaging

Using imaging to analyze molecular events in living cells

Ann Cowan


Function of microscopy l.jpg
FUNCTION OF MICROSCOPY

  • Function of any microscopy is NOT simply to magnify!

  • Function of the microscope is to RESOLVE fine detail.



Magnification in the microscope is not perfect the magnified image is blurred by diffraction l.jpg
Magnification in the microscope is not perfect; the magnified image is blurred by diffraction

Magnification


Resolution means objects can be seen as separate objects l.jpg
RESOLUTION means objects can be seen as separate objects magnified image is blurred by diffraction

Resolution


Resolution l.jpg
RESOLUTION magnified image is blurred by diffraction

l

d

N.A.

The resolution of a microscope is the shortest distance two points can be separated and still be observed as 2 points.

Not resolved

just resolved

Well resolved

MORE IMPORTANT THAN MAGNIFICATION !!


How to get better resolution l.jpg
How to get better resolution? magnified image is blurred by diffraction

Image plane

Objective lens

specimen


Slide8 l.jpg

specimen magnified image is blurred by diffraction

How to get better resolution?

Image plane

Objective lens


Slide9 l.jpg

specimen magnified image is blurred by diffraction

How to get better resolution?

Image plane

Objective lens


What determes resolution l.jpg
WHAT DETERMES RESOLUTION? magnified image is blurred by diffraction

  • Contrast is necessary to detect detail (edges) from background

  • Diffraction fundamentally limits resolution

    diffraction occurs at the objective lens aperture


Image of a self luminous point in the microscope l.jpg
IMAGE OF A SELF-LUMINOUS POINT IN THE MICROSCOPE magnified image is blurred by diffraction

maximum

First minimum

Light from each point of the object is spread out in the microscope because light diffracts at the edges of the lens

= Airy Disk

Objective lens


Rayleigh criterion generally accepted criterion of resolution l.jpg
RAYLEIGH CRITERION magnified image is blurred by diffractionGenerally accepted criterion of resolution

Single point sourcce

Just resolved

Just resolved

Wel resolved

Intensity

Central maximum of one peak overlies 1st minimum of neighboring peak


What determines the distance between peaks l.jpg
What determines the distance between Peaks? magnified image is blurred by diffraction

Objective

θ

θ

specimen

The maximum angle of light collected by the objective lens.

Larger angle of collection =

Better resolution


Maximum angle of light collected from a point determines width of airy disk l.jpg
Maximum angle of light collected from a point determines width of Airy Disk

q

specimen

Objective

lens

Image plane

Min distance between points:

wavelength

refractive index

λ

d

sinq

n

Numerical Aperture (N.A.) = n sinq


Resolution therefore is given by l.jpg
Resolution therefore is given by: width of Airy Disk

l

d

N.A.

  • To reduce d, and therefore achieve better resolution:

    •  wavelength

    •  N.A.

  • Light microscope:

    • maximum N.A. is 1.4,

    • for visible (e.g. green light),  = 500 nm

  • thus best resolution is 0.2 um.

  • Useful magnification is limited to 500-1000 X N.A., so about 1,000 X


    Contrast is required to see objects l.jpg
    Contrast is required to see objects width of Airy Disk

    Increasing

    Contrast

    light from an object must either be different in intensity or color (= wavelength) from the background light


    Airy disk l.jpg
    Airy Disk width of Airy Disk


    Airy disk18 l.jpg
    AIRY DISK width of Airy Disk


    Airy disk19 l.jpg
    AIRY DISK width of Airy Disk

    255

    INTENSITY

    0

    Z-POSITION


    Airy disk20 l.jpg
    AIRY DISK width of Airy Disk

    255

    INTENSITY

    0

    Z-POSITION


    Airy disk21 l.jpg
    AIRY DISK width of Airy Disk

    255

    INTENSITY

    0

    Z-POSITION


    Psf z l.jpg
    PSF Z width of Airy Disk


    Z psf l.jpg
    Z psf width of Airy Disk


    Slide24 l.jpg

    FWHM width of Airy Disk

    Z-POSITION

    INTENSITY

    Z resolution

    Z Resolution defined as FWHM

    = the full width at half maximal intensity of a z line of a point source

    For 1.4 N.A. lens, Z resolution ~ .5 um

    By Nyquist theorem, need to collect at 0.25 um Z steps


    Objective lens l.jpg

    width of Airy Disk

    NA

    NA4

    mag2

    OBJECTIVE LENS

    • Resolution

    • Intensity 

    • > corrections Intensity

    (For epiflourescence; for transmission it is NA2 of objective time NA2 of condenser)


    Digital images are arrays of numbers l.jpg
    Digital Images Are Arrays of Numbers width of Airy Disk

    Value at each point is the amount of light collect from each point in an image

    2-D Image becomes array of intensity values (grey levels) from 0 -255 (for 8 bit image) or 0-4,126 for 12 bit image. Each point in the array is a pixel


    How ccd cameras make an image l.jpg
    How CCD cameras Make an image width of Airy Disk

    Figure 1. The pixels of a CCD collect

    light and convert it into packets of electrical charge

    Figure 2. The charges are quickly moved across the chip.

    Figure 3. The charges are then swept off the CCD and converted to analog electrical impulses, which are then measured as digital numerical values.


    Rgb color image l.jpg
    RGB (color ) IMAGE width of Airy Disk

    Display

    Red channel

    Green channel

    Blue channel


    Voxels are 3d pixels l.jpg
    VOXELS ARE 3D PIXELS width of Airy Disk

    2-D Image becomes array of intensity values (grey levels) from 0 -255 (for 8 bit image) or 0-4,126 for 12 bit image. Each point in the array is a pixel

    For successive Z section, 2D arrays are stacked into 3D arrays of values, each element is called a “voxel”


    Digital image maniputations l.jpg
    DIGITAL IMAGE MANIPUTATIONS width of Airy Disk

    (manipulating arrays of numbers in meaningful ways)

    • Frame averaging

    • (time averaging on CCD)

    2

    +

    =


    Digital image maniputations31 l.jpg
    DIGITAL IMAGE MANIPUTATIONS width of Airy Disk

    Output value

    Input value

    LUT

    (manipulating arrays of numbers in meaningful ways)

    • look up table (LUT) manipulations e.g. contrast stretching


    Digital image maniputations32 l.jpg
    DIGITAL IMAGE MANIPUTATIONS width of Airy Disk

    (manipulating arrays of numbers in meaningful ways)

    • image math e.g. ratio imaging

    =


    Image enhancement l.jpg
    Image enhancement width of Airy Disk


    Slide34 l.jpg

    Original image width of Airy Disk

    enhanced image

    background image

    enhanced - background image

    frame averaged

    enhanced - background


    Fluorescence microscopy l.jpg
    FLUORESCENCE MICROSCOPY width of Airy Disk


    Flourescence l.jpg
    FLOURESCENCE width of Airy Disk

    Excited Energy States

    E

    Ground State

    lifetime

    t


    Stokes shift l.jpg
    Stokes Shift width of Airy Disk


    Epifluorescence l.jpg
    EPIFLUORESCENCE width of Airy Disk

    First barrier filter

    Second

    barrier filter

    dichroic

    mirror

    objective lens

    specimen


    Slide39 l.jpg
    Flourescence detection is linear and can be used to quantify relative or absolute amounts of molecules

    • If conditions are identical, 2X fluorescence = 2X amt of fluorophore

    • Because light in the microscope is spread out by diffraction, conditions within and between images are not always identical.

    • As with any measurement, need to be careful with measurements

    • Must be within linear range of detector (no 0’s, not above maximum level)

    • Must subtract background (generally cell-free area)

    • ALL conditions in microscope must be identical


    Fluorescent ion indicators l.jpg
    Fluorescent Ion Indicators relative or absolute amounts of molecules

    Fluorescence properties change when specific ion is bound.

    For example:

    fura-2 in low Ca2+ excitation maximum at 360nm

    fura-2 in high Ca2+ excitation maximum at 340nm

    ratio of fluorescence intensity at the two wavelengths is a

    measure of the concentration of Ca2+.


    Calcium dependent excitation spectra of fura 2 l.jpg
    Calcium-dependent Excitation Spectra of FURA-2 relative or absolute amounts of molecules


    Image math l.jpg
    Image Math relative or absolute amounts of molecules

    Bkgd corrected image 340ex

    Cell with 340ex

    Bkgd with 340ex

    _

    =

    Cell with 360ex

    Bkgd with 360ex

    Bkgd corrected image 360ex

    _

    =


    Image math44 l.jpg
    Image Math relative or absolute amounts of molecules

    Bkgd corrected image 340ex

    Ratio image (340/360)

    Bkgd corrected image 360ex


    Slide46 l.jpg

    Dual Wavelength Ratios are Independent of the relative or absolute amounts of molecules

    Amount of Fluorescent Indicator

    Ratioing helps eliminate bleaching

    and dye leakage artifacts and thus

    are sensitive only to the concentration

    of analyte


    Slide47 l.jpg

    Dual Wavelength Ratios Normalize for relative or absolute amounts of molecules

    Variable Thickness within a Sample

    (e.g. a cell under a microscope)


    Slide48 l.jpg

    Courtesy of Billy Tedford and John Carson relative or absolute amounts of molecules


    Total internal reflection fluorescence tirf l.jpg
    TOTAL INTERNAL REFLECTION FLUORESCENCE relative or absolute amounts of molecules(TIRF)



    Confocal microscopy l.jpg
    CONFOCAL MICROSCOPY to the substrate


    Diffracted light is spread out in z as well as x and y l.jpg
    Diffracted light is spread out in Z as well as x and y. to the substrate

    x,z plane

    x,y plane


    Slide53 l.jpg

    coverslip to the substrate

    coverslip

    specimen

    specimen

    slide

    slide

    Conventional illumination

    Point scanning illumination


    Slide54 l.jpg

    CONFOCAL MICROSCOPY to the substrate

    photomultiplier

    Imaging aperture

    illuminating

    aperture

    dichroic

    in-focus rays

    Out-of-focus rays

    objective lens

    focal plane



    Slide56 l.jpg

    Widefield Fluorescence to the substrate

    Confocal

    White et al. 1987. J. Cell Biol. 105: 41-48


    Scan time issues l.jpg

    X = 128 to the substrate

    t = 0

    Y = 128

    t = 0.25 sec

    Scan Time Issues

    Typical scan rate 1s /scan 512X512

    t = 0

    X = 512

    Y = 512

    t = 1 sec


    Scan time issues58 l.jpg
    Scan Time Issues to the substrate

    Two scan types:

    1.

    Unidirectional

    Bidirectional

    2.

    Bidirectional scanning can have speed limitations and alignment requirements


    Digital zoom l.jpg
    Digital Zoom to the substrate

    10 X 8 = 80 points

    How close together can we scan?


    Sampling theory l.jpg
    Sampling Theory to the substrate

    • The Nyquist Theorem describes the sampling frequency (f) required to represent the true identity of the sample.

      • i.e., how close together should you sample an image to know that your sample truly represents the image?

    • To capture the periodic components of frequency f in a signal we need to sample at least 2f times

    • in essence you must sample at 2 times the highest frequency.


    Sampling theory61 l.jpg
    Sampling Theory to the substrate

    Sample at = frequency of image resolution

    Sample at ½ frequency of image resolution


    Sampling theory62 l.jpg
    Sampling Theory to the substrate

    Using 1.4 N.A. lens, max resolution is 0.2 um

    To get 0.2 um resolution in the final image, you must sample at 0.2/2 = .1 um/pixel.

    Over sampling (< 0.1 um/pixel) causes more bleaching and phototoxicty with no increase in resolution. It can also cause problems in quantifying fluorescence images.

    Sampling in Z works by the same principle. Sample at 1/2 x the z resolution defined by the lens and confocal aperture size.


    Analyzing dynamic events with fluorescence microscopy l.jpg
    ANALYZING DYNAMIC EVENTS WITH FLUORESCENCE MICROSCOPY to the substrate

    (THE "F" TECHNIQUES)





    Slide67 l.jpg

    NO DIFFUSION to the substrate

    BLEACH

    INITIAL

    INTENSITY

    DIFFUSION

    INTENSITY

    INTENSITY

    POSITION

    POSITION

    INTENSITY

    POSITION

    FLUORESCENCE

    REDISTRIBUTION

    AFTER PHOTOBLEACHING


    Photobleaching of cytoplasmic components l.jpg
    Photobleaching of cytoplasmic components to the substrate

    Images are collected every 0.345 s


    Photobleaching of cytoplasmic components69 l.jpg
    Photobleaching of cytoplasmic components to the substrate

    Methods for analyzing the data start with an appropriate model of the biology


    Slide70 l.jpg
    “FLIP” to the substrate

    • Method: Repetitive bleach and redistribution cycles, where movement of fluorescent probe out of unbleached region is analyzed.

    • Uses:

      • Best method to analyze binding rates, has been used to measure off rates of membrane binding proteins such as rac.

      • Used also to measure continuity within/between cellular compartments



    Photoactivatable gfp l.jpg
    Photoactivatable GFP to the substrate

    photoactivated for ~1 s at 413 nm



    Fluorescence fluctuations l.jpg
    Fluorescence Fluctuations to the substrate

    Intensity

    time


    Analysis of fluorescence fluctuations l.jpg
    Analysis of fluorescence fluctuations to the substrate

    2 molecules

    Intensity = # molecules

    1 molecule

    1 molecule

    time

    Related to concentration

    Related to D

    Correlation function

    amplitude: number of molecules

    Decay time: diffusion time

    G(t)

    Time


    Fluctuation trace l.jpg
    Fluctuation trace to the substrate


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