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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
Quantitative Imaging

Using imaging to analyze molecular events in living cells

Ann Cowan

function of microscopy
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
Magnification in the microscope is not perfect; the magnified image is blurred by diffraction

Magnification

resolution
RESOLUTION

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
How to get better resolution?

Image plane

Objective lens

specimen

slide8

specimen

How to get better resolution?

Image plane

Objective lens

slide9

specimen

How to get better resolution?

Image plane

Objective lens

what determes resolution
WHAT DETERMES RESOLUTION?
  • 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
IMAGE OF A SELF-LUMINOUS POINT IN THE MICROSCOPE

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
RAYLEIGH CRITERIONGenerally 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
What determines the distance between Peaks?

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
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
Resolution therefore is given by:

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
Contrast is required to see objects

Increasing

Contrast

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

airy disk19
AIRY DISK

255

INTENSITY

0

Z-POSITION

airy disk20
AIRY DISK

255

INTENSITY

0

Z-POSITION

airy disk21
AIRY DISK

255

INTENSITY

0

Z-POSITION

slide24

FWHM

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

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
Digital Images Are Arrays of Numbers

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
How CCD cameras Make an image

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
RGB (color ) IMAGE

Display

Red channel

Green channel

Blue channel

voxels are 3d pixels
VOXELS ARE 3D PIXELS

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
DIGITAL IMAGE MANIPUTATIONS

(manipulating arrays of numbers in meaningful ways)

  • Frame averaging
  • (time averaging on CCD)

2

+

=

digital image maniputations31
DIGITAL IMAGE MANIPUTATIONS

Output value

Input value

LUT

(manipulating arrays of numbers in meaningful ways)

  • look up table (LUT) manipulations e.g. contrast stretching
digital image maniputations32
DIGITAL IMAGE MANIPUTATIONS

(manipulating arrays of numbers in meaningful ways)

  • image math e.g. ratio imaging

=

slide34

Original image

enhanced image

background image

enhanced - background image

frame averaged

enhanced - background

flourescence
FLOURESCENCE

Excited Energy States

E

Ground State

lifetime

t

epifluorescence
EPIFLUORESCENCE

First barrier filter

Second

barrier filter

dichroic

mirror

objective lens

specimen

slide39
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
Fluorescent Ion Indicators

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+.

image math
Image Math

Bkgd corrected image 340ex

Cell with 340ex

Bkgd with 340ex

_

=

Cell with 360ex

Bkgd with 360ex

Bkgd corrected image 360ex

_

=

image math44
Image Math

Bkgd corrected image 340ex

Ratio image (340/360)

Bkgd corrected image 360ex

slide46

Dual Wavelength Ratios are Independent of the

Amount of Fluorescent Indicator

Ratioing helps eliminate bleaching

and dye leakage artifacts and thus

are sensitive only to the concentration

of analyte

slide47

Dual Wavelength Ratios Normalize for

Variable Thickness within a Sample

(e.g. a cell under a microscope)

slide53

coverslip

coverslip

specimen

specimen

slide

slide

Conventional illumination

Point scanning illumination

slide54

CONFOCAL MICROSCOPY

photomultiplier

Imaging aperture

illuminating

aperture

dichroic

in-focus rays

Out-of-focus rays

objective lens

focal plane

slide56

Widefield Fluorescence

Confocal

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

scan time issues

X = 128

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
Scan Time Issues

Two scan types:

1.

Unidirectional

Bidirectional

2.

Bidirectional scanning can have speed limitations and alignment requirements

digital zoom
Digital Zoom

10 X 8 = 80 points

How close together can we scan?

sampling theory
Sampling Theory
  • 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
Sampling Theory

Sample at = frequency of image resolution

Sample at ½ frequency of image resolution

sampling theory62
Sampling Theory

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.

slide67

NO DIFFUSION

BLEACH

INITIAL

INTENSITY

DIFFUSION

INTENSITY

INTENSITY

POSITION

POSITION

INTENSITY

POSITION

FLUORESCENCE

REDISTRIBUTION

AFTER PHOTOBLEACHING

photobleaching of cytoplasmic components
Photobleaching of cytoplasmic components

Images are collected every 0.345 s

photobleaching of cytoplasmic components69
Photobleaching of cytoplasmic components

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

slide70
“FLIP”
  • 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
Photoactivatable GFP

photoactivated for ~1 s at 413 nm

analysis of fluorescence fluctuations
Analysis of fluorescence fluctuations

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